Chapter+4

=toc=
 * CHAPTER 4**

Section 1

 * What do you see/think?**

In this picture I see a man on a chair and a women pushing him. The women is pushing him in all different directions in order to resemble a roller coaster. The part of a roller coaster that produces the most screams from the passengers is when the roller coaster reaches its peak height then drops. This is because it produces the greatest amount of acceleration and has a very high GPE and converts to a very high KE. The more energy and acceleration involved in the roller coaster creates the scariest moments.


 * Articles**
 * http://www.sixflags.com/greatadventure/rides/kingdaka.aspx **
 * This roller coaster, Kingda Ka, is most known for its high speed and huge drop. The most important features of this roller coaster is that it accelerates from 0 to 128 mph in 3.5 seconds. **

- Distance is a scalar quanity - Displacement is a measured distance with a direction included - Vector is a quantity that has both magnitude and direction - Speed is the distance traveled divided by the time elapsed - Velocity is the displacement divided by time elapsed - Acceleration is change in velocity divided by time elapsed
 * Physics Talk**

1. Distance is the total amount of distance traveled, while displacement is distance in a certain direction. 2. The displacement is 0 meters you ended where you started. 3. Speed used distance, while velocity used displacement. 4. The acceleration of an object is found by finding the change in velocity divided by the time elapsed.
 * Checking Up**

The part of the roller coaster that creates the most screams is when the roller coaster has a high acceleration. Using the data recorded in the investigate, whenever there was a sudden increase in speed with a turn, the rider had the biggest "thrill". So, the way to produce thrills in a roller coaster is by creating a high acceleration.
 * What do you think Now?**

1. 2. The biggest thrill of terminator express would be hilltop #1 because it has the highest speed at the bottom of the ramp. 3a. La Paz has a greater speed because they travel a greater distance in the same amount of time. b. 40000 km/24 h>1666.67 km/h c. You don't get a thrill because the speed is constant with no acceleration. 4. a=vf-vi/t--->a=16-4/3--->a=4 m/s^2 5a. Speed b. Velocity c. Acceleration d. Displacement and velocity e. Displacement 6.v=d/t--->v=.1/2--->v=0.5 m/s 7. v=d/t--->0.5=0.5/t--->t=1 s 8. a=delta V/delta t--->a=25/10--->a=2.5 m/s^2 10a. Two changes I would make for the Terminator Express are to lower all hilltops, the other change I would make is making more horizontal curves. b.
 * PTG**

Section 2
In this picture I see a roller coaster where one group is on a straight track and they appear really bored. The other group is going down an incline and they appear to be having lots of fun. The steel roller coaster at an angle of 90 degrees will have a bigger thrill because it will have a greater acceleration.
 * What do you see/think?**

- The height a roller coaster starts at increases or decreases the speed, not the length of the track - GPE and KE are used to measure the energy of a ball going down an ramp - As the height lowers, GPE lowers and KE increases - KE is irrelevant to direction - Energy is measured in Joules - Mechanical Energy is the sum of GPE and KE - At the midpoint of an incline, the KE and GPE are equal - Mechanical energy remains the same throughout every stage of the incline - KE=GPE--->v^2=2gh
 * Physics Talk**

1. The length of the incline has no effect on the speed of the ball at the bottom. 2. The GPE decreases with a smaller height and mass. 3. The greater the mass and the greater the speed, the greater amount of energy. 4. The GPE decreases and is converted to KE. 5. The roller coaster will have 3000 Joules of KE.
 * Checking Up**

1. The speed of the carts will be the same at the bottom because they both start at the same height. Height is the direct variable that affects speed. 2. The law of conservation of energy applies to roller coasters because through each stage of drop, the roller coaster has the same total energy. At the top of a hill, the roller coaster has a very high GPE due to its max height and gravity. Then, as the roller coaster goes down the hill the GPE decreases as KE increases due to the increase of velocity. 3. 4. 8. The speed of the roller coaster will not change with a higher mass. This is because GPE=KE, in this scenario the mass from mgh=1/2mv^2 cancels. This leaves the mass completely irrelevant to the speed. 9a. The roller coaster is traveling at its highest speed at point B. This is because the max height at point A creates a high velocity at the bottom of the ramp. b. The roller coaster is traveling at the same speed at points C and E. This is because they both are at the top of a hill without a drop yet, thus leaving them at rest. c. The roller coaster is traveling faster at point D because the roller coaster went down a ramp and not up, thus creating a higher velocity.
 * PTG**
 * Position of cars height (m) || GPE(J)=mgh || KE(J)=1/2mv^2 || KE+GPE(J) ||
 * Top(30m) || 60000 || 60000 || 60000 ||
 * Bottom(0m) || 0 || 60000 || 60000 ||
 * Halfway(15m) || 30000 || 30000 || 60000 ||
 * ThreeQuatersOfWayDown(7.5m) || 15000 || 45000 || 60000 ||

