Ch4_OringerP

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Section 1
I see a boy in a chair with wheels being pushed by a girl. They are thinking about a roller coaster, but she is just moving him around in crazy directions. Shows that both have changing velocities and directions.
 * What do you see?**

The drop part of the roller-coaster ride produces the loudest screams because people get nervous and don't expect such a big drop after the peak.
 * What do you think?**

**Look up roller coaster design on the Internet and list at least two roller coasters mentioned. Describe their most important features.** Steel Force at Dorney Park in Allentown, PA The ride gets to speeds of 75 mph. It has out-and-back configuration, "air" time, and banked turns.

Cyclone at Astroland in Brooklyn, New York The ride breaks records in speed and height. It has an unparalleled 58.6 degree drop at 60 mph. It also has banked turns.

**Physics Talk** 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. 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

**PTG** 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 5e. train ride takes you 150 km NW - displacement 6. v = d/t v = .1m/2s .05 m/s 7. v = d/t .05 m/s = .05 m/s s = 1 8. a = change in V / change in t a = 25 m/s / 10s a = 2.5 m/s^2 10a. If I were to add 2 more changes to it for children, I'd decrease the angle of plunge and make the radius bigger for the curve, because it reduces the force as you go around. 10b.

Section 2
**What do you see?** There is a cart going straight and not on a slopes, so they are bored. The other cart that is accelerating down the steeper hill is screaming with thrill.

**What do you think?** The coaster going down the slope with the bigger angle (90 degrees) will get the bigger thrill because the acceleration will be greater.

**Physics Talk** Gravitational Potential Energy and Kinetic Energy Energy Transformations in the Roller coaster GPE: the energy a body possesses as a result of its position in a gravitational field KE: the energy an object possesses because of its speed KE depends on speed, GPE depends on height, and both depend on mass GPE = mgh (J) KE = 1/2mv^2 (J) mechanical energy: the sum of kinetic energy and potential energy the sum of KE and GPE is the same at any point in the rollercoaster when GPE increases, KE decreases and vice versa Calculating KE from GPE Calculating Speed from Kinetic and GPE Mechanical energy (bottom) = mechanical energy (top) KE (bottom) + GPE (bottom) = KE (top) + GPE (top) 1/2mv^2 (bottom) = mgh (top)

1. The higher up the ball is released, the greater speed it has at the bottom. 2. As the height increases so does the GPE. The mass affects it the same way. As the mass gets decreases, the GPE decreases. 3. As the speed of an object increases, the KE increases. Also, as the mass gets bigger, the KE does, too. 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. 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.
 * Checking Up**

1. The speeds of carts A and B are the same at the bottom. Although their inclines are different, their initial height is the same. 3. 4. 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. The least GPE & greatest KE 9b. The roller-coaster is traveling at the same speed at points C and F. This is because their heights are the same. Equal GPE & KE 9c. The roller-coaster is traveling faster at D because it just dropped from C, rather than traveling up from D.
 * PTG**
 * 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 ||

5. 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 mgh = 1/2mv^2 (9.8)h = 1/2(3.83)^2 h = .75 m 10b. The roller coaster cannot reach point H. This is because the height of the original GPE is less than the height of H. With the transfers between GPE and KE adding up to the same amount, the height of H would make that sum impossibly higher.
 * 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 ||

11.
 * Position || Height (m) || GPE = mgh (J) || KE = 1/2mv^2 (J) || GPE + KE (J) ||
 * bottom of hill || 0 || 0 || 50,000 || 50,000 ||
 * top of hill || 25 || 50,000 || 0 || 50,000 ||
 * top of loop || 15 || 30,000 || 20,000 || 50,000 ||
 * horizontal loop || 0 || 0 || 50,000 || 50,000 ||

What do you think now? I think that 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. I did say that the one on the rights will have the greater thrill because of its greater acceleration.

Section 3
What do you see? The students are testing out the SPE GPE and KE of a spring toy. They are probably using a photogate timer to test the speed of the toy. They are measuring how high it jumps with a meter stick, most likely to measure the GPE

What do you think? A roller coaster gets up to its highest point by being pulled by chains and cables. Also, the roller coaster probably has a motor. I don't think it costs more to lift a roller coaster full of people because the mass cancels out.

