CbrownThrillsandChillsChapter4

=Chapter 4= toc =Thrills and Chills=

Section 1
In the picture there is a person on a chair and another person is pushing them. The person is imagining being on a roller coaster and seems to be very anxious about what may be happening next. I think that the part of the roller coaster that produces the loudest scream is the the acceleration down after going up the hill. I think this because you go the fastest and you feel a lot lighter than you normally do. Also, you're being pushed back and it's a feeling that you only feel on roller coasters so it causes the most screams and gives you more of an adrenaline rush.
 * //What do you see/think?//**

//The Hulk at Universal Studios// -pneumatic breaks powered by air pressure -shoulder straps that lock //King Da Ka at Six Flags// -head rests that keep your head from being taken off from the speed -air powered breaks
 * //Roller Coaster Assignment//**

//**Physics Talk**//
 * Measuring velocity and acceleration
 * **scalar quantity**: can be measured with a flexible piece of string or a metric tape measure placed along a path. The units used is meter.
 * **displacement**: a measured distance with a direction included. Depends only on the endpoints, not on the detailed path. This is a vector.
 * **vector**: has magnitude- size or length and direction
 * If one were to walk from school back to their house, the distance traveled would be 5 km, but the displacement would be 0 because the final and initial position are the same.
 * **speed**: the distance traveled divided by the time elapsed. (scalar and has no direction)
 * **velocity**: the displacement divided by the time elapsed. (vector and has direction and magnitude)
 * [[image:numeroo_unnnee.png width="344" height="89"]]
 * [[image:numero_dosie.png width="325" height="42"]]
 * **acceleration**: the change in velocity divided by the time elapsed. (vector and will be the direction of the change in velocity)
 * [[image:alalsldallast.png width="388" height="120"]]

1) Distance is how far an object travels and is a scalar quantity, meaning that it has no direction. Displacement is how far an object goes with direction included, making it a vector quantity. 2) The displacement is 0 because you started home, then went to school, then back home. The endpoints are exactly the same which means that the displacement must be 0. 3) Speed is how fast an object goes during a certain time frame with no direction or magnitude included *scalar. Velocity is how far an object goes during a certain elapsed time but it included direction and magnitude *vector. 4) To find velocity you need to know the change in distance and the change in time. Then you can divide the change in distance by the change in time and find the velocity of an object.
 * //Checking Up//**

1)
 * //Physics Talk//**

2) The biggest thrill on the terminator express would be when you're going down the inclines because it is in free fall mode. It is the part of the ride when you're going the fastest and at the end of the incline, you feel very heavy. It is the most drastic change in how the person feels (weight wise).

3) a) The equator because the radius is larger. b) 400,000 km / 24 hours = **1667** **km/h** c) You do not get a big thrill from going such high speeds because the Earth is constantly moving and we are used to the speeds.

4) a = Δv / Δ**t** a = 16 m/s - 4 m/s / 3 s a = 12 m/s / 3 s a = 4 m/s^2

5) a) a car traveling at 50 km/h : **speed** b) a student riding a bike at 4 m/s toward home : **velocity** c) a roller-coaster ride whips around a left turn at 5 m/s : **acceleration** d) a roller-coaster car is dragged up a hill at 12 m tall traveling at 4 m/s : **velocity and displacement** e) a train ride takes you 150 km northwest : **displacement**

6) v = d / t 10 m / 2 s = .5 m/s

7) v = d / t 5 cm / s = 5 m/s 5 t = 5 t = 1 s

8) a = Δv / Δt a = 25 m/s / 10 s a = 2.5 m/s^2

10) a) To make the terminator express safer for younger children, I would take away some of the harsher parts of the coaster. The hills would become less steep and the back curve would be wide instead of really sharp and fast. Then the horizontal loop would become a wide turn to the side and the third hill would not be steep. There would also be smaller seats and restraints so that they fit in the seat without falling out. b) After inclines when you drop and during loops produces the largest screams. This is because when you drop down you are going faster than you do during the rest of the roller coaster. The greatest thrill comes from both the drop and the loop as well. The loop causes thrill because you are going moving really fast and you're pushed back into your seat because of the force being put on you from the speed of the roller coaster.
 * //What do you think now?//**