A roller coaster with a very high max height will have the biggest thrill. This is due to the reason the roller coaster will have a very high GPE which will result in a very high KE at the bottom of the hill. Thus leaving the roller coaster with a very high speed at the bottom of both tracks. The speed will be the same on a curve or a straight track because KE is irrelevant to dircetion.
 * What do you think now?**

Section 3
In this picture, I see a few students at a desk with a pop-up frog toy. One of the is holding a photogate timer and the other is holding a meter stick to measure how high it reaches. The person in the background is writing GPE, KE, and SPE on the board. A roller coaster reaches its highest point by going uphill by using mechanical tracks that raise it up and the more people on the cart does not cost more lift.
 * What do you see/think?**

- This story relates to energy in the sense that even though the coins are different, it still equals $6. Just like the law of conservation of energy - Spring Potential Energy: The energy stored in a spring due to its compression or stretch - The sum of energy in a roller coaster always must remain the same - In some cases such a bouncing ball, energy is lost but is only converted to heat or sound energy - Thus energy is never lost - A larger mass pop-up toy does not reach as high as a lighter one - Larger mass=smaller height. Smaller mass=higher height - When the roller coaster breaks, the KE converts to thermal energy - SPE=1/2kx^2
 * Physics Talk**

1. The SPE converts to a high KE and a low GPE. 2. The pop-up toy's KE will be 2 J due to the law of conservation of energy. 3. The pop-ups toy GPE at max height will be 2 J as well. 4. The spring constant and the distance compressed determine the SPE.
 * Checking Up**

5. The second hill cannot be as high as the first hill because the roller coaster will lose energy and not be able to obtain that height. There is not enough GPE available to reach that height. 6. A roller coaster does not go on forever due to friction stopping the roller coaster. This friction is work, and this work takes away energy from GPE and KE. 7. GPE=mgh GPE=(300)(9.8)(15) GPE=44,100 J--->It requires 44,100 Joules of electrical energy to raise the roller coaster. 8a. KE=1/2mv^2 KE=(1/2)(400)(15)^2 KE= 45000 J
 * PTG**

b. The GPE would be 45000 J when KE is equal to zero.

c. GPE=mgh 45000=(400)(9.8)h h=11.58 m.

9. While the ball is traveling up in the air, the GPE of the ball is increasing. 10. The GPE is the same along each path because they all reach the same max height at the end of the path. 11a. GPE and KE both have the same values because they are equal. The law of conservation of energy supports this claim.

GPE=mgh GPE=(.02)(9.8)(.4) GPE=0.0784 J

KE=1/2mv^2 KE=(1/2)(.02)(2.7)^2 KE=0.0729 J

b. GPE=mgh GPE=(.02)(9.8)(.4) GPE=0.0784 J>SPE=0.0784 J

c. GPE=mgh 0.0784=(.06)(9.8)h h=0.13 m.

12a. GPE=mgh GPE=(300)(9.8)(18) GPE=52920 J

SPE=1/2kx^2 52920=(1/2)(4)^2k k=6615 N/m

b. GPE=mgh GPE=(400)(9.8)(18) GPE=70560 J

SPE=1/2kx^2 70560=(1/2)(6615)x^2 x=4.62 m

13. SPE=1/2kx^2 SPE=(1/2)(40)(.3)^2 SPE=1.8 J

KE=SPE KE=1.8 J

A roller coaster gets to its highest point by electric cables that pull it. As the roller coaster rises, the GPE increases as well. When more people are added to this roller coaster, it costs more energy to actually lift the roller coaster to its highest point. In the investigate, we learned that with the increase of mass, the max height decreases. In order to obtain the max height, the electric cables must be able to pull any given mass up to the top. The law of Conservation of Energy helps explain this because the energy required to reach the max height will also be the GPE at the top of the hill.
 * What do you think now?**

Section 4
In this picture I see a roller coaster on the moon and a roller coaster on jupiter. The roller coaster on the moon shows the passengers very sleepy while on jupiter the passengers seem to be thrilled. I think that gravity does have a direction, where everything points down towards the pull. People in Australia are able to be held by gravity because they are being pulled in by Earth's gravity.
 * What do you see/think?**

