Cudequest+4

Chapter 4 toc

What Do You See? 1
I see the two people thinking about a roller coaster because the girl is pushing the boy in every direction possible. There is a lot of turning creating a lot of excitement.

What Do You Think? 1

 * The drops can produce the loudest screams because your body feels like it's free falling.

Roller Coaster assignment 1
> The ride gets to speeds of 75 mph. It has out-and-back configuration, "air" time, and banked turns.
 * Steel Force at Dorney Park in Allentown, PA
 * The Comet at the Great Escape in Lake George NY, is famous because of design full of hills and drops that give the riders the sense of floating out of their seats in the air.

Physics Talk 1
scalar: a quantity that has magnitude (size/amount), but NO direction speed: distance traveled divided by time elapsed. scalar vector: a quantity that has both magnitude and direction displacement: the difference in positions; it depends only on the endpoints, not on the path. vector velocity: displacement divided by the time elapsed; vector acceleration: the change in velocity divided by the time elapsed. vector

Checking Up 1
1. distance is scalar (no direction) and displacement is vector (direction). If I were to walk from my chair to the wall and back, the distance would be 3 meters, but the displacement would be 0 because the initial and final positions are the same. 2. If I went to school and back, the displacement would be 0. 3. speed is distance/time (scalar) and velocity is displacement/time (vector) 4. acceleration = change in velocity / time elapsed

Physics To go 1
1. (in the side view, the back curve would bring the 3rd hill down and the horizontal loop to the left of it)  2. The thrills will come from the accelerations along the curve, the drops, and the horizontal circle.  3a. La Paz, Bolivia has the greatest speed. It travelsthe greatest distance (biggest radius) in 24 h.  3b. v = d/t  40000 km / 24 h  1666.7 km/h  3c. although it is such a high speed, it is constant so we don't feel any accelerations.  4. a = delta v / delta t  a = 16 m/s - 4 m/s / 3s a = 4 (m/s)/s  5a. car traveling at 50 km/h - speed  5b. student riding bike at 5 m/s toward home - velocity  5c. roller-coaster ride whips around a left turn at 5 m/s - velocity, acceleration  5d. roller-coaster dragged up a hill 12 m tall and traveling at 3 m/s - displacement, velocity <span style="font: 12px/19px Helvetica; margin: 0px;"> 5e. train ride takes you 150 km NW - displacement <span style="font: 12px/19px Helvetica; margin: 0px;"> 6. v = d/t v = .1m/2s .05 m/s <span style="font: 12px/19px Helvetica; margin: 0px;"> 7. v = d/t <span style="font: 12px/19px Helvetica; margin: 0px;"> .05 m/s = .05m / s <span style="font: 12px/19px Helvetica; margin: 0px;"> s = 1 <span style="font: 12px/19px Helvetica; margin: 0px;"> 8. a = change in V / change in t <span style="font: 12px/19px Helvetica; margin: 0px;"> a = 25 m/s / 10s <span style="font: 12px/19px Helvetica; margin: 0px;"> a = 2/5 (m/s)/2 <span style="font: 12px/19px Helvetica; margin: 0px;"> 10a. If I were to add 2 more changes I'd put a clothoid loop and a hill after the horizontal loop. Both of these add additional thrills due to the accelerations and changes in direction. <span style="font: 12px/19px Helvetica; margin: 0px;"> 10b.

<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;">What Do you think now? 1
The parts of the roller coaster that provide the most thrills are the sharp turns and the drops, after putting people through a virtual simulation of it, you could tell these were the parts that scared people the most. The higher change in velocity made it scarier too.

What Do You See? 2

 * I see a group of kids having a lot of fun going down a huge incline and I see a bunch of kids going steady acting really bored.

What Do you Think? 2

 * The Roller Coaster with the steeper slope will give a bigger thrill because it gets people very scared.

Physics Talk 2
<span style="font: 13px/19px Arial; margin: 0px;"> Gravitational Potential Energy and Kinetic Energy <span style="font: 13px/19px Arial; margin: 0px;"> Energy Transformations in the Roller coaster <span style="font: 13px/19px Arial; margin: 0px;"> GPE: the energy a body possesses as a result of its position in a gravitational field <span style="font: 13px/19px Arial; margin: 0px;"> KE: the energy an object possesses because of its speed <span style="font: 13px/19px Arial; margin: 0px;"> KE depends on speed, GPE depends on height, and both depend on mass <span style="font: 13px/19px Arial; margin: 0px;"> GPE = mgh (J) <span style="font: 13px/19px Arial; margin: 0px;"> KE = 1/2mv^2 (J) <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> mechanical energy: the sum of kinetic energy and potential energy <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> the sum of KE and GPE is the same at any point in the rollercoaster <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> when GPE increases, KE decreases and vice versa <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> Calculating KE from GPE <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> Calculating Speed from Kinetic and GPE <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> Mechanical energy (bottom) = mechanical energy (top) <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> KE (bottom) + GPE (bottom) = KE (top) + GPE (top) <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 1/2mv^2 (bottom) = mgh (top)