Section 2
There are two carts. One is on a steeper slope and the people seem to be enjoying the roller coaster more than the one with the smaller slope. This is because they seem to have a larger thrill than the people on the smaller slope. The 90 degree angle steel roller coaster would give more of a thrill because the drop after the incline would be extremely fast, even faster than the 70 degree wooden roller coaster. It would be a very drastic change in speeds which would cause the largest thrills and screams.
 * //What do you see/think?//**


 * //Physics Talk//**
 * Gravitational Potential Energy and Kinetic Energy
 * Energy transformations in the roller coaster
 * Varying slope of the incline and changing speeds
 * **GPE (gravitational potential energy)**: the energy an object has as a result of its position in a gravitational field.
 * [[image:GPEPEEPEPPE.png width="527" height="167"]]
 * **KE (kinetic energy)**: the energy an object possesses because of it's motion, in particular, due to it's speed.
 * [[image:KEKEKEKEKE.png width="503" height="149"]]
 * **joules**: the unit for energy
 * **mechanical energy**: the sum of GPE and KE
 * Calculating Kinetic Energy from Gravitational Potential Energy
 * The sum of the GPE and KE is constant
 * GPE + KE = constant
 * Calculating Speed from Kinetic Energy and Gravitational Potential Energy
 * [[image:TOATS_ENERGY_WEE_!.png width="575" height="263"]]
 * [[image:TOATS_ENERGY_WEE_@.png width="468" height="135"]]

1) No affect. The height and angle affect the speed at the bottom of the incline. 2) As the height and mass get bigger the GPE gets bigger. As the height and mass get smaller, so does the GPE. They are directly proportional. 3) When the height and mass get bigger the KE gets bigger. When the height and mass get smaller, so does the KE. They are also directly proportional. 4) The GPE that a roller coaster loses as it rolls down a hill is transferred into kinetic energy. 5) 30,000
 * //Checking Up//**

1. They are the same 3.
 * //Physics To Go//**
 * Position of cart ->heigh || GPE (J) = mgh || KE (J) = 1/2 mv^2 || GPE + KE (J) ||
 * top (30 m) || 60,000 || 0 || 60,000 ||
 * bottom (0 m) || 0 || 60,000 || 60,000 ||
 * Halfway down (15 cm) || 30,000 || 36000 || 60,000 ||
 * three-quarters way down (7.5 m) || 15,000 || 45,000 || 60,000 ||

4. 8. It will change slightly. KE=1/2mv^2. The masses cancel 9. a) At point B because it has the lowest height b) C and F because they are at the same height. c) D because it has more kinetic energy and less potential. It is at a very low point after an acceleration. 10. b) You have no kinetic energy because you are not moving. The highest hill is alwayst he first one. 11.
 * Position of cart ->heigh || GPE (J) = mgh || KE (J) = 1/2 mv^2 || GPE + KE (J) ||
 * top (30 m) || 75,000 || 0 || 75,000 ||
 * bottom (0 m) || 0 || 75,000 || 75,000 ||
 * Halfway down (15 cm) || 37,500 || 37,500 || 75,000 ||
 * three-quarters way down (7.5 m) || 15,000 || 60,000 || 75,000 ||
 * Position of cart ->height || GPE (J) = mgh || KE (J) = 1/2 mv^2 || GPE + KE (J) ||
 * top (30 m) || 200 (10) (25) =50,000 || 50,000 || 100,000 ||
 * bottom (0 m) || 50,000 || 0 || 50,000 ||
 * Halfway down (15 cm) || 30,000 || 20,000 || 50,000 ||
 * three-quarters way down (7.5 m) || 0 || 45,000 || 50,000 ||

Roller coaster B would cause the largest thrill because it changes speed faster (acceleration) than roller coaster A. This is because of the steepness of the track. They move at the same speed because they start at the same initial height, the only difference is that B accelerates much faster than A.
 * //What Do You Think Now?//**

Section 3
I see students trying to find the spring potential energy, kinetic energy, and gravitational potential energy of a spring toy. They are finding the height at which it bounces with a meter stick and using a photo gate type device to measure the speed (as it appears). A roller coaster today uses a chain and hook type system to crawl up slopes in order to get to their highest points. It is harder to lift a roller coaster that is full because the weight is heavier. The heavier is it the harder it is to get up the slope.
 * //What do you see/think?//**

Spring potential energy (EPE) is the energy stored in a spring due to its compression or stretch.
 * Physics talk **
 * SPE= 1/2kx2.