Physics Talk Conservation of Energy energy in a system can vary between KE GPE and EPE spring potential energy: the energy stored in a spring due to its compression or stretch ex of EPE: bungee cords, trampolines EPE = SPE a bouncy ball does not get to the same height in each successive bounce because some of the energy is converted to sound/heat energy The total energy of an object can be GPE, SPE, or KE, but the sum of the energies is always to same all energies are measured in joules, and total # of joules must always be the same pop-up toy: GPE (bottom) KE & some GPE (just after leaving table) equal KE & GPE (halfway up) GPE (top) a higher mass pop-up toy won't go as high as a lower-mass one even though both had the same SPE. The less massive and more massive pop-up toys can have the same GPE if the more massive pop-up toys don't go as high Since GPE = mgh, the larger mass has a smaller height and the smaller mass has a larger height a roller coaster has all its GPE at the highest hill. This becomes KE as the coaster is released. electric energy pulls the coaster up a hill. The electrical energy comes from a powerplant after the cars are pulled up to the top of the hill, the total GPE and KE remains the same except for the losses due to thermal and sound energy as the breaks stop, KE is converted to thermal energy if brakes fail, a large spring may stop the car as the car compresses it SPE = 1/2kx^2 k=spring constant x=amount of stretch or compression of the spring

GPE + KE + SPE = constant

Checking up Questions 1.) The spring potential energy turns into both kinetic and gravitational potential energy as it bounces off the table. 2.) It will have 2J of Kinetic Energy. 3.) At the top it will have 2 J of Gravitational Potential Energy. 4.) The spring constant and the distance it is stretched or compressed.

Physics to Go 5.) It can't be higher than the first because it won't have enough GPE (initial is the max) to get to the top of the higher second hill. 6.) Friction puts resistance on the ride. Some of the GPE is converted into Work. Therefore, the remaining GPE isn't enough to keep the ride going. 7.) (300)(10)(15)= 45,000 J - electrical energy to raise the cars to 1.5 m 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.) GPE = KE .078 is approx = to .073 The GPE and KE should give approximately the same values. GPE = (0.02)(9.8)(.4) GPE = .078 J 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 = 6615 N/m 12b.)GPE= SPE GPE= mgh 400(9.8)(18) 70,560= 1/2 kx^2 70,560= 1/2(6615)x^2 J x= 4.62 m 13.) KE= SPE KE= 1/2kx^2 KE=1/2 40(.3)^2 KE= 1.8 J

What do you think Now? 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.

Section 4
What do you see? The kids on the ride to the left look bored on a roller coaster on the moon. The kids on the Jupiter (a lot of gravity) roller coaster are thrilled and having fun.

What do you think? Gravity does have direction. People in Australia can be held onto Earth when they are "Upside down" because the gravity is in the direction of the Earth. All of the gravity is in the direction of its largest mass, which in this case is Earth.

Physics Talk Newton's Law of Universal Gravitation **gravitational field**: the gravitational influence in the space around a massive object Earth of the source of its gravitational field because it is the first object that sets up in the space around it second object interacts with this field--moon (response/test object) Inverse-Square Relationship acceleration due to gravity becomes less as an object moves further from the surface of Earth **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 force of gravity between 2 objects decreases by the square of the distance between them Ex: if you triple (3x) the distance, the force is (1/9) the original **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 : the force of attraction between two bodies due to their masses Equation of Newton's law of universal gravitation 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 The moon orbits Earth and the planets orbit the Sun in elliptical paths  plants don't move in exact ellipses b/c planets tug on on another

Checking Up 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 3. If you triple the distance between two masses, the force is (1/9) the original 4. Gravity is the force that holds the Moon in its orbit around Earth 5. The shape of the orbit of the plants around the sun is approximately elliptical.

PTG 1. If the gravitational force between the two asteroids doubles, the force would be 125 N. ( 1/4 inverse square) 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 the Earth and always will. Also, nothing can float around in the air because to do gravity of Earth, what goes up must come down. We have never experienced no gravity. As long as you have mass, the gravitational force will be present. 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. All masses are attracted to other masses. 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. There is an attraction to the moon. 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. Gravity holds the water down to the Earth. 6b. Gravity holds a fish "down" on Earth because the mass of a fish is MCUH less than the mass of the Earth. Masses are attracted, so the larger mass of the Earth attracts the fish. 7. a) 1/4 b) 1/9 c) 1/16 d) 4x 8. a) 2x b) 3x c) 4x d) 1/2x 9. a) 4x b) 9x c) 16x d) 1/16x 10. a) 2x b) 9x c) 6x

MASS IS DIRECT PROPORTION TO FORCE DIRECTION IS INDIRECT PROPORTION TO FORCE

Physics PLus 1. rm = 1/60rE ag inverse square proportion 1/d^2 1/60^2 1/3600 x 10 Ag = 0.0025 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 4. T62 / R^3 2.9 x 10^-19 s^2/m^3 / (1.5 x 10^11m)^3

What do you think now? 1. Gravity does have a direction. It is the direction of force on a mass. Gravity is directed towards the largest mass. (center of Earth) 2. People in Australia 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.