Checking Up 2
<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 1. The higher up the ball is released, the greater speed it has at the bottom. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 2. As the height increases so does the GPE. The mass affects it the same way. As the mass gets decreases, the GPE decreases. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 3. As the speed of an object increases, the KE increases. Also, as the mass gets bigger, the KE does, too. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 4. As a roller-coast car rolls down a hill, the GPE decreases because it is losing height, but the lost energy is converted into KE. The KE increases because of the increase in velocity. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 5. If the ride has 40,000 J of GPE at the top of a hill, it has 30,000J KE 3/4 the way down. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">

<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">**PTG 2** <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 1. The speed of carts A and B are the same at the bottom. Although their inclines are different, their initial height is the same. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> 3. 4. 5.
 * height (m) || GPE =mgh || KE = 1/2mv^2 || GPE + KE ||
 * top (30) || 60,000 || 0 || 60,000 ||
 * bottom (0) || 0 || 60,000 || 60,000 ||
 * halfway down (15m) || 30,000 || 30,000 || 60,000 ||
 * 3/4 way down (7.5) || 15,000 || 45,000 || 60,000 ||
 * height (m) || GPE (J) = mgh || KE (J)= 1/2mv^2 || GPE + KE (J) ||
 * top (25 m) || 75,000 || 0 || 75,000 ||
 * bottom (0 m) || 0 || 75,000 || 75,000 ||
 * halfway down (12.5 m) || 37,500 || 37,500 || 75,000 ||
 * further down (5 m) || 15,000 || 60,000 || 75,000 ||

GPE = mgh (300)(10)(25) 75,000 then replace h with 0, 12.5, and 5 6.  7a. GPE = mgh (.2)(9.8)(.75) 1.47 J  7b. GPE = KE mgh = 1/2mv^2 (9.8)(.75) = 1/2v^2 3.83 m/s = v 7c. GPE = KE <span style="border-collapse: separate; font: 13px/19px Arial; margin: 0px;"> mgh = 1/2mv^2 <span style="border-collapse: separate; font: 13px/19px Arial; margin: 0px;"> (9.8)h = 1/2(3.83)^2 <span style="border-collapse: separate; font: 13px/19px Arial; margin: 0px;"> h = .75 m 8. The speed will not change if there are 6 passengers or 26 passengers. The speed is independent of the mass of the car. This is because in the equation GPE (top) = KE (bottom), mass cancels out 9a. The roller-coaster is traveling fastest at point B because its initial height was the highest before the drop. 9b. The roller-coaster is traveling at the same speed at points C and F. This is because their heights are the same. 9c. The roller-coaster is traveling faster at D because it just dropped from C, rather than traveling up from D.

What Do You Think Now? 2
The roller coaster on the right will have a greater acceleration, so there will be a bigger thrill. Even though that may be true, their speeds at the bottom will be the same because their initial heights are equal. The only reason the coaster on the right will have a greater thrill because there is a greater acceleration.

What Do you See? 3

 * I see two kids using a photo-gate timer to calculate the time the time it take the pop-up toy to get off the ground. I see one kid taking measurements and another kid writing down calculations.

What Do You Think? 3

 * The roller coaster gets to the highest point by having a spring shoot off the coaster. In order for this to happen you need a high elastic potential energy.
 * It cost more energy if there is more people. I think mass effects the amount of energy released.

Physics Talk 3
All energy in a system is conserved. It can leave the system in the form of sound, light, or heat energy, but the total amount of energy is never destroyed, just transferred out of the system. In order to get the roller coaster moving there needs to be work done by a chain to bring it to the top of the hill so it gets its GPE. The energy can come from a generator or a power system. Once the cart is at the top of the hill it is released and the work done by the chain to get the cart to its max GPE is transferred into KE and back into GPE (as the cart goes up and down). At the end the brakes will slow the cart back down, but if that fails the cart will need to be stopped by an emergency spring. The spring has a certain stiffness, or spring constant, and a distance over which it applies its force. The distance multiplied by the amount of resistance equals the springs EPE (SPE).

Checking Up 3
1. The SPE gets completely converted into KE and GPE 2. It will have almost exactly 2 J, with a very minimal amount of GPE 3. It will have 2 J at the exact top 4. The spring force constant and the distance the spring is compressed determine the spring potential energy

Physics To Go 3
5.) It can't be higher than the first because it won't have enough GPE/KE to get to the top of the higher second hill. 6.) The roller coaster doesn't travel forever because as the roller coaster keeps going, it loses its kinetic energy and GPE because it turns into heat and sound energy therefore it can not travel forever. 7.) (300)(9.8)(15)= 44,100 J 8a.) KE= 1/2 mv^2 KE= 1/2 (400) (15)^2 = 45,000J 8b.) KE=GPE 45,000 J 8c.) 45,000= (400)(h)(9.8) 11.48 meters high 9.) As a ball is thrown upwards, its gravitational potential energy is increasing because its height is increasing. GPE = mgh 10.) The gain is the same for each path because they are all going up to the same height so they will all have the same gravitational potential energy at the end. 11a.) The GPE and KE should give approximately the same values. 11b.) SPE=KE SPE= 1/2 mv^2 SPE= 1/2 (0.020)(2.7)^2 SPE= 0.0729 J 11c.) KE=GPE 1/2mv^2= mgh 1/2 (.006)(2.7)^2= (.006)(9.8)h .02187= .006(9.8)h h= .37 m 12a.) GPE = SPE mgh = 1/2kx^2 300(9.8)18 = 1/2k(4^2) k = 91.88 N/m 12b.)GPE= SPE GPE= mgh 400(9.8)(18)= 70,560 J 70,560= 1/2 kx^2 70,560= 1/2(91.88)x^2 x= 39.19 m 13.) KE= SPE KE= 1/2kx^2 KE=1/2 40(.3)^2 KE= 1.8 J