1) SPE (EPE) is converted into Kinetic Energy when the pop up toy "pops" 2) 2 Joules 3) 2 Joules 3) Distance - either stretched or compressed - and the constant
 * Checking Up**

b. 0.13 m 11) 12) 6600 n/m 4.62m 13) KE = EPE mgh = .5kx^2 1.8 joules
 * Physics To Go**
 * 5) There is only a certain amount of KE that is provided by the first hill and there isn't enough energy to make it over a higher hill. **
 * 6) There is work and friction that slows the roller coaster **
 * 7) GPE =mgh = (300) (9.8) (15) = 44,100 Joules **
 * 8) **
 * b. 45,000 Joules **
 * c. KE=GPE **
 * 1/2 mv^2 = mgh **
 * 1/2(15)^2 = 9.8h **
 * 11.5m = h **
 * 9) Increasing **
 * as H increases GPE also increases **
 * 10) They reach the same end point and end up at the same GPE **


 * What do you think now?**
 * A roller coaster uses a chain and hook type system to crawl up slopes in order to get up slopes. The heavier is it -more people in the coaster- the harder it is to get up the slope. **

**Section 4**
There are two different roller coasters, one on the moon and one on jupiter. On the mood there is more gravity so this means that the more gravity a roller coaster has the faster you go.
 * What do you see? **

<span style="font-family: Arial,Helvetica,sans-serif;">Gravity's direction is towards the earth's crust. Australia stays on Earth because it is being pushed into the core because of the gravity.
 * <span style="font-family: Arial,Helvetica,sans-serif;">What do you think? **

<span style="font-family: Arial,Helvetica,sans-serif;">Earth's gravitational field is the gravitational influence in the space around a massive object. <span style="font-family: Arial,Helvetica,sans-serif;">It needs a source of the field and a second object to interact with the field, the response object. <span style="font-family: Arial,Helvetica,sans-serif;">Inverse-Square Relationship is the relationship between the magnitude of a gravitational foe and the distance from the mass. It also describes how electrostatic forces depend on the distance from an electrical charge. Newton's law of universal gravitation is that 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.
 * Physics Talk**

1. The direction of the strongest gravitation is towards the center of the earth. 2. The closer to an object, the stronger the field is. 3. It is divided by 9 4. Gravity holds the moon in its orbit around the Earth. 5. Its a somewhat circular path.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Checking up **

1) 1/4 (500) 125 2) a) 1/4 b) 1/9 c) 1/16 3) There has never not been gravity. We don't know how the Earth would feel if we didn't have gravity 4) Its the same at all points of the roller coaster. 5) a) The tide closer to the moon. It is the higher tide. b) There is different tides at all sides of earth. The tide closer to the moon is at high tide while the one further way is at a low tide. 6) Water is together with really weak bonds. If there was no gravity a fish would not have water to swim in. Gravity holds the water down. 7) a) 1/4 the fouse b) 1/9 the force c) 1/16 the force d) 4 times the force 8) a) double the force b) triple the force c) quadroupled the force d) half the force 9) a) 4 times b) 9 time c) 6 times
 * Physics To Go**

Fg = 1/ (3.84x10^8) Fg = 2.60916 x10 ^-9 C = 2πr T = 2415793158/2440800 v = 988.505 m/s a = 988.505^2/3.84 x 10^2 a = .0025 m/s^2
 * Physics Plus**


 * What do you think now?**
 * Gravity's direction is always pointing toward the center of the earth. Australians can be held on the earth even though they are upside down because gravity is pushing towards the center of the earth at all times basically holding the Australians to the Earth. This is how they are held on the planet **

** Section 5 **
I see meat being weighed in a deli with a push down scale and an object being weighed in a lab with a spring scale. it does not matter what kind of scale you use, the object should weigh the same.
 * What do you see?**

A scale that could handle an elephant's weight wouldn't really detect the weight of the canary. A scale that could measure the weight of a canary would be too sensitive for the elephant to stand on and the scale would probably break. A bathroom scale works by detecting gravities push on the person standing on the scale. The larger they are, the more gravity there is pushing down on the person which in turn pushes down on the scale.
 * What do you think?**


