Chapter+4+6-10

Chapter 4 Section 6
toc **What do you Think?**


 * Does your weight change when you are riding on a roller coaster when you are riding on a roller-coaster?
 * Yes, there are different sections on a roller-coaster and there is a different affect by gravity in different areas.
 * If you were sitting on a bathroom scale, would the scale give different readings at different places on the roller-coaster?
 * Yes, due to the the different accelerations

** Physics Talk **
 * Newton's 1st law: an object at rest has no net force acting on it
 * Newton's 2nd law: 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
 * Apparent Weight- the weight you FEEL like you are.
 *  Air Resistance - "friction" of air. For example on a roller coaster

**Checking Up**  1. What is the sum of all forces acting on object if it is moving at constant speed? 2. What does a bathroom scale read if the roller coaster is going up? 3. When you accelerate upward why do you feel as if you weigh more? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">4. What does the scale read when you are falling from an elevator? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">5. What is the force that is slows a falling raindrop?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">The sum of all the forces acting on an object when it is moving up at constant speed is zero.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">greater then you actual weight
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">contact forces and stretching stomach tissues, apparent weight
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">The force reading on the scale would be zero and you'd feel weightless.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">Air resistance

<span style="font-family: Arial,Helvetica,sans-serif;">**Physics To Go**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">1. How fast will each object be going after it has fallen from rest after each length of time? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">2. On moon. How fast will each object fall after it has fallen from rest after each length of time? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">a. (1.6)(2) = 3.2 m/s <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> b. (1.6)(5) = 8 m/s <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> c. (1.6)(10) = 16 m/s <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 4. Complete graph
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">a. (9.8)(2) = 19.6 m/s
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">b. (9.8)(5) = 49 m/s
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">c. (9.8)(10) = 98 m/s


 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">**Motion of the Elevator** || <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">**Acceleration (up, down, zero)** ||  || <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">**Relative Scale Reading (greater, less or equal to weight)** ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">At rest, bottom floor || <span style="font-family: Arial,Helvetica,sans-serif;">zero ||  || <span style="font-family: Arial,Helvetica,sans-serif;">equal ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">Starting at Rest, Increasing Up || <span style="font-family: Arial,Helvetica,sans-serif;">up ||  || <span style="font-family: Arial,Helvetica,sans-serif;">greater ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">Continuing to move, Constant Up || <span style="font-family: Arial,Helvetica,sans-serif;">zero ||  || <span style="font-family: Arial,Helvetica,sans-serif;">equal ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">Slowing down to top floor, Decreasing Up || <span style="font-family: Arial,Helvetica,sans-serif;">down ||  || <span style="font-family: Arial,Helvetica,sans-serif;">less ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">At rest, top floor || <span style="font-family: Arial,Helvetica,sans-serif;">zero ||  || <span style="font-family: Arial,Helvetica,sans-serif;">equal ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">Starting at rest, Increasing Down || <span style="font-family: Arial,Helvetica,sans-serif;">down ||  || <span style="font-family: Arial,Helvetica,sans-serif;">less ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">Continuing to move, Constant Down || <span style="font-family: Arial,Helvetica,sans-serif;">zero ||  || <span style="font-family: Arial,Helvetica,sans-serif;">equal ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 19px; text-align: center;">Coming to a stop on the ground floor || <span style="font-family: Arial,Helvetica,sans-serif;">up ||  || <span style="font-family: Arial,Helvetica,sans-serif;">greater ||