What Do You Think Now? 3

 * The roller coasters today get up to its highest point by cables, electronics, motors.
 * It does cost more to lift the roller coaster if is full because there is a higher mass & has more GPE. That GPE is turned into Work, which is required to pull the coaster up-->increase in electrical bill.

What Do You See? 4

 * I see two people on the moon not having any fun on the roller coaster, then I see two more people having fun on the roller coaster on Jupiter.

What Do You Think? 4

 * Gravity has two different types of directions, up and down.
 * I think it is about where they are located and each planet has a gravitational pull.

Physics Talk 4
<span style="font: 13px/19px Arial; margin: 0px;">Newton's Law of Universal Gravitation <span style="font: 13px/19px Arial; margin: 0px;"> **gravitational field**: the gravitational influence in the space around a massive object <span style="font: 13px/19px Arial; margin: 0px;"> Earth of the source of its gravitational field because it is the first object that sets up in the space around it <span style="font: 13px/19px Arial; margin: 0px;"> second object interacts with this field--moon (response/test object) <span style="font: 13px/19px Arial; margin: 0px;"> Inverse-Square Relationship <span style="font: 13px/19px Arial; margin: 0px;"> acceleration due to gravity becomes less as an object moves further from the surface of Earth <span style="font: 13px/19px Arial; margin: 0px;"> **inverse-square relationship**: the relationship between the magnitude of a gravitational force and the distance from the mass. this also describes how electrostatic forces depend on the distance from an electrical charge <span style="font: 13px/19px Arial; margin: 0px;"> force of gravity between 2 objects decreases by the square of the distance between them <span style="font: 13px/19px Arial; margin: 0px;"> Ex: if you triple (3x) the distance, the force is (1/9) the original <span style="font: 13px/19px Arial; margin: 0px;"> **Newton's law of universal gravitation**: all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bogies increases <span style="font: 13px/19px Arial; margin: 0px;"> : the force of attraction between two bodies due to their masses <span style="font: 13px/19px Arial; margin: 0px;"> Equation of Newton's law of universal gravitation <span style="font: 13px/19px Arial; margin: 0px;"> Fg = (Gm1m2)/r^2 (Fg = force between the bodies, r = the distance between their centers, m1 & m2 = masses of the bodies, G = universal constant equal to 6.67 x 10^-11 <span style="font: 13px/19px Arial; margin: 0px;"> The moon orbits Earth and the planets orbit the Sun in elliptical paths <span style="font: 13px/19px Arial; margin: 0px;"> plants don't move in exact ellipses b/c planets tug on on another

Checking Up 4
<span style="font: 13px/19px Arial; margin: 0px;">1. The direction of the gravitational field in the classroom is to the ground 2. The gravitational field is the strongest near the surface of Earth <span style="font: 13px/19px Arial; margin: 0px;">3. If you triple the distance between two masses, the force is (1/9) the original <span style="font: 13px/19px Arial; margin: 0px;"> 4. Gravity is the force that holds the Moon in its orbit around Earth <span style="font: 13px/19px Arial; margin: 0px;"> 5. The shape of the orbit of the plants around the sun is approximately elliptical.

Physics To Go 4
<span style="font: 13px/19px Arial; margin: 0px;">1. If the gravitational force between the two asteroids doubles, the force would be 125 N. <span style="font: 13px/19px Arial; margin: 0px;"> 2a. The gravitational force would be 1/4 of original. 2b. The gravitational force would be 1/9 of the original. 2c. The gravitational force would be 1/16 the original. 3. Everyone trusts gravity because it keeps our bodies down on Earth. Also, nothing can float around in the air because of Earth's gravity, what goes up must come down. We have never experienced a moment with no gravity. 4. The is more acceleration due to gravity is higher at the bottom of a roller coaster than at the top of a roller coaster. 5a. The water on the side of Earth facing the moon is closer to the moon than the center of Earth. 5b. There are high tides on the side of earth facing the moon because the water moves independently to the Earth. Also, the water is a much less mass than the moon. The gravitational field around the moon attracts the water so it rises up with the force. 5c. There is an an uneven distribution of water on Earth's surface because there is land on the other parts. Also, the water is at different distances from the moon so the gravitational force is different. They are inverse-square relation. Therefore, there are some points that the water is not closer to the moon because the waves do not reach as high. 6a. A fish's life would be different without gravity because it would not be pulled down into the water and would be flopping around in the air. The would die. 6b. Gravity holds a fish "down" on Earth because the mass of a fish is less than the mass of the Earth. Masses are attracted, so the larger mass of the Earth attracts the fish. <span style="font: 13px/19px Arial; margin: 0px;">7. a) 1/4 b) 1/9 c) 1/16 d) 4x <span style="font: 13px/19px Arial; margin: 0px;"> 8. a) 2x b) 3x c) 4x d) 1/2x <span style="font: 13px/19px Arial; margin: 0px;"> 9. a) 4x b) 9x c) 16x d) 1/16x <span style="font: 13px/19px Arial; margin: 0px;"> 10. a) 2x b) 9x c) 6x