 * Physics Talk**
 * Hooke's Law describes the restoring force a spring exerts
 * stretching a string more, requires a larger force
 * Many springs have the property that the stretch of the spring is directly proportional to the force applied to it (ex: if you double the force, the stretch of the spring doubles)
 * If the spring is not moving, the spring exerts a restoring force equal in magnitude of the force that stretched the spring
 * Hooke's law: explains what restoring force a spring exerts if it is stretched. The more you stretch a spring, the larger othe restoring force of the spring.
 * Fs = -kx
 * Force exerted by the spring = - spring constant x spring stretch
 * Force is opposite direction of x
 * Interpolation: points inside
 * Extrapolation: points outside
 * bigger k, bigger slope, less soft
 * negative sign: pull by the spring is opposite to the direction it is stretched or compressed
 * Weight is a force. When an object is moved from Earth to the Moon, the mass stays the same, but it's weight changes due to the gravitational field change. Earth (9.8 N/kg) Moon (1.6 N/kg)

1) The stretch of the spring would increase five times because stretch of the spring is directly proportional to the force which is also five times as great. 2) The spring constant is an indication of how easy or difficult it is to stretch or compress a spring 3) Newton's mass is multiplied by 9.8. 4) The heavier a person is standing on the scale, the more the spring compresses. The lighter the person is, the less the spring in the scale compresses.
 * Checking Up**

1﻿. a) w=mg w = 100 (9.8) w=980 N b) w = mg w = 10 (9.8) w = 98 N c) w = 60 (9.8) w = 588 N 2. a) 1/4 = 1 N or 1 N = 4.45 N 130 (4.45) = 578.5 N b) 1000 (4.45) = 4,450 N c) 50 (4.45) = 222.5 N d) Slope is the spring constant. The k value. 3. F = kx 12 = k (.03) 12 = k (.03) k = 400 N/m 5. Hooke meant that if there is a force acting on something, there will be a stretch or compression. The string will stretch if a force is put on it (stretch or compression). There is a direct relationship. (double force, double stretch) 6. The 15 bigger the number the harder it is to stretch. 150 N/m 8. A spring scale is based off of the spring inside the scale. When something is put on the scale the spring compresses. The distance the spring compresses relates to the weight. The scale can convert the compression of the scale into pounds with the arrow moving in front of the number (Weights). The more compression the scale undergoes, the more weight is put on the scale.
 * Physics To Go**

A canary and an elephant cannot be weighed on the same scale. A scale that measures a canary has a much smaller spring constant. It would be very sensitive to the weight put on it. If an elephant stepped on the same scale as the canary, the spring would break and uncoil and wouldn't give the weight of the elephant. A scale that measures an elephant would have a much higher spring constant because it needs to handle much heavier weights. If the canary stood on the scale that the elephant was weighed on, the scale wouldn't recognize the canary. The spring wouldn't even compress. A scale works by the compression from the weight of the object on top of the scale. When the spring compresses it finds the weight that is pushing down on it and pushes the same force back.
 * What do you think now?**

**Section 6**
** What do you see? ** ** There are two elevators, one moving up, the other moving down. Both men in the elevators are standing on scales, but the elevator is moving upwards and his weight is heavier and he is clearly the smaller man. The heavier, larger man, moving downward, the man is lighter. This is because both the elevator and man are moving the same way and the same speed. **

** What do you think? ** Your weight does not change when you are riding a roller coaster. When making a roller coaster, the creators have to be conscious of the weight of their riders therefore, the riders are not going to be changing weight. Although weight won't be changing, if you were sitting on a bathroom scale and riding a roller coaster, the weights would change. This is because when you are going downwards, both the roller coaster and the rider will be going in the same direction at the same velocity. When the rider is going upwards, their weight will be heavier because of the force pushing downwards on them.