<span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">5. Student weighs 140 lb, but scale reads 137 for a few moments, what happened? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">6. Person on elevator at rest weighs 600 N, he moves up 4 floors what happens? <span style="font-family: Arial,Helvetica,sans-serif;">7. Elevator on top floor descends at 1.5 m/s2 <span style="font-family: Arial,Helvetica,sans-serif;">8. A 50 kg student is on a scale in an elevator <span style="font-family: Arial,Helvetica,sans-serif;"> 9. Explain meanings of the three sketches below <span style="font-family: Arial,Helvetica,sans-serif;"> 10. Record which parts of the Terminator Express you would modify for your audience
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">Decreased upward acceleration or increased down acceleration
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">The person will observe that her weight increases. An increased upward acceleration increases the weight on the scale
 * <span style="font-family: Arial,Helvetica,sans-serif;">a. Will bathroom scale reading increase or decrease?
 * <span style="font-family: Arial,Helvetica,sans-serif;">decrease
 * <span style="font-family: Arial,Helvetica,sans-serif;">b. What will it read if person weighs 50 kg during acceleration
 * <span style="font-family: Arial,Helvetica,sans-serif;">W - Fscale = ma
 * <span style="font-family: Arial,Helvetica,sans-serif;">(50)(9.8) - Fscale = (50)(1.5)
 * <span style="font-family: Arial,Helvetica,sans-serif;">Fscale = 415 N
 * <span style="font-family: Arial,Helvetica,sans-serif;">a. What will the scale read when the elevator is at rest?
 * <span style="font-family: Arial,Helvetica,sans-serif;">The scale will read zero
 * <span style="font-family: Arial,Helvetica,sans-serif;"> b. What will the scale read when the elevator is rising 2 m/s^2?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Fnet = ma (acceleration is up, so the bigger force is Fscale)
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Fscale - weight = ma
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Fscale - (50)(9.8) = (50)(2)
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Fscale = 590 N
 * <span style="font-family: Arial,Helvetica,sans-serif;"> c. What will the scale read when the elevator travels up at a constant speed?
 * <span style="font-family: Arial,Helvetica,sans-serif;">It will read zero because acceleration = 0
 * <span style="font-family: Arial,Helvetica,sans-serif;">Drawing 1: Since the up and down forces are equal they are zero and the scale reads your accurate weight
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Drawing 2: Since you are in free fall, you are only pushing on the scale and that = gravity
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Drawing 3: Since there is more force pushing up, the scale will read a larger weight then what you are
 * <span style="font-family: Arial,Helvetica,sans-serif;">Since our groups roller-coaster is directed to younger kids, we would modify it to be safe for them. We would do this by making more supports so it's less wobbly. We would also trim the acceleration a little more so its fun, not terrifying.

<span style="font-family: Arial,Helvetica,sans-serif;">**What do you Think Now?**


 * <span style="font-family: Arial,Helvetica,sans-serif;">Does your weight change when you are riding on a roller coaster?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Yes, your apparent weight, meaning you get the sensation that your weight changes, but it really doesn't. This is because of the different and rapid changes in acceleration and velocity.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Would the scale give different readings on different parts of the roller-coaster?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Only when moving. For example, if I'm increasing Up my scale reading would get greater because my velocity and acceleration are going up

<span style="font-family: Arial,Helvetica,sans-serif;">Chapter 4 Section 7
<span style="font-family: Arial,Helvetica,sans-serif;"> **What do You Think?**


 * <span style="font-family: Arial,Helvetica,sans-serif;">Why don't you fall out of the roller-coaster cart when it goes upside down during a loop?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Because you are going so fast that you are able to stay on the seat. Also, you're wearing seat-belts and safety harnesses and they keep you on there

<span style="font-family: Arial,Helvetica,sans-serif;">**Physics Talk**


 * <span style="font-family: Arial,Helvetica,sans-serif;">Centripetal Force - the force that keeps an object moving in a circle at a constant speed
 * <span style="font-family: Arial,Helvetica,sans-serif;">always directed towards center
 * <span style="font-family: Arial,Helvetica,sans-serif;">Normal Force - Perpendicular force to object acting on it
 * <span style="font-family: Arial,Helvetica,sans-serif;">Roller Coaster Safety - Acceleration more then 9x gravity causes unconsciousness
 * <span style="font-family: Arial,Helvetica,sans-serif;">G's 1 g = 10 m/s^2; 7 g = 70 m/s ^2

<span style="font-family: Arial,Helvetica,sans-serif;">**Checking Up**

<span style="font-family: Arial,Helvetica,sans-serif;">1. What is required to make an object travel in a circle?<span style="font-size-adjust: none; font-size: 12px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 0px; min-height: 14px;">Checking Up <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">2. If you are traveling in a circle at constant speed, are you accelerating? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 3.At the top of a roller-coaster loop, what provides centripetal force <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 4.What force is responsible for your apparent weight on a roller-coaster <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 5. How does centripetal force acting on an object depend upon the objects mass, radius of the curve, and objects speed?
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Centripetal force
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Yes, Centripetal Acceleration
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">gravitational force and normal force
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Normal force
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Large when speed is increased
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Large when mass is increased
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Large when radius of circle is shorter


 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">Physics To Go **

<span style="font: 13px/19px Arial; margin: 0px 0px 0px 36px; text-indent: -36px;">
 * <span style="font: 12px/19px Helvetica; margin: 0px;">1. A path-operated toy car is attached to a string. **
 * a. If the loose end of the string is held to the ground, draw the path of the car while the battery is running.
 * the path would be a circle