What Do You Think Now? 4

 * Gravity does have a direction, It's the direction of force on a mass. Gravity is directed towards the largest mass. (center of Earth)
 * People on the other side of the Earth are held onto the Earth even though they are upside down due to gravity. Gravity attracts the mass of people with the mass of Earth. People are forced down onto Earth.

Physics Plus 4
1. a = v^2 / r 2. v = d/t (2 x pi x [3.84x10^8) / 2440800 v = 998.505 m/s 3. a = v^2 / r a = 998.505^2 / 3.84x10^8 a= 0.0025 m/s^2

What Do You See? 5

 * I see one person is using newton's law and weighing something. One at a deli and one with scientists.

What Do You Think? 5

 * No because both are in different sets of units when calculating how much each one ways.
 * You step on it and it calculates how much you weigh by how much pressure you put on the scale.

Physics Talk 5
Hooke's Law Describes the Restoring Force a Spring Exerts Stretching a rubber band or a spring requires a force There is a linear relationship between the amount of force required for each stretch of the spring. It is a straight line. Robert Hooke discovered this property of springs stretch of spring is directly proportional to the force applied to it If the spring is not moving, the spring exerts a restoring force equal in magnitude to the force that stretched the string. Hooke's law: the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring force exerted by the spring = -spring constant x spring stretch (or compression) Fs = -kx negative shows that the pull by the spring is opposite to the direction it is stretched or compressed k is an indication of how easy or difficult it is to stretch/compress a spring a stiff spring will have a large value for k; a soft spring will have a small value for k Hooke's law : F = kx Straight line: y = slope x weight = mg force = ma weight: the force exerted on a mass as a result of gravity; the weight force on an object due to Earth is downward, in the vertical direction Stretch and Compress bathroom scales work by compressing a spring. When you step on the scape, the spring compresses just enough to provide an upward force equal to your weight. The more weight, the more compression of the spring is required. The spring is connected to a scale that has been calibrated to give your weight. As the spring compresses, the arrow points to a different number corresponding to the compression and force of the spring.

Checking Up 5
1. If the force on the spring is increased 5 times, the stretch of the spring increases 5 times. 2. the spring constant represents how easy or difficult it is to stretch/compress a spring 3. weight of an object in newtons compares to its mass in kg. N = Kg x m/s^2. The mass is a part of the weight. 4. On a bathroom scale, the more weight, the more compression of the spring is required.

Physics To Go 5
1a. W = mg W = (100)(9.8) W = 980 N 1b. W = mg W = 10(9.8) W = 98 N 1c. W = mg W = 60(9.8) W = 588 N 2a. .25 / 130 = 1 / x x = 520 N 2b. .25 / 1000 = 1 / x x = 4000 N 2c. .25 / 50 = 1 / x x = 200 N 3a. 3b. 3c. slope = 0.1491 N/(cm) = 14.91 N/m 3d. The slope is the spring constant 3e. This spring would be lesser and more stretched than the previous spring. It's slope is less steep and requires less weight to stretch it the same distance. 4. F = -kx 12 N = k (.03m) k = 400 N/m 5. Hooke wrote "as the force, so the stretch" because the stretch/compression of a spring is directly proportional to the force pulling or pushing on the spring. The larger a spring is stretched, the larger restoring force is needed. 6. The spring with the lower constant is more difficult to stretch, so in this case 10.0 N/m would be more difficult to stretch. 7. F = kx 3N = k(.02m) k = 150 N/m 8. Spring scales are based on Hooke's law. The stretch of the spring is directly proportional to the force pulling/pushing on the spring. When at rest, the spring exerts a restoring force equal in magnitude to the force stretching or compressing the spring. F = -kx

What Do You Think Now? 5

 * The same scale cannot be used to weigh a canary and an elephant. This is because of the compression and dials on scales are calibrated with the spring. The spring can only compress to a certain amount, therefore the scale can only read off a number to a maximum.
 * bathroom scales work by compressing a spring. When you step on the scale, the spring compresses just enough to provide an upward force equal to your weight. The more weight, the more compression of the spring is required. The spring is connected to a scale that has been calibrated to give your weight.

What Do You See? 6

 * I see that a fat guy has a weight of 0 because he is falling and a little person has a weight of 100 because there is force pushing him up.