Section 5
**What Do You See?** in the Deli, meat is being weighed and pushes down on the scale. In the lab, meat is being weighed on a spring scale. Shows different ways of measuring, but shows that they are related. Weighing is weighing, doesn't matter how it is done.

**What Do You Think?** 1. You can't use the same scale to weigh a canary and an elephant because their weights are not comparable. Weight is mass times gravity. Measuring their mass would take two different approaches because their sizes are so different. 2. The bathroom scales works by measuring the person's mass and then multiplying it by gravity. W = m x g

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.
 * Physics Talk**

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.
 * Checking Up**

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 loser and more stretch 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 higher constant is more difficult to stretch, so in this case 15.0 N/m would be more difficult to stretch. Greater constant 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.
 * PTG**

1. 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. If the elephant is too large, the spring will fully compress but will need to compress even more to give an accurate reading of its weight. The compression distances would be much different and the springs required would have to be different sizes. 2. 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 think now?**

Section 6
What do you see? The tiny man who is going up on the elevator has a weight of 200 lbs on the scale. The big man who is going down on the elevator has a weight of 0 lbs on the scale.

What do you think? Your weight does not change when riding on a roller coast, you just may feel lighter, heavier, or weightless. If you were sitting on a bathroom scale, the scale would give different readings at different places on the roller coaster. This is because the bathroom scale's force changes as you move up or down. As you move up, the scale exerts more of an upward force, so the reading is higher. When going down, your weight exerts more of a force than the scale exerts up, so the weight is read lower.

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

Class Notes Newton's 1st Law: object at rest stays at rest, or in motion stays in motion, unless acted on by unbalanced force Newton's 2nd Law: unbalanced force creates acceleration; the bigger force is in the same direction as acceleration & vice versa show this w/ motion map & FBDs. (increase in v & a same direction, decrease v & a opposite motion) Net Force = ma increasing speed: velocity and acceleration point in same direction decreasing speed: velocity and acceleration point in opposite directions Net Force and Acceleration point in the same direction the bigger force is in the same direction as net force

Checking Up 1. The sum of all the forces acting on an object when it is moving up at constant speed is zero. 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. 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 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. 5. Air resistance slows a falling raindrop.

PTG 1. Vf = Vi(0) + at 1a. (9.8)(2) = 19.6 m/s 1b. (9.8)(5) = 49 m/s 1c. (9.8)(10) = 98 m/s 2a. (1.6)(2) = 3.2 m/s 2b. (1.6)(5) = 8 m/s 2c. (1.6)(10) = 16 m/s 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 || up ||  || greater ||

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. Net Force = m a Nscale - W = ma  137 - 140 (negative number so the acceleration is down  v & a are both down, which means increase down  v is up & a is down, which means decrease up  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 the person downward. Seams heavier.  v is up & a is up ; therefore the bigger force points up, which is the scale 7a. Once the elevator starts to descend, the scale's reading will decrease. 7b. Fnet = ma (accelerating down so the weight will be the bigger force) W - Fscale = ma (50)(9.8) - Fscale = (50)(1.5) Fscale = 415 N 8a. The scale will read zero Fnet = ma Fnet = 0 Scale reading = 490 N 8b. Fnet = ma (acceleration is up, so the bigger force is Fscale) Fscale - weight = ma Fscale - (50)(9.8) = (50)(2) Fscale = 590 N 8c. The scale will read zero as it travels up at constant speed because the acceleration is zero. Fnet = m(0) = 0. Therefore, the scale reading is 490 N 9a. At rest, the force up (scale) and force down (gravitation) are both equal, so the Fnet is zero. When the Fnet = zero, the scale reads your accurate weight. 9b. An elevator in free fall has no force from a scale pushing up, so there is only the force of you pushing down. Therefore, the scale reads as 0. g = a 9c. The scale reads a greater number than that at rest because it is accelerating upward. When acceleration is up, that means the bigger force is the Fscale. When Fscale is bigger than weight, the number is positive, and the scale reads a higher number. 10. They were find the loops exciting because they feel heavier the whole time in the loop. They'd also like the change between increasing upward/downward acceleration and decreasing upward/downward acceleration. The increase acceleration upward would make them feel heavy and the increase down would change their feeling to light. The decrease upward would then keep them feeling light, but the decrease downward would have them feeling heavier -- Thats exciting!