<span style="font: 13px/19px Arial; margin: 0px 0px 0px 36px; text-indent: -36px;">
 * b. If the string were to break while the car was moving in a circle, draw the path the car would follow
 * the car would follow a line, tangent to the point from which the string broke off

2. Consider a real car on a road making a turn 6. A roller-coaster is traveling east at 20 m/s. After 2 s, it is traveling north at 20 m/s. 7. Roller-coaster is traveling east at 20 m/s in circular path. After 16s, it is traveling north at 20 m/s. The circular curve has a radius of 200m. Calculate the acceleration of the car and give its direction 10. Fill in the missing values
 * a. What force has replaced the string in the toy car from Q.1
 * Friction
 * b. If the car were to hit a section of ice, draw the path the car would follow
 * [[image:proringer:tancircle4.png]]
 * same as part B for Q.1 because the ice takes away friction and the car will move straight
 * a. Did the speed of the roller-coaster car change?
 * No, it remained 20 m/s.
 * b. Did the velocity change?
 * Yes, because of the change in direction
 * c. What was the change in velocity of the roller-coaster car? Give magnitude and direction
 * 28.2 m/s at 45 degrees NW
 * v2 - v1 = change in velocity
 * 20m/s North ; 20 m/s East
 * 20^2 + 20^2 = c ^ 2
 * c = 28.2 m/s
 * tan theta = 20/20
 * theta = 45
 * theta = 45
 * Ac = v^2 / r
 * Ac = (20)^2 / 200
 * Ac = 2 m/s^2


 * Fast Moving Roller Coaster **

<span style="font-family: Arial,Helvetica,sans-serif; font-size: small;">Slow-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 ||
 * || 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 ||

<span style="font-family: arial,helvetica,sans-serif;">13. Use diagram of Terminator Express. Indicate which points the rider will feel lighter, heavier, etc.
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">a. Bottom of hill #1- regular weight **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">b. Top of vertical loop- heavy **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">c. Bottom of vertical loop- heavy **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">d. Bottom of hill #2- uncertain **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">e. Lift hill (going up at constant speed)- regular weight **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">14. Indicate when centripetal force is up down sideways or zero. **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">a. Bottom of hill #1- zero **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">b. Top of vertical loop- down **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">c. Bottom of vertical loop- up **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">d. Bottom of hill #2- zero **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">e. Lift hill (going up at constant speed)- zero **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">f. Horizontal loop- sideways **
 * **<span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">g. Back curve- sideways **


 * Physics Plus**


 * 1a. The Fnet will increase **
 * 1b. If the velocity increases, the Fnet also increases due to the squared relationship. **
 * 2. If the speed is doubled, the force must be quadrupled **
 * 3. If the radius gets larger the Fnet will get smaller. That means it is indirectly proportional **
 * 4. If the radius of the circle is large, less force is needed to maintain the circular motion. When it gets tighter, a lot more force is required **
 * 5. The stopper would go in a path tangent to the point it was released from if it was released. **


 * What do you Think Now? **


 * Why don't you fall out of the roller-coaster car when it goes upside down during a loop?
 * Because the normal force is always pointing towards the center and there is centripetal force. Also the centripetal acceleration is very fast. The only way you would fall off is if the acceleration stops or the roller-coaster goes slowly

**Chapter 4 Section 8**

 * What do you Think**

Does it take more energy to pull the roller-coaster up a steep incline then a gentle incline? Why is it more difficult to walk up a steep incline than a gentle incline
 * Steep = more energy because it gets to a greater height faster
 * Because less force is required to climb up a gentle hill so its easier to do that then a steep incline

<span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">**Physics Talk**


 * <span style="font: 12px Arial,Helvetica,sans-serif; 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: 12px Arial,Helvetica,sans-serif; 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: 12px Arial,Helvetica,sans-serif; margin: 0px;"> P = work done / time elapsed
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> watts: the SI unit for power
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">1 W = 1 J/s

<span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> **Checking Up** <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1. Where has the energy gone when the cart is at rest at the top <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 2. Where does the roller - coaster get its GPE when it is at the top of the hill? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 3. Why do truckers use a ramp when loading a truck if the work required is the same with or without a ramp <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 4. When the breaks stop a roller-coaster, what happens to the coaster's kinetic energy? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 5. What is the unit for power?
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">It has become GPE
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">from work done by the spring (electricity or heat)
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">because it makes it easier because less force is required. With a presence of a ramp, you don't have to lift it fully vertical
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> the KE is converted into thermal energy
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">watts 1 W = 1 J/s