 * Physics Talk Summary**
 * Forces Acting During Acceleration
 * Using Newton's First and Second Law to Explain Forces Acting During Constant Speed and Acceleration
 * When an object is at rest, the sum of the forces on that object equal zero. Both Newton's first and second laws can be used to explain that fact. (1st law: an object at rest stays at rest and an object in motion stays in motion unless acted upon by a force- the object is at rest and no net force acts on it. 2nd law: the object is at rest and therefore has zero acceleration and therefore has no no force acting on it.
 * The object moving down at constant speed is identical (in terms of forces and accelerations) to the object moving up at constant speed.
 * Calculating Acceleration
 * F(net) = ma (net force or calculating acceleration)
 * F(w) = mg or m = F(w) / g (finding acceleration)


 * **Checking Up**
 * 1) 0
 * 2) The person's weight would be less than what is being read on the scale. This is because there is more force pushing up and acceleration is pushing up.
 * 3) You feel like you way more because if a person is at rest, you want to stay at rest but there is a net force pushing on you. To get you moving, you need to put a larger force on the scale.
 * 4) The scale reads 0. This is because the force you are exerting on the elevator is not pushing back on you. Instead, everything is falling in the same direction at the same speed with no upwards force. You are in free fall and are not pushing down on anything.
 * 5) Air resistance

<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">1) Vf = Vi (0) + at <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">a. 9.8 (2) = 19.6 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> b. 9.8 (5) = 49 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> c. 9.8 (10) = 98 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2) 1.6 (2) = 3.2 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> b. 1.6 (5) = 8 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> c. 1.6 (10) = 16 m/s <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">4) N=w || N>w || N=w || N<w || N=w || N<w || N=w || N>w ||
 * Physics To Go**
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || v=0, a=0, ∑=0 ||  || equal
 * Starting at Rest, Increasing Up || v=up, a=up, ∑=up ||  || greater
 * Continuing to move, Constant Up || v=up, a=0, ∑=0 ||  || equal
 * Slowing down to top floor, Decreasing Up || v=up, a=down, ∑=down ||  || less
 * At rest, top floor || v=0, a=0, ∑=0 ||  || equal
 * Starting at rest, Increasing Down || v=down, a=down, ∑=down ||  || less
 * Continuing to move, Constant Down || v=down, a=0, ∑=0 ||  || equal
 * Coming to a stop on the ground floor || v=down, a=up, ∑=up ||  || greater

<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">5. The elevator could be accelerating downward, or decreasing acceleration upwards. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> Nscale - W = ma <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 137 - 140 = negative acceleration <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">v is up and a is down, which means decrease up v and a are both down, which means increase down <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">6) The person's weight appears larger because the acceleration and net force are upwards. The bigger force is up. 7) a. Once the elevator goes downward, the scale's will read a decreased number. b. accelerating down so the weight will be the bigger force ∑F = ma N - w = ma N = ma + mg N = (50) (-1.5) + (50) (9.8) N = 415 N 8) a. a = 0, ∑F=0, N=w w = 490 N b. a=up, v=up, ∑F=up N = w = mg = 490 ∑F = ma N - (50)(9.8) = (50)(2) N = 590 N c. There is no acceleration therefore, the scale reading is 490 N N = m(0) = 0. 9) a. Everything is falling at the same time with the same velocity. There is no support and you're basically floating. b. 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 c. The scale reads a greater number than that at rest because it is accelerating upward. When acceleration is up, the ∑F is up. 10) They enjoy the change in acceleration and the change in velocities. The changes in height cause them to feel heavier and lighter at different times.

Your weight does not change when you are on a roller coaster. If you were to ride a roller coaster while sitting on a spring scale, while increasing upwards, your acceleration and net force would be upwards and the scale reading would be greater than your actual weight. While decreasing downwards, the acceleration and net force would be upwards and the scale reading would also be greater. If you were decreasing up, the acceleration and net force would be down, meaning that the scale reading would be less than your actual weight. If you were increasing down, the acceleration and net force would be down which in turn would make the scale reading less than your actual weight.
 * What Do You Think Now?**

** Section 7 **
There are people on a roller coaster. One of the people's hats are falling off because they just got off of a loop and their acceleration is very fast causing them to want to go straight but they are on a curve so they're being pushed to the side.
 * What do you see?**

You don't fall out of the roller-coaster cart when it goes upside down during a loop because the force pushing you to stay in your seat. Because you are going so fast, you are being pushed in your chair and do not move out of it.
 * What do you think?**

<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">**Physics Ta**lk <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">Normal + weight = net centripetal force //added notes:// centripetal force: ALWAYS POINTS TO THE CENTER; normal, tension friction weight centripetal acceleration: causes an object to move in a circle, point to center if Ac = 0 you are then moving in a straight line tangential veocity: 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
 * 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
 * **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
 * 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
 * Safety on the Roller coaster
 * Keep acceleration less than 4 gs
 * 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.