What do you think now? Your actual weight does not change when you are riding on a roller coaster because your true weight is gravity. It is your apparent weight that changes. If you were sitting on a bathroom scale, the scale would give different readings for different places on the roller coaster. This is due to the direction of acceleration and the direction of the net force. If the bigger force is pointing up, then your apparent weight is greater. If the bigger force is pointing down, then your apparent weight is less. When you are almost at the top of a hill and the cart is decreasing up, your weight would read less that it actually is because the force pushing you up the hill is less than that of your body. Also, the acceleration is downwards.

Section 7
What do you see? There is a cart going up and down hills and in a loops. At a curve, the cart and people in it begin to top over to the side.

What do you think? You don't fall out of a cart during a loops because it has enough speed and momentum to keep you on the track. Also, it depends on the mass of the cart. The acceleration and gravitational forces both point down.

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

Class Notes centripetal force: force that points to center of circle; normal, tension friction weight centripetal acceleration: causes an object to move in a circle, point to center -if Ac = 0, then moving in a straight line tangential velocity- the direction the car is actually moving in, constant (usually) increase radius: Fc goes down increase velocity: Fc goes up increase mass: Fc goes up

Checking Up 1. Centripetal force is required the make an object travel in a circle. 2.If you are traveling in a circle at constant speed, you are accelerating, which is called centripetal acceleration 3. At top of a loop, the gravitational force and normal force provide the Fc. 4. Normal force is responsible for your apparent weight on a roller coaster. 5. Centripetal force is larger when speed is increased (direct), mass is increased (direct), and radius is shorter (inverse).

PTG

1a. the path of the car would be in a circle 

1b. if the string were to break while the car was moving in a circle, the car would follow a straight line tangent to the circle 

2a. Friction has replaced the string of the toy car. 2b. 6a. The speed of the roller coaster did not change, it stayed 20 m/s. 6b. The velocity of the roller changed because it changed direction. 6c. The change in velocity was 28.2 m/s at 45 degrees NW V2 - V1 = change in V  20m/s ^, 20 m/s < 20^2 + 20^2 = c ^ 2 c = 28.2 m/s tan theta = 20/20 theta = 45 7. Ac = v^2 / r Ac = (20)^2 / 200 Ac = 2 m/s^2 10. Fast Moving Roller Coaster Slow-moving roller coaster 13a. Bottom of hill #1- heavier  13b. Top of vertical loop- uncertain  13c. Bottom of vertical loop- heavier  13d. Bottom of hill #2- heavier  13e. Lift hill (going up at constant speed)- "normal"
 * || 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 ||
 * || 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 ||

14a. Bottom of hill #1- up  14b. Top of vertical loop- down  14c. Bottom of vertical loop- up  14d. Bottom of hill #2- up  14e. Lift hill (going up at constant speed)- zero  14f. Horizontal loop- to center <span style="font-family: arial,helvetica,sans-serif;"> 14g. Back curve- to center

Physics Plus 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? 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. You are not upside long enough to move because you are already on another part of the circle or curve.

Section 8
What do you see? There is a roller coaster with a large hill and people doing work to pull a cart up. They are sweating, carrying the cart up the hill. Once at the top of a hill, the cart flies down the incline really fast.

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

Checking Up 1. When a spring scale is used to do work pulling a cart to the top of an incline, the energy has gone into GPE 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 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 4. When the brakes stop a roller coaster, the KE is converted into thermal energy 5. The unit for power is watts. 1 W = 1 J/s

PTG 1a. The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline. 1b. As the cart went from the top to the bottom, all of the work is done by gravity. 1c. All of the work is don't by the spring as the spring compressed 1d. SPE = 1/2kx^2 1e. The total energy just before it hits the spring is GPE. 1f. You begin to slow down just when you first touch the spring. 2a. W = F x d  work is zero because the force and distance are perpendicular, or not in the same direction. 2b. W = F x d W = 60 x .5 W = 30 N 2c. W = F x d W = 75 x 40 W = 3000 N 2d. W = F x d W = 500 x .7 W = 350 N 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. 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. Then, the GPE and KE would increase 5a. W = F x d W = 10,000 x 20 W = 200,000 N 5b. P = work / change in t P = 200000 / 150 P = 1333 1/3 J/s 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. Up the first incline (W --> GPE) down hill (GPE-->KE) up loop at the top (KE & GPE) back curve (KE) up second hill (GPE & KE) horizontal loop (KE) braking (work)

What do you think now? <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"> <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">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. <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">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.