<span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> PTG <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1a. Compare the GPE of the cart at the top of the incline and at the bottom. <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1b. How much work was done on the cart by the force of gravity as the cart went from the top to the bottom? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1c. How much work was being done by the spring as it was being compressed? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1d. What is the springs SPE when it is compressed by the distance x? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1e. Describe the total energy of the cart just before it hits the spring <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 1f. At which point does the cart begin to slow down? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 2a. A waiter applies a force of 150 N to hold a tray filled with plates on his shoulder. He then moved 7m towards the kitchen door. What is the work done on the tray by the waiter? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 2b. A bowler lifts 60N bowling ball from the rack to his chest, a vertical distance of .5m. What is the work done of the bowling ball by the bowler <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 2c. A girl pulls her sled up a hill. The length of the hill is 40m and the pulling force required was 75N. What is the work done by the girl on the sled? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 2d. The weight of the dumbbell is 500N. It is lifted over a body builders head, a distance of .7 m. What is the work done on the dumbbell by the bodybuilder <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 3. Why are you told to conserve energy if the law tells you energy is conserved. Create a better way to say "conserve energy" <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 4. What would you have changed in the experiment? <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 5a. Calculate the work done by the motor <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 5b. Calculate the power of the monitor. <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> 6. Describe one trip on the coaster around the ramp in terms of work and energy
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">GPE at top is greater then bottom
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">As the cart went from the top to the bottom, all of the work is done is by gravity
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">All of the work is done by the spring
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> SPE = 1/2kx^2
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">GPE
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> when you first touch the spring.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">W = F x d
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;"> work is zero because the force and distance are perpendicular, or not in the same direction.
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">W = F x d
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 60 x .5
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 30 N
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">W = F x d
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 75 x 40
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 3000 N
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = F x d
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 500 x .7
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 350 N
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">Instead of saying conserve energy, you could say "prevent excessive energy use." Energy is conserved in terms that it is transferred to a different type rather then being destroyed.
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">If clay was added, the mass would increase, so the force would increase.
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">W = F x d
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 10,000 x 20
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> W = 200,000 N
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">P = work / t
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> P = 200000 / 150
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> P = 1333 1/3 J/s
 * <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;">On the way up the ramp the roller coaster is gaining GPE. The motor is performing work on the roller coaster cart. On the first incline Work turns into GPE. Down hill the GPE is turning into KE. Up the loop KE is turned into GPE.


 * <span style="font-family: Arial,Helvetica,sans-serif; font-size-adjust: none; font-size: 12px; font-stretch: normal; font-style: normal; font-variant: normal; line-height: normal; margin: 0px;"> What do you think now? **

Does it take more energy to pull the roller-coaster Why is it more difficult to walk up a steep incline then a gentle incline
 * <span style="font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">It takes more energy to pull the roller coaster up a steep incline than a gentle incline because the height is higher
 * <span style="font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">It is less difficult to walk up a gentle incline because more force is needed to get up a shorter distance

<span style="font-family: Arial,Helvetica,sans-serif;">Chapter 4 Section 9

 * <span style="font-family: Arial,Helvetica,sans-serif;">What do you Think? **
 * <span style="font-family: Arial,Helvetica,sans-serif;">Which parts of The Snake will be most thrilling?
 * <span style="font-family: Arial,Helvetica,sans-serif;">The drop in the hills, the loops, etc.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If the speed of The Snake always remains the same, why will it still be fun?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Because different shifts in velocity give you the illusion that you are going faster


 * Physics to Go**
 * energy - scalar
 * force - vector
 * vectors have direction in comparison with scalar quantities
 * scalar - regular arithmetic to add
 * vector - vector addition techniques that take direction into account
 * Same direction - add
 * Opp. direction - subtract
 * Right Angles - Pythagorean Theorum
 * Use energy when... changing accelerations and heights
 * Acceleration is the link between energy and forces
 * Forces cause work creates change in energy
 * Newtons second law is connected to L.C.E


 * Checking Up**

1. What process is needed to add vector quantities? 2. Is energy and force a vector or scalar? 3. For roller-coasters, what three things do energy considerations tell you about the coaster at different points? 4. Does the energy of the roller-coaster depend upon the path that the roller-coaster takes? 5. What is required to provide a change in the energy of a roller-coaster
 * Pythagorean theorum
 * Energy is a scalar quantity and force is a vector.
 * KE and GPE will always equal the same thing, gravity and mass are constant so the GPE is depended on its height, and if the roller coasters are at the same height, they will be going at the same speed too.
 * The path doesn't affect it
 * A force is required.