- Gravitational Field: The gravitational influence in the space around a massive object - Direction of the gravitational field is the direction of the force on a mass. - The gravitational field is stronger when closer to the mass - Gravitational fields are always present - Inverse-Square Relationship: Relationship between the magnitude of a gravitational force and the distance from the mass. - Tripling the distance decreases the force by 1/9 - Gravity: The force of attraction between two bodies due to their masses - 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 each mass gets larger; the force decreases as the square of the distances between the two bodies increase
 * Physics Talk**

1. The direction of the gravitational field is towards the classroom. 2. The gravitational field is the strongest when its closest to the center of a mass. 3. The force of gravity is now 1/9 when the distance is tripled. 4. The force that holds the moon in its orbit is Earth's gravitational field and the other planets gravitational fields. 5. The shape of the orbit is an ellipse.
 * Checking Up**


 * Physics Plus**

2. v=d/t--->v= (2*pi*3.84*10^8))/2440800--->v=998.505 m/s 3. a=v^2/r--->a=998.505^2/3.84*10^8--->a=.0025m/s^2

1. If the distance was doubled the force would be 125 N because it would be 1/4 of 500 N. 2a. The Fg is 1/4 of the original b. 1/9 the original c. 1/16 the original 3. Everyone trusts gravity because it is a constance force that holds all objects down on Earth, it never fails and people are just floating in the air. 4. The acceleration due to gravity at the top of a roller coaster is less than the bottom, but not enough to notice. 5a. The water on the side of the Earth is closer to the moon. b. High tide is when the moon is on a certain side of the earth, and the moon's gravity is pulling the water towards it. c. The water levels are uneven because the moon does not orbit around the top and only pulls towards the sides. 6a. If there was no gravity, a fish would simply float out of the water and up in the air. The fish could not survive without gravity. b. Gravity holds the water down on earth's surface, which enables the fish to be able to swim freely without any problems. 7a. Force is 1/4 the original b. Force is 1/9 the original c. Force is 1/16 the original d. Force is doubled. 8a. Force is doubled. b. Force is tripled. c. Force is quadrupled. d. Force is halved. 9a. Quadrupled b. 9 times as great c. 16 times as great d. 1/4 the original force 10a. Doubled b. 9 times as great c. 6 times as great
 * PTG**


 * What do you think now?**

Gravity does in fact have a direction, it pulls everything down towards the center of the mass. The force of gravity is constantly acting on us at all times which pulls us down towards the center of the earth keeping us from floating in the air. People that live "upside down" in Australia are able to be held by earth's gravity because they are constantly being pulled towards the center of the earth.

Section 5
In this picture I see two pictures of a man weighing meat in a store. Each picture shows the man weighing meat on a different scale. A bathroom scale works by taking the mass of the person and multiplying the mass by acceleration due to gravity to find the weight. You cannot use the same scale for a canary and an elephant because their masses are so far apart.
 * What do you see/think?**

- It requires force to stretch a spring - There is a linear relationship in stretching a spring due to the spring constant - The stretch of a spring is directly proportional to the force applied to it - Hooke's Law: The restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring - Force of Spring=Spring Constant x Stretch Distance - Fs=-kx - The negative sign indicates that the pull by the spring is opposite to the direction it is stretched or compressed - The spring constant (k) indicates how easy or difficult it is to stretch or compress the spring - The slope of a graph for the spring is equal to the spring constant - Weight= mass of object x gravity - w=mg - Weight: The force exerted on a mass as a result of gravity; the weight force of an object due to Earth is downward, in the vertical direction - A scale works by compressing a spring that provides an equal force back to the object on the scale
 * Physics Talk**

1. If the force of the spring is increases 5 times, the stretching distance also increases 5 times. 2. A spring constant says how easy or difficult it is to stretch or compress a spring. 3. The weight of an object is equal to the mass in kilograms times acceleration due to gravity 4. The force of compression on the spring exerts the same amount of force back on the object.
 * Checking Up**

1a. w=mg w=(100)(9.8) w=980 N
 * PTG**

b. w=mg w=(10)(9.8) w=98 N

c.w=mg w=(60)(9.8) w=588 N

2a. 130(4)=520 N b. 1000(4)=4000 N c. 50(4)=200 N

3a. b. See graph c. The slope of the graph is 0.1491 d. The slope of the graph is the spring constant e. The slope for this graph is smaller than the previous one, meaning that this spring is actually easier to stretch than the original spring.