What Do You Think? 6

 * Yes, I think your weight is constantly changing depending upon the hill you are on, when you go down, your weightless and when you go up, your heavy.
 * Yes a bathroom scale would read differently for every point in the roller coaster you were falling or going up.

Physics Talk 6
<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">**Using Newton's First and Second Law to Explain Forces Acting During Constant Speed and Acceleration** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Newton's 1st (object at rest/motion stays at rest/motion) : an object at rest has no net force acting on it <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Newton's 2nd law (a=F/m) object at rest, has zero acceleration, and has no net force acting on it <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> an object in motion at constant speed has no net force acting on it <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> sitting on a scale on a level roller-coaster at rest or constant velocity - the scale reads equal to weight <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Accelerating Up on Roller coaster: there must be a net force pushing you up <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -moving up on the scale, the reading will be greater in magnitude than your weight <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -the magnitude of the force of the Earth pulling on you would be less than the magnitude of the force of the compressed spring within the bathroom scale <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> if the elevator and the person are accelerating down, the net force on the person must be down <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **Apparent Weight** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> when the elevator is at rest or moving at constant velocity, your weight readings are identical <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> when an elevator accelerates up, you also accelerate up (Earth pulls down on you with a force smaller than the force the scale exerts on you upward, so the scale reads a larger force than before) <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -you weight like you weigh more because of the contact forces <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -force hold your stomach in place against gravity <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> when elevator accelerating down, the scale reads a smaller force than before because force of the scale up on you is less that force of your weight down <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -feel like you weight less because the contact force w/ the bathroom scale is smaller and because the connective tissues stretch a bit less <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Weightless feeling is due to contact force between you and bathroom scale is zero & tissues relax <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **Air Resistance** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> a coaster in free fall accelerates at 9.8 m/s every second. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> can't ignore air resistance on roller coaster

Checking Up 6
<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">1. The sum of all the forces acting on an object when it is moving up at constant speed is zero. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2. When accelerating up on a bathroom scale on a roller coaster, the reading on the scale will be greater than your weight in magnitude. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 3. You feel as if you weight more when you accelerate upward because of contact forces and stretching stomach tissues, and forces are holding your stomach in place <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 4. If the elevator cable were to break, you would only have the force of your weight pulling you down & nothing pushing you up. The force reading on the scale would be zero and you'd feel weightless. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 5. Air resistance slows a falling raindrop.

PTG 6
<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">1a. (9.8)(2) = 19.6 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 1b. (9.8)(5) = 49 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 1c. (9.8)(10) = 98 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2a. (1.6)(2) = 3.2 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2b. (1.6)(5) = 8 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2c. (1.6)(10) = 16 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 5. A student who weighs 140 lb and is 137 lb on a scale on an elevator has just and increased down acceleration, or they had a decreased upward acceleration. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 6. The person will observe that her weight increases. An increased upward acceleration increases the weight on the scale because the force that the scale is exerting is greater than the force of weight exerted downward.

<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">Section 6, PTG #4
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || zero ||  || equal ||
 * Starting at Rest, Increasing Up || up ||  || greater ||
 * Continuing to move, Constant Up || zero ||  || equal ||
 * Slowing down to top floor, Decreasing Up || down ||  || less ||
 * At rest, top floor || zero ||  || equal ||
 * Starting at rest, Increasing Down || down ||  || less ||
 * Continuing to move, Constant Down || zero ||  || equal ||
 * Coming to a stop on the ground floor || down ||  || less ||

What Do You Think Now? 6

 * No because your weight will only change if you change your position according to physics.
 * Yes if you were going down at an increasing speed, your weight would be less and if you were increasing up, your weight would be greater.

What Do You See? 7

 * The People are about to fall off the course because of the turn that is too wide.

What Do You Think? 7

 * because of the motion and the speed that is keeping you in check.

Physics Talk 7
<span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;">**centripetal force and acceleration** <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> normal force: the force acting perpendicular to the surface <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -coaster curve where car tilts vertically and the wheels face outside, normal force is the force towards the center <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -track acts directly on the wheels of the car <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> centripetal force: any force directed toward the center that causes an object to follow a circular path at constant speed <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -roller coaster around a curve on its side has the force of the track as its centripetal force <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -centripetal force is larger when speed is increased, mass is increased, and radius is shorter <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Fc = mv^2 / r <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> centripetal acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -contact forces between you and seat and you and the side of cart that causes the acceleration <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -acceleration and related contact produce thrill <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> In vertical loop, the Fc is gravitational force, a normal force of track on the coaster car or a combo <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -when it is a combo, the two vectors are added <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -at bottom of circle, the normal force points toward center & gravitational points downward (sum is towards center, so the normal force is larger) <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -at top of circle, the gravitational force and normal force both act downward towards center and the sum is the Fc. <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Mass and speed of the car determines how much of the normal force is needed to keep the car moving in a circle <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -There is more Fc at the bottom than the top because there is more speed at the bottom <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -the weights at bottom and top are the same <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -normal force is smaller at the top because the weight contributes to the centripetal force & if the speed decreases, the required Fc would be less. there comes a point when gravitational force is all that is needed to keep it moving in a circle, so the normal force is zero & there would be a a gap at the top between car and track <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -at bottom, the car needs a normal force of the track that is greater than the weight because it has to be towards the center of the circle <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Normal + weight = net centripetal force <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **apparent weight and the roller-coaster ride** <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -feel lighter at the top of the loop because acceleration is downward <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -feel heavier at the bottom of the loop because acceleration is upward <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -on a level track at constant speed, the sum of forces is 0 <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -at the bottom, there is a force up keeping you moving in a circle <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -at the top there is a force down to continue to the circle <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> clothoid loop: big radius at bottom and small radius at the top, so the coaster is moving in a small circle at the top <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -these ensures that it can turn at the top but not have an accel. at the bottom that is greater than 4 g's. <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **Safety on the Roller coaster** <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> experiencing an accel more than 9 x gravity causes unconsciousness <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> accelerations other than 9.8 or 10 (acceleration due to gravity) is referred to as 1 g. <span style="border-collapse: separate; font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2 gs = 20 m/s/s, 8 gs = 80 m/s/s