**Physics Talk**

1a. Determine the change in velocity of the roller coaster cart using the vector diagram 1b. Determine the change in velocity of the roller-coaster cart using the Pythagorean theorum 2. Explain why these roller-coasters provide the same change in speed when a cart goes from top to the bottom 3a.distance 3b. displacement 3c. speed 3d. velocity 3e. acceleration 3f. force 3g. kinetic energy 3h. potential energy 3i. work 4a. Mark traveled 30 km 4b. Maia's weight is 600N 4c. The roller-coaster car has a KE of 1200J 4d. The car was traveling 30 m/s towards center of town 5. Sometimes it is easier to look at a roller-coaster as an energy ride, while other times it is best to look at it as a force ride. Give an example of each approach. 6a. Draw the forces that are acting at points A, B, C, and D 6b. Draw the forces acting on roller coaster 2 6c. 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. 7a. Label all three points on roller coaster 3 that have the same GPE 7b. Compare the total energies of the roller coaster at these points 7c. Compare the KE of the roller coaster at these points 7d. Why are you able to ignore other points on the roller coaster when comparing the KE, GPE, and total energy
 * a^2+b^2=c^2
 * 3^2+5^2= C^2
 * c= 6 m/s south west
 * they have the same change in speed because they have the same GPE at the top and the same KE at the bottom
 * scalar
 * vector
 * scalar
 * vector
 * vector
 * vector
 * scalar
 * scalar
 * vector
 * scalar
 * vector
 * scalar
 * vector
 * Energy: The roller coaster has GPE and it gets converted to KE as it goes down the hill. When it is going back up, it uses work and it gets reconverted to GPE as it goes up
 * Force: As the cart goes farther up the hill, there is more weight holding the cart down and the normal force is decreasing as well.
 * A: Weight and Normal
 * B: Weight and Normal
 * C: Weight and Normal
 * D: Weight and Normal
 * Middle of first decline
 * Top of first hill
 * Top of second hill
 * The cart has the same amount of energy at each point because it has the same GPE.
 * The kinetic energy is equivalent because their GPE is also the same, which means they are going at the same speed.
 * Because at these points the height is the same. The mass and the gravity are always constant in the GPE formula, so the total GPE is controlled by the height. GPE and KE will always total up the same amount of energy so the GPE and the KE must be equal


 * What do you Think Now?**


 * Which parts of the snake will be most thrilling?
 * I think that when the roller coaster turns is the most thrilling because it provides a change in speed and changes in speed are exciting if the rest of the ride is level.
 * If the speed always remains the same, why will it still be fun
 * Because the turns add thrill and they provide changes in speed

Chapter 4 Section 10

 * What do you Think?**


 * Does the knowledge that people can get hurt of die change the thrill of a ride?
 * YES, It would make it a lot more scarier and I would potentially not go on it
 * Would your answer change in 1/2 of the rides ended in death?
 * OF COURSE! I would not even risk it. That's a 50% chance I'd die!


 * Physics Talk**


 * Acceleration - safe values - up to four g's
 * ac = v^2/r
 * How to fix if values greater then 4 g's
 * Radius increase
 * Lower Velocity
 * Reduce height at start
 * increase height of position


 * Checking Up**

1. What is the maximum safe acceleration for a roller coaster 2. List two ways to keep the acceleration of coaster cart low enough to be safe 3. At what part of the loop is the acceleration the greatest on the roller coaster cart 4. At what part of the loop is the normal force the greatest
 * 4 g's
 * You can decrease the height of the coaster which will decrease the GPE as well as the kinetic energy.
 * At the end of the loop
 * At the top of the loop