4. Fs=-kx 12=3k k=4 N/m

5. As the force, so the stretch means as the force increases, so the stretch increases and vice vera. This is because they are both directly proportional to each other. 6. The spring that has a spring constant of 15 N/m would be harder to stretch because it is a greater spring constant.

7. k=weight/stretch distance k=3/2 k=1.5 N/m

8. A spring scales works when a mass is on the scale. The mass exerts a certain force onto the spring scale, which compresses the spring. The spring compresses a certain distance and applies the same force back onto the object. Fs=-kx so the strecting distance gets multiplied by the spring constant to get the force.

After learning about how spring scales work, I can now say that it is impossible to use the same spring scale for a canary and an elephant. This is because the spring used for an elephant would be much harder to stretch because the spring constant is so much greater. If an elephant were to use the same scale as a sanary, the elephant would most likely break the spring. A bathroom scale work when a mass is on the scale. The mass exerts a certain force onto the spring scale, which compresses the spring. The spring compresses a certain distance and applies the same force back onto the object. Fs=-kx so the strecting distance gets multiplied by the spring constant to get the force. As the force is applied to the scale, the arrow on the scale points in a certain direction to give a weight.
 * What do you think Now?**

Section 6
In this picture, I see two elevators. One elevator has a rather large man going down and the other has a little kid going up. Your weight does not change during a roller coaster ride, the only difference is the acceleration which creates a different force. If you were sitting on a bathroom scale while on a roller coaster, the scale would give different readings only because of the acceleration.
 * What do you see/think?**

- The feeling in your stomach when on a roller coaster is actually important to physics - When an object is at rest, the sum of the forces is zero - Newtons First Law: An object at rest, stays at rest, an object in motion stays in motion unless acted upon by an unbalanced force - Newtons Second Law; a=F/m - When traveling up, the force is up - An object at constant speed has no acceleration and a net force of zero - When accelerating up, there is an increase in weight. Force is up - When accelerating down, there is a decrease in weight. Force is down - F=ma - A spring scaled bounces up and down until it exerts the same force back on the object - Nscale-weight=ma - Air resistance is the opposite force to gravity
 * Physics Talk**

1. The sum of all forces is zero 2. The apparent weight on on the scale is greater. 3. You feel you weigh more because force is up 4. The bathroom scale reads zero because you are falling with the scale 5. Air resistance slows a raindrop
 * Checking Up**

1a. vf=vi+at vf=0+(9.8)(2) vf= 19.6 m/s
 * PTG**

b. vf=vi+at vf=0+(9.8)(5) vf= 49 m/s

c. vf=vi+at vf=0+(9.8)(10) vf=98 m/s

2a. vf=vi+at vf=0+(1.6)(2) vf=3.2 m/s

b. vf=vi+at vf=0+(1.6)(5) vf=7.5 m/s

c.vf=vi+at vf=0+(1.6)(10) vf=16 m/s

4. 5. A student normally weighing 140 lbs in an elevator is on a scale that reads 137 lbs. This means that the elevator would be increasing speed down. This would cause the student's apparent weight to drop because force and acceleration are both down. 6. The reading on the scale would be greater because net force, acceleration and velocity are all pointing up. This means the apparent weight will be greater. 7a. The bathroom scale's reading will decrease because net force and acceleration are both down. b. ∑f=ma N-w=ma N=ma+mg N= 50(-1.5)+50(9.8) N=415 N 8a. The scale would read the normal weight of the person because there is no acceleration taking place. w=mg w=(50)(9.8) w=490 N
 * **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 ||

b. ∑f=ma N-w=ma N=ma+mg N=(50)(2)+(50)(9.8) N=100+490 N=590 N

c. The scale reading would remain at 490 N because there is no acceleration and the net force is 0. 9a. The bathroom scale reads the same as the weight of the person because there is a net force of 0. Meaning weight stays the same. b. The bathroom scale reads 0 because the person is not on the scale. The elevator and person are both in free fall, which means there is no force to keep him down or to go against gravity. Thus showing a weight of 0. c. In this picture, the reading of the scale is greater than the normal weight. This is because the elevator is accelerating up, which means force is up and pushing up on the person. 10. Our group's roller coaster is only for beginner riders or young kids. Our track does not have a huge hill with a high acceleration to give the riders too much of a thrill for their first time. The first hill would be our steepest, but not too steep. This leads right to a small vertical loop with a medium velocity. It then goes around the back curve, then to a small second hill straight to a horizontal loop and finish. Overall our roller coaster has thrill, but not too much of a thrill. In order to get a scream or high thrill, you would need a high amount of acceleration. This means steep hills, or turns and loops. A high acceleration with a change in direction leads to a high thrill. A dangerous thrill would be too much acceleration or a free fall.