Physics To Go 7
<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">1a. the path of the car would be in a circle <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 1b. if the string were to break while the car was <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> moving in a circle, the car would follow a straight line tangent to the circle <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;">

<span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 2a. A centripetal force has replaced the string of the toy car. <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 2b. <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 6a. The speed of the roller coaster did not change, it stayed 20 m/s. <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 6b. The velocity of the roller changed because it changed direction. <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 6c. The change in velocity was 20 rt 2 m/s NE. (??) <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 7. Ac = v^2 / r <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> Ac = (20)^2 / 200 <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> Ac = 2 m/s^2 NE <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;">10. Fast Moving Roller Coaster


 * Required Fc ||  || Force of gravity (weight) ||   || Normal force (the force of the track on the car) ||


 * at the bottom of the loop ||  || 4000 N ||   || 500 N ||   || 3500 N ||


 * at the bottom of the loop ||  || 6000 N ||   || 500 N ||   || 6500 N ||

Slow-moving roller coaster
 * ||  || Required Fc ||   || Force of gravity (weight) ||   || Normal force (the force of the track on the car) ||


 * at the top of the loop ||  || 800 N ||   || 500 N ||   || 300 N ||


 * At the bottom of the loop ||  || 2800 N ||   || 500 N ||   || 3300 N ||

13a. Bottom of hill #1- uncertain 13b. Top of vertical loop- heavier 13c. Bottom of vertical loop- heavier 13d. Bottom of hill #2- uncertain 13e. Lift hill (going up at constant speed)- no change

<span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14a. Bottom of hill #1- zero <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14b. Top of vertical loop- down <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14c. Bottom of vertical loop- up <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14d. Bottom of hill #2- zero <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14e. Lift hill (going up at constant speed)- zero <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14f. Horizontal loop- sideways <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin-bottom: 0px; margin-left: 36px; margin-right: 0px; margin-top: 0px; text-indent: -36px;"> 14g. Back curve- sideways

Physics Plus 7
1a. The Fnet increases. As the mass increases, the velocity stays the same, the radius stays the same, this increases the net force. 1b. Iv the velocity increases, the Fnet also increases by a lot because it has a squared relationship (quadruples if velocity doubles). 2. The strength of the track (force) must be quadrupled. 3. The Fnet also gets smaller if the r gets larger (indirectly proportional) 4. The larger the radius for the curve, the smaller the force required to keep the car moving along the curve. If the curve is tight (r is very small) then a larger force is required. 5. If you were to let go of the stopper, it would continue in a straight line motion without any force.

What Do You Think Now? 7
<span style="font-family: arial,helvetica,sans-serif;">You don't fall out of a roller coaster car when you are upside down because you feel pressed into your seat due to inertia. Also, net force or centripetal force points towards the center, so the acceleration is towards the center.

What Do You See? 8
There is a roller coaster with a large hill, they are sweating, carrying the cart up the hill. Once at the top of a hill, the cart flies down the slope really fast.

What Do You Think? 8
It takes more energy to pull the roller coaster up a steep incline than a gentle incline because the height is higher. It is less difficult to walk up a gentle incline because the steepness is not as hard on our muscles and force we need to use to get us up the hill is decreased.

Physics Talk 8
<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">**work**: the product of displacement and the force in the direction of the displacement; the energy transferred to an object <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> W = force (parallel to the displacement) x displacement <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -W is the same regardless to the angle of the incline <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -Force is larger on a steeper incline ; but the distance along the incline was smaller <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -the work done by a force on an object is the energy transferred to the object <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -work is needed to bring the coaster to the top of hill <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -work increases the energy of the system <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -work to lift cart up the ramp is = work to lift it vertically to that height <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -when you lift vertically, the force = in magnitude to weight of the cart <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -vertical displacement is the height that it must be lifted <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> W = F x d <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> W = weight x height <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> W = mgh <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **More Roller Coaster Energy** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -cart is raised with electrical energy supplied by a motor <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -electrical energy calculated by measuring voltage, current, and time <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -steam also could raise it <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -work is done by the spring (by electricity or by heat) <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -coaster system gains that amount of energy & GPE is increased by that amount <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -work is also done by friction and air resistance which for example will become heat energy and dissipate into the air <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **Braking the Roller Coaster** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -brakes use friction to convert KE into thermal energy <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> -need back-up too = large spring that could compress, as it compresses, KE is stored as SPE <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **Power** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> P = work done / time elapsed <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> **watts**: the SI unit for power; 1 W = 1 J/s