 * Physics to Go**

1. What factors will the company check to make sure the roller coaster is safe? 2a. Calculate the initial height of a roller-coaster 2b. Calculate the acceleration at the bottom of the loop 2c. Is this a safe acceleration? 2d. At what speed would this loop with a radius of 12 m begin to be a safety concern 2e. At what speed would this loop with a radius of 7 m begin to be a safety concern 3a. Calculate the acceleration of the cart at the bottom of the loop 3b. Is this a safe acceleration 4a. What speed is the roller-coaster at the bottom of the incline 4b. Is this a safe acceleration? 4c. What will be the speed at the top of the loop 4d. What will be acceleration at top of the loop if cart moving in a circle? 4e.Is it safe? 5a.What speed must the Roller coaster have at the top of the loop? 5b. How high must the first hill be to achieve this speed 6a. What is the centripetal acceleration 6b.What will the centripetal force of the cart be?
 * In order to make sure the roller coaster is safe, you want to make sure the acceleration does not exceed 4 g's. Doing so might cause unconsciousness
 * GPE = KE
 * mgh = .5mv^2
 * 9.8h =.5(20) ^2
 * 20m
 * a = v^2/r
 * a = 20^2/12
 * 33 m/s^2
 * 33/9.8 = 3.4 G's // The acceleration does not exceed 4 g's so it is safe
 * 9.8(4) = 39.2 m/s^2
 * 39.2 = v^2/12
 * v = 22 m/s
 * 39.2 = v^2/7
 * 17 m/s
 * ac = v^2/r
 * ac = 25^2/10
 * 63 m/s ^2
 * Roller coaster not safe because it exceeds 4 g's
 * GPE = KE
 * mgh = .5mv^2
 * 9.8(50) = .5v^2
 * 31 m/s
 * ac = v^2/r
 * ac = 31^2/10
 * 96 m/s ^2
 * ac = v^2/r
 * 96 = v^2/10
 * 24 m/s
 * ac = v^2/r
 * ac = 24^2/10
 * 58 m/s ^2
 * Yes, it is safe because it doesn't exceed 4 g's
 * ac = v^2/r
 * 9.8 = v^2/r
 * ac = 8.9 m/s
 * GPE = KE
 * mgh = .5mv^2
 * 9.8h = .5(12.52)^2
 * h = 20 m
 * a= v^2/r
 * a= 12^2/18
 * a= 8 m/s^2
 * F=mv^2/r
 * F= 900(12)^2 / 18
 * F= 7,200 N

6c.What will provide the centripetal force? 7a.What will the centripetal acceleration of the car be? 7b. What is the centripetal force? 8 a. Will the centripetal acceleration change as a result to a change in mass 8b. Will the roller coast change speed at the bottom of the loop with extra passengers 8c. Will the roller-coaster track require a strong material because of the increased number of riders?
 * The normal force on the track and the weight will provide the centripetal force.
 * a= v^2/r
 * a= 20^2/15
 * a= 26.67 m/s^2
 * F= mv^2/r
 * F= 900(20)^2/15
 * F= 24,000 N
 * no change because the mass doesn't affect the centripetal acceleration.
 * same because the mass doesn't affect it.
 * It could need a stronger material to hold more people.


 * Physics Plus**

1. 2.
 * a.
 * GPE = KE
 * mgh = .5mv^2
 * 9.8h = 1/2(30)^2
 * h = 45.9m
 * b. Find acceleration of loop
 * ac = v^2/r
 * = (30)^2/9
 * = 100 m/s^2
 * c. Is it safe?
 * 100/9.8 = 10g
 * Not Safe because 10g > 4g
 * d. When does it start being dangerous
 * 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. At what speed would a loop with a smaller radius of 7m begin to be a safety concern?
 * ac = v^2/r
 * 39.2 = v^2/7
 * 274.4 = v^2
 * 16.6 m/s = v
 * f. How fast would it be traveling at the top of the loop?
 * GPE = GPE + KE
 * mgh1 = mgh3 + .5mv^2
 * (9.8)(45.9) = (9.8)(18) + .5(v)^2
 * v = 23.4 m/s
 * g. Calculate the acceleration of the loop
 * ac = v^2/r
 * =23.4^2/9
 * = 60.8 m/s ^2
 * h. Is it safe?
 * 60.8/9.8 = 6 g's (NOT SAFE)
 * i. Describe if the results you found in b-g fit these safety limits
 * N + w = ma (if you fall, N = 0)
 * mg = ma
 * a = g
 * 9.8 = v^2/9
 * v = > 9.4m/s
 * N-w = ma
 * N = 9800N
 * N-w = ma
 * N = ma + w
 * N+w = ma
 * N = ma - w
 * N = ma - w


 * What do you Think Now?**


 * Does the knowledge that people can get hurt of die change the thrill of a ride?
 * YES, It would make it a lot more scarier and I would potentially not go on it
 * Would your answer change in 1/2 of the rides ended in death?
 * OF COURSE! I would not even risk it. That's a 50% chance I'd die! There could be many things that would be unstable in the ride that could result in my death. For example, if the top of the loop is less then 1 g, I could fall, or if the roller coaster exceeds 4 g's I can be unconscious