<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px; min-height: 14px;">**Checking Up** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">1) Centripetal force is required in order to have an object travel in a circle. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 2) If you are traveling in a circle at constant speed (you're accelerating) called centripetal acceleration <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 3) At top of a loop, the gravitational force and normal force provide the Fc. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 4) Normal force is the cause of your apparent weight on a roller coaster. <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;"> 5) Centripetal force is larger when the speed is increased (direct), the mass is increased (direct), and the radius is shorter (inverse).

<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">**Physics To Go** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">**<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">1) a. The car would move in a circle ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** b) The car would move in a path tangent to the circle ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** 2) a. The "string" is now the friction of the tires. ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** 6) a. The speed of the roller coaster did not change. It is accelerating though. ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** b. The velocity of the roller changed. This is because it changed direction. ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** c. 28.2 m/s, 45 degrees NW ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** V2 - V1 = (delta) V ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** 20m/s up, 20 m/s west ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** 20^2 + 20^2 = c ^ 2 ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** c = 28.2 m/s ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** 7) a = v^2 / R ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** a = (20)^2 / 200 ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** a = 2 m/s^2 ** <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** 10) Fast Moving Roller Coaster **

<span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">** Physics Plus ** 1) a. F(net) = mv^2 / r trial 1: m= 7 kg v= 10 m/s r= 2 F(net) =(7)(10)^2 / 2 F(net) = 350N trial 2: m= 15 kg (15)(10)^2 / 2 F (net) = 750 N The F(net) gets larger as the mass increases. b. trial 1: m= 7 kg v= 10 m/s r= 2 F(net) = (7)(10)^2/3 F(net) =350 N trial 2: v= 30 m/s F(net) = (7)(30)^2 / 2 F(net) = 3150 N The F(net) gets a lot larger when the velocity is raised. 2) The track must be four times as large for a doubling speed. 3) Because they are inversely proportional, when the r gets smaller, the F(net) gets larger. 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 path tangent to the circle. //Sample Problem:// a. a = v^2 / r = (12)^2 / 20 = 7/2 m/s^2 b. F(net) = ma(c) = (300)(7.2) = 2200 N

You don't fall out of a roller coaster when a roller coaster cart is upside down during a loop because of centripetal force. You are being pushed into your seat because of the force pushing you to move in a circular path.
 * What do you think now?**

**Section 8**
**What do you see?** There are people pulling a roller coaster cart up a hill and having a lot of difficulty. On the other side of the hill (increasing speed) the person who would have pulled the cart up the hill is being dragged down with the cart going down the hill.

**What do you think?** The longer the incline, the harder it is to get the roller coaster up. More energy is required. It is harder to walk a steep incline because you need more energy to get yourself up.

**Physics Talk** W = Fd
 * When a cart is moved up to the top of an inclined ramp from applying a force with a spring scale over a certain distance you find that the product of the force applied and the distance remained the same, regardless of the slope of the ramp.
 * The product of force multiplied by distance is called work
 * (W = Fd)
 * the definition of work involves only that part of the force that is in the same direction or opposite direction of the displacement.
 * The vertical displacement is the height that is it must be lifted.


 * The work done on the roller coaster is mgh. This is equal to the change in gravitational potential energy (GPE) of the roller coaster.
 * power: work done/ time elapsed


 * P = ∆t
 * The SI unit for power is a watt. One watt = 1 J/s

1. The work turns into GPE 2. From the work done to pull it up the incline 3. There is less work required when using a ramp because it changes the distance moved 4. It escapes through heat 5. Watt or J/s
 * Checking Up**