**Checking Up 8** <span style="font-size: 13px; font-weight: normal; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">1. When a spring scale is used to doing work, like pulling a cart to the top of an incline, the energy has gone into GPE <span style="font-size: 13px; font-weight: normal; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 2. The roller coaster gets its GPE at the top of the first hill from work done by the spring (electricity or heat) that gains that amount of energy <span style="font-size: 13px; font-weight: normal; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 3. Truckers use a ramp when loading a truck because the force is decreased so it is not as difficult to do. work to lift up the ramp is = work to lift it vertically to that height, when you lift vertically, the force = in magnitude to weight of the cart, vertical displacement is the height that it must be lifted <span style="font-size: 13px; font-weight: normal; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 4. When the brakes stop a roller coaster, the KE is converted into thermal energy <span style="font-size: 13px; font-weight: normal; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 5. The unit for power is watts. 1 W = 1 J/s

<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;">Physics To Go 8
<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">1a. The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 1b. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 1c. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 1d. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 1e. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 1f. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"><span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2a. W = F x d <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px; padding: 0px;"> W = 150 N x 7 m <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px; padding: 0px;"> W = 1,050 N <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 2b. W = F x d <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 60 x .5 <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 30 N <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 2c. W = F x d <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 75 x 40 <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 3000 N <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 2d. W = F x d <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 500 x .7 <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 350 N <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 3. Instead of simply saying to "conserve energy," you could say "conserve energy within a system" because this relates directly to KE, SPE, GPE, and W. This energy is constantly being transferred and conserved except when it is lost to friction, heat energy, sound energy, etc. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 4. If clay was added, the mass would increase, so the force would increase. Therefore, the distance it would travel would decrease to keep Work consistent. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 5a. W = F x d <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 10,000 x 20 <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 200000 N <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 5b. P = work / change in t <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> P = 200000 / 150 <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> P = 1333 1/3 J/s <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> 6. On the way up the ramp the roller coaster is gaining GPE and the motor is performing work on the roller coaster cart. The work from the motor increases the energy of the roller coaster. At the top, there is not more work by the motor, but there is some work by friction with the air and track.

<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">What Do You Think Now

 * It takes more energy to pull the roller coaster up a steep incline than a gentle incline because the height is higher and W = GPE. and GPE is mass times gravity times height.
 * It is less difficult to walk up a gentle incline because more force is needed to get up a shorter distance. It takes less force to get us up a longer distance.

What Do You See? 9

 * I see two kids thinking about force and energy and their thought process is showing a crazy roller coaster.

What Do You Think? 9

 * The parts with the twists and turns will be the most thrilling in the roller coaster.
 * It will still be fun because there are different parts of the roller coaster, it is not just a straight line so it is not boring.

Physics Talk 9

 * A quantity with both a number and direction is called a vector. A quantity with magnitude and no direction is a scalar. Displacement is taken into account with vectors.
 * Vectors need to make a triangle and do Pythagorean theorem to get the hypotenuse because vectors need direction along with size. Energy is a scalar. The total mechanical energy (KE plus GPE) is equal at all points of the roller coaster ignoring friction. Force on the other hand is a vector quantity. Force of gravity is always down. The normal force is always perpendicular to the track.
 * The changes in acceleration in size and direction create the bouncy feelings. Force and energy are related. Weight does work on the roller coaster and increases its KE. *Force in the direction of motion creates work energy and any work done creates changes in energy (Newton's Second Law).* In order to have a net force, you need an acceleration and visa versa (Law of Conservation Energy).

Checking Up 9
1. The pythagorean theorem is used when adding vector quantities. 2. Energy is a scalar quantity, Force is a vector quantity. 3. GPE and KE are equal at all the points on the coaster, GPE only depends on the height, if two points have the same heights than its moving at the same speed at those points. 4. Energy considerations are path independent. Energy will remain the same throughout the coaster. 5. To provide a change in energy, work must be in affect.

PTG 9
1a. a^2+b^2=c^2 c=7.07 m/s inverse tan (5/5)=45 degrees NW 1b. a^2+b^2=c^2 5^2+5^2=c^2 c= 7.07 m/s NW 2. This is because they are dropped from the same and all the GPE is at the top. Therefore you have the same KE and the same velocity. 3a. scalar 3b. vector 3c. scalar 3d. vector 3e. vector 3f. vector 3g. scalar 3h. scalar 3i. scalar 4a. scalar (no direction) 4b. vector (direction) 4c. scalar (energy) 4d. vector 5. As an energy ride, it is easier when you are trying to find speeds, know the heights. It isn't useful when trying to find accelerations for energy. 6a. 6b. 6c. The forces are the same everywhere. There is an x-component of weight. It is constant and the same at all four points. 7a. 7b. The total energies at these three points are equal. 7c. The KE at these points are the same because velocity is practically the same. 7d. You can ignore other points on the roller coaster because at all points, the GPE plus the KE are equal.