When riding a roller coaster, your apparent weight changes due to acceleration and force, but not your actual weight. If you were to sit on a bathroom scale during a roller coaster, the scale would give different readings. At the top of a hill the scale would read your actual weight, but when accelerating down, force is down making the scale read a smaller weight. When accelerating up a hill, force is up which reads a higher weight. Overall, your actual weight does not change on a roller coaster.
 * What do you think now?**

Section 7
**What do you see/think?** In this picture I see I see a roller coaster going along the track on a curve and the cart appears to be tipping over. A roller coaster cart does not fall off the track when upside down or going along a loop because the high velocity enables the cart to get through it safely.

**Physics Talk** - Centripetal Force: the force that points to the center of the circle - Can be normal, friction, tension, or weight - Centripetal force always points toward the center of the circle - Tangental Velocity: Usually constant velocity - There is always centripetal acceleration because the cart is always changing dircetion - Fc=mv^2/r - ac=v^2/r - Increasing radius decreases centripetal force - Increase in mass increases centripetal acceleration - Increase in velocity increases velocity - The bigger force always points toward the center of the circle - Clothoid loops have different radii than a circle

**Checking Up** 1. A centripetal force is required to make an object travel in a circle. 2. Yes there is acceleration because you are changing direction. 3. Normal and weight both provide the centripetal force. 4. Normal is responsible for your apparent weight on a roller coaster. 5. Mass has a direct relationship, radius has an inverse relationship, and speed has a direct squared relationship.

**PTG** 1a. b. 2a. Friction replaces the string of the toy car. b. 6a. The speed of the roller coaster not change, however the velocity does because of the change of direction. b. Yes, the velocity changed because it is now going north. c. 20^2 + 20^2 = c^2 c=28.2 m/s tan-1 = 20/20---> 45 degrees--->28.2m/s @45 degrees 7. Ac=v^2/r Ac=20^2/200 Ac= 2 m/s^2 10a.


 * || Required Centripetal Force (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 4000 N || 500 N || 3500 N ||
 * bottom of the loop || 6000 N || 500 N || 6500 N ||

13a. heavier  b. uncertain  c. heavier  d. heavier  e. normal  14a. up  b. down  c. up  d. up  e. zero  f. Sideways toward the center of the circle  g. Sideways toward the center of the circle
 * b. ||  || Required Centripetal Force (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 800 N || 500 N || 300 N ||
 * bottom of the loop || 2800 N || 500 N || 3300 N ||
 * bottom of the loop || 2800 N || 500 N || 3300 N ||

1a. As the mass increases, so does the net force. The equation for net force shows that it has a direct relationship to mass. b. As velocity increases, so does net force. This is because they have a direct squared relationship. 2. The doubling of the velocity would mean that the force of the track must be 4 times stronger because they have a direct square relationship. 3. The net force decreases as radius increases, this is because they have an inverse relationship. 4. The larger the radius for the curve, the __less__ the force required to keep the car moving along the curve. If the curve is tight (r is very small) then a __greater__ force is required. 5. The longer the string meant the less force required. 6a. Ac=v^2/r Ac=12^2/20 =7.2 m/s^2
 * Physics Plus**

b. Fc=mv^2/r Fc= (300)(12^2)/20 Fc=2160 N

**What do you think now?** You do not fall off the track while at the top of a clothoid loop because of centripetal force. The centripetal force points towards the center of the circle, so when in motion the direction of the force keeps changing. Since there is a velocity, this allows the cart to keep moving in a full circle safely. Also, the force of track pushes on the cart to keep the cart on the track.