1) a. GPE will be larger at the top and at the bottom it will be less b. W = GPE c. W = SPE d. SPE = 1/2kx^2 e. Kinetic and GPE f. As it reaches the top of the incline it will slow gradually 2) a. zero because the force and distance are not in the same direction b. W = Fd = 60 x .5 = 30 J c. W = Fd = 40 x 75 = 3000 J d. W = Fd = 500 x .7 = 350 J 3) Instead of "conserving energy" you should not use energy when it is unnecessary. Conservation in physics means that energy is never lost but in real life, conserving energy is not using it when its not needed. 4) The cart would be heavier which would mean that there would be more work to put onto the cart which would add to the GPE. The force stays the same. 5) a. W = Fd = 10000 x 20 = 200,000 J b. P = F/t = 200000/150 = 1,333.33 W 6) You move up the incline using work you get to the top where you have GPE. You go down the incline where the GPE is converted into KE. When you go around a loop you have GPE and KE and then go around a back curve with both GPE and KE. Once you're in the horizontal loop, you have KE. While stopping there is work due to friction on the cart.
 * Physics To Go**


 * Class Notes:**
 * -power is the rate add which energy is dissipated (the rate at which energy goes away) **

The amount of work done to pull a roller coaster up a steep hill rather than a gentle hill stays the same. If it's the same distance and force then it will be the same. It is more difficult to walk up a steep incline than a gentle incline because if there is a longer distance, then it takes more work. If it is a shorter distance, then there is less work that needs to be done to get up the incline.
 * What Do You Think Now?**

Section 9
There is a boy who is thinking about force and there is nothing on the paper. There is a girl who is thinking about energy and she has a lot of calculations. Both the boy and girl are thinking about roller coasters.
 * What do you see?**

The parts of The Snake that will be the most thrilling are the loops and the drops because it is when your speed changes which adds to the thrill. If the speed of The Snake always remained the same it would not be fun because the changes are the thrill. If it was all the same speed you would not have the same thrill you'd have if the speeds changed very often.
 * What do you think?**


 * Physics Talk Summary**
 * **Adding Scalars and Adding Vectors**
 * **Energy- A Scalar Quantity**
 * measured in joules
 * The total mechanical energy (GPE + KE) is the same at every point (as long as friction is not significant or motors do not add energy)
 * The GPE depends only on the height from a reference position (GPE = mgh) since the mass and the gravitational force remain the same.
 * If two points on a roller coaster have the same height, the roller coaster is moving at the same speed at those two points.
 * **Force - A Vector Quantity**
 * On the straight incline, the gravitational force and the normal force remain in fixed directions. The car has an acceleration that is constant in magnitude and direction.
 * On the curved incline, the normal force changes direction (it must be perpendicular to the incline) and changes in magnitude. The cart has an acceleration that changes both in magnitude and in direction. This provides big thrills.
 * The speeds of the carts are identical on the two inclines at the points shown. When the heights above the ground are the same, the GPE is the same. If the GPE is the same and the total energy is the same, the KE is the same. If the KE is the same, then the speed is the same.
 * **When to Consider Force and When to Consider Energy**
 * Forces and accelerations are related to how long something will take because acceleration is the change in velocity with respect to time.

** 1.) To solve a vector addition problem, you need to use the pythagorean theorem. ** ** 2.) Energy -scalar quantity, force -vector. ** ** 3.) When friction is insignificant on the ride KE and GPE together will always be equal and when gravity and mass are constant, the GPE is based off of the height. If the coasters are the same height then they will have the same speeds. **  ** 4.) The path doesn't affect it. ** ** 5.) Work would be required. **
 * Checking Up**

** 1) a. ** ** b. a^2+b^2=c^2 **  ** 3^2+5^2= C^2 **  ** c= 6 m/s south west **  ** 2) They have the same gravitational potential energy at the top because they start at the same height so at the bottom they will have the same kinetic energy, and therefore the same velocity. ** ** 3) a. distance- scalar **  ** b. displacement- vector **  ** c. speed- scalar **  ** d. velocity- vector **  ** e. acceleration- vector **  ** f. force- vector **  ** g. kinetic energy- scalar **  ** h. potential energy- scalar **  ** i. work- vector **  ** 4) a. scalar ** ** b. vector ** ** c. scalar ** ** d. vector ** ** 5) On a ride concerned with energy: The roller coaster approaches the first hill. It uses its kinetic energy and work to get up the hill. At the top it is converted into GPE. As is goes down the hill though it is converted back into kinetic energy. ** ** On a ride concerned with force: As the cart goes farther up the hill, there is more weight holding the cart down. The normal force decreases. **  ** 6) ** ** c. It is easier to measure the force in roller coaster 2 because it is a straight track. Normal force is always perpendicular to the track which is why it is easier. **
 * Physics To Go**

**What do you think now?** The loops and drops will be the most thrilling because of the changes in velocity. If there was no change in velocity the ride would be boring because you'd be going the same speed the whole time. It would not be fun.