What Do You Think Now? 9

 * When a snake shape changes direction or with consistent sharp turns that go left or right will create thrill.
 * Cork screws and loops are the ones that make people scream. Any change in direction is a change in velocity, and thrills are caused where there is acceleration.

What Do You See? 10

 * I see a large roller coaster with many loops, sharp turns, it also appears that people are falling which is making the ride severely dangerous.

What Do You Think? 10

 * If a person can get hurt on the ride, generally people do not want to go on that ride then. It is a hazard and creates a very negative thrill.

Physics Talk 10

 * The max amount of g's in an acceleration that are considered safe in a roller coaster ride is 4.
 * Centripetal acceleration equals velocity squared over the radius of the loop/circle. You can increase the radius, decrease the speed, decrease the initial hill height, and increase the height of the curve. Decreasing the speed around the loop will decrease the acceleration. Increasing the radius also decreases the acceleration.
 * To find the amount of g's, you take the acceleration of the point and divide it by 9.8. The largest centripetal acceleration requires the larges centripetal force. The sum of the normal force from the track and the weight must equal the required net force. Fnet=mv^2/r.
 * Another safety feature is that the cart needs enough speed to complete the loop. Normal is 5gs at the bottom of the curve and 3 g's at the top of the curve. Acceleration has to be greater than 9.8 m/s^2 at the top of a loop.

Checking Up 10
1. The maximum safe acceleration on a roller coaster is 4 g's. 2. Two ways too keep the acceleration low are to make the radii larger and lower the velocity. 3. The end of the loop is the greatest acceleration. 4. The bottom of the loop is the greatest normal force.

Physics Plus 10
a. GPE = KE mgh = 1/2mv^2 masses cancel 9.8(h) = 1/2(30)^2 H1 = 45.9 m

b. Ac = v^2/r Ac = (30)^2/9 Ac = 100 m/s^2

c. 100/9.8 = 10g Not Safe

d. 4g = 39.2 m/s^2 Ac = v^2/r 39.2 = v^2/9 352.8 = v^2 18.8 m/s = v

e. Ac = v^2/r 39.2 = v^2/7 274.4 = v^2 16.6 m/s = v

f. GPE = GPE + KE mgh1 = mgh3 + 5mv^2 (9.8)(45.9) = (9.8)(18) + .5(v)^2 v = 23.4 m/s

g. Ac = v^2/r = 23.4^2/9 = 60.8 m/s^2

h. 60/9.8 = 6g's (not safe)

i. N + w = ma mg = ma a = g 9.8 = v^2/9 v = > 9.4 m/s

Physics To Go 10
1. Make sure the acceleration is good, also check if there is enough speed to make it over the loop and last make sure it is safe enough for riding. 2a. 20m 2b. a=v^2/r =20^2/12 =33.3 m/s^2 2c. 33.3 m/s^2 / 9.8=3.4 g's. (safe) 2d. 9.8*4=39.2 m/s^2 39.2=v^2/12 v=21.7m/s. (Safety concerns) 2e.39.2=v^2/7 v=16.57m/s. (Safety concerns) 3a. Ac=v^2/r =25^2/10 =62.5 m/s^2 3b. a/9.8 62.5/9.8 =6.4 g's. (Not safe) 4a.GPE=KE mgh=1/2mv^2 (9.8)(50)=1/2(V^2) v=31.3m/s. The speed will be this at the bottom. 4b. a=v^2/r a=31.3^2/10 a=97.9 at the top. 4c. 24 m/s 4d. 58 m/s 4e. yes 5a. GPE=KE mgh=1/2mv^2 (9.8)(16)=1/2v^2 v=17.7m/s 5b. GPE=KE mgh=1/2mv^2 9.8(h)=1/2(17.7^2) h=16m 6a. Ac=v^2/r =12^2/18 =8m/s^2 6b. Fc=mv^2/r =(900)(12)^2/18 =7,200 N 6c. The centripetal is the weight and the normal force from the track. 7a. Ac=v^2/r =20^2/15 =26.7 m/s^2 7b. Fc=mv^2/r =(900)(20)^2/15 =24,000 N 7c. Yes, the roller coaster is safe. If it can hold 25,000 newtons, the centripetal force is 24,000 newtons, which is less than the maximum. 8a. No, it will not change because mass is not a factor of centripetal acceleration. 8b. It is the same speed because only mass is being added. 8c. Yes it will require a stronger material because the normal force from the track will need to be greater because weight is increasing.

What Do You Think Now? 10

 * Yes it will make people less interested in the ride and some people will not even want to go on the ride because of how dangerous it could be.
 * Of course, it is so dangerous to even have a risk of death. That just makes people lose their interest and people lose business because no one wants to go on the ride.