Section 10
There is a broken roller coaster and people are falling out of the cart and using parachutes. The roller coaster looks overly fast and the ride looks dangerous. They are also falling in the water, spinning out of control, and sharp turns that wouldn't work in a roller coaster. No one would go on this roller coaster if it existed.
 * What do you see?**

People wouldn't on the ride if people were constantly dying. It would add to the thrill but no one would go on the ride because of the deaths that have occurred. No, my answer would still not change even if I knew that one-half of all roller-coaster riders die. I would not go on a ride that people die on. It just wouldn't be worth it even if the thrill was large.
 * What do you think?**

//Class Notes// 1) 4g 2) Decreasing the speed and changing the height. 3) The bottom of the loop has the highest acceleration. 4) The bottom of the loop has the highest
 * Physics Talk**
 * **Roller-Coaster Safety**
 * a = v^2 / r
 * When the roller coaster rips around a corner or moves through the bottom of a vertical loop, the acceleration can be much more than 1 g.
 * Accelerations can not be greater than 4 g.
 * //Qualitative (no numbers):// Decreasing the speed at fast point will lower the acceleration. This can be accomplished by changing the height from which the coaster descends. Less GPE will result in less KE, therefore lowering the speed.
 * Fnet = mv^2 / r
 * Max acceleration in a curve = 4g = 39.2 m/s^2
 * ac = v^2 / r
 * max (a) = 39.2
 * find radius to make roller coaster safe (increase)
 * decrease speed by
 * decreasing the height
 * increasing height of the curve
 * *find velocity that would be safe
 * Forces - apparent weight
 * a = 4g -> N = 5g at the bottom of a loop
 * N = 3g at the top of a loop
 * Minimum Speed Required at the Top of a Loop
 * You need an acceleration greater than free fall in order to make it around a loop or curve (greater than 1g)
 * a > 9.8 m/s^2
 * Checking up**

1) Under 4g acceleration everywhere in roller-coaster ride, the track must be strong enough to support the forces (apparent weight: minimum support force), and having enough speed to get through the loop (acceleration at top of the loop has to be great than 1g and less than 4g. 2) a. mgh + 1 / mv^2 20 m b. a = v^2 / r a= 20^2 / 12 33 m/s^2 c. Yes d. 4g= 39.2 m/s e. 17 m/s 3) a. a= v^2/r a= 25^2/ 10 a= 62.5 m/s^2
 * Physics To Go**

b. No 4) a. GPE= MGH mgh= mv^2  9.8(50)= v^2  490=v^2  v= 31 m/s b. a= v^2/r  a= 22.14 ^2/ 10  a= 96 m/s^2 c. v= sqrt(a*r)  v= sqrt(49.02*10)  v= 22.14 m/s e. No 5) a. mgh= mv^2 9.8(16)=v^2 v= 8.9 m/s b. GPE= KE mgh=1/2mv^2 9.8h= 1/2(12.52)^2 h= 20 m

6) a. a= v^2/r a= 12^2/18  a= 8 m/s^2 c. track on wheels 7) a. a= v^2/r a= 20^2/15 a= 26.67 m/s^2 b. F= mv^2/r F= 900(20)^2/15 F= 24,000 N 8) a. Mass doesn't affect centripetal acceleration but it does affect centripetal force. b. No, it is not mass dependent as long as friction is ignored. c. If more normal force is necessary than you will need a stronger material.


 * Physics Plus**

Knowing the ride can cause death or injury, can add to the thrill of the ride but can repel people to go on the roller coaster. If one-half of all roller-coasters rides ended in death it would still repel people from riding the ride because no one wants to die on a roller coaster. Obviously, there is always risks in riding a roller coaster, but if you had the knowledge that multiple or every rider died on the ride, no one would ride the ride and it would probably close down.
 * What do you think now?**