Section 8
In this picture I see a roller coaster with a high hill. In the picture, it shows a cart being pulled up the hill where the people are struggling to pull it. Then there is a cart going down the hill where a person is barely hanging on to it. I think that it takes more energy to pull a cart up a steep incline than a gentle incline because it is harder to go up something steep. Its harder to walk up a steep incline because it takes more energy.
 * What do you see/think?**

- Work: The product of displacement and the force in the direction of the displacement; the energy transfered to an object - W=Fd - Getting to the top of the first hill is done by a spring pulling the cart up - Calculating how much work is done by this is equal to the GPE - Force is in the same direction of displacement - It requires a force and work to pull the cart up the incline - As the cart travels up the incline, the GPE increases - A roller coaster gains its energy through electrical energy which is transfered to GPE - A roller coaster breaks by friction, which lowers the KE and transfers to thermal energy - Power: The work done divided by the time elapsed; the speed at which work is done and energy is transfered - P=W/t
 * Physics Talk**

1. The energy becomes all GPE at the top of the roller coaster. 2. The roller coaster gets its GPE from the Work to get up to the hill. 3. It requires less force when using the incline. 4. The kinetic energy is transfered to thermal energy. 5. The unit for Power is Watts (W)
 * Checking Up**

1a. GPE is greater at the top of the incline than the bottom b. The work is equal to the GPE c. The energy the spring had is equal to the GPE d. EPE=1/2kx^2 e. The total energy is mostly GPE with a little KE, this is because the cart is moving slowly f. The cart decreases speed when it hits the spring 2a.No work is involved b. W=Fd W=(60)(.5) W=30 J
 * PTG**

c.W=Fd W=(75)(40) W=3000 J

d. W=Fd W=(500)(.7) W=350 J

3. A better way of telling someone to conserve their energy is to not use an unnecessary amount of energy when trying to do something. 4. By adding clay figures, the mass of the cart would increase. By increasing this mass, it would also increase the GPE because GPE=mgh. Also, since GPE is equal to W, the W would increase as well. 5a.W=Fd W=(10000)(20) W=200000

b.P=W/t P=200000/150 P=1333.3 W

6. Work is done in order to bring the cart to its first hill. This work changes to GPE. As the cart goes down the hill, KE increases as GPE decreases. At the bottom of the first hill, the cart has almost all KE. When going up the vertical loop, the cart has both GPE and KE, then at the bottom of the loop it is mostly KE again. When you reach the back curve, the cart will have both KE and GPE again. Next is the horizontal loop where the cart has KE. When the cart comes to a stop work is done again. The cart is stopped by friction.

It takes more energy to pull a roller coaster up a steep incline than a gentle one because it requires more Work due to a greater force and distance. In the investigate, it required a greater force when pulling the cart up a steep incline than a gentler one. This also supports that it is harder to walk up a steeper incline than a gentler one because it requires a greater force, thus more energy to get up (work).
 * What do you think now?**

Section 9
In this picture I see two students with one student thinking about force and the other thinking about energy. They are both also picturing a roller coaster. The one thinking about energy has a bunch of work done on her paper, where as the one thinking about force has no work done on his paper. The part of the snake roller coaster that would be most thrilling is when the cart turns left and right. This is because there is an acceleration present. The snake roller coaster would still be fun even though it remains the same speed because it changes direction, which is acceleration.
 * What do you see/think?**

- Force always has direction - Force is a vector because it has direction - Energy is scalar because it is a quantity and has no direction - Scalar quantities are added simply - Speed is a scalar quantity - Displacement is a vector - In order to add vectors you must draw them and find the magnitude - All energies can be calculated because it is scalar - KE will always remain the same at a certain height no matter what part of the roller coaster - The same KE means the same speed - Total mechanical energy is the same at any point - GPE only depends on height - If two points on the roller coaster have the same height, then they have the same speed - No matter how steep the incline, it still has the same speed at the bottom - Accelerations that use magnitude and direction cause a bigger thrill - Acceleration is a vector - Energy and Force are both related because a certain force creates a certain energy - Normal force is always perpendicular to the track
 * Physics Talk**

1. The Pythagorean Theorem is used for vectors 2. Energy is scalar while force is a vector 3. Total mechanical energy is the same at any point, GPE only depends on height, if two points on the roller coaster have the same height, then they have the same speed 4. It does not matter because the roller coaster will always have the same total mechanical energy 5. To change energy, there must be a force because work equals force over a certain distance
 * Checking Up**

1a. a^2+b^2=c^2 (5)^2+(5)^2=c^2 c=7.07 m/s tan-1(5/5)=45 degrees b.7.07m/s @45 degrees SW 2. They provide the same speed at the bottom because they both have the same height at the bottom, the only difference is that it will take the steeper decline less time to reach the bottom. 3a. Scalar b. Vector c. Scalar d. Vector e. Vector f. Vector g. Scalar h. Scalar i. Scalar 4a. Scalar b. Vector because weight has a direction c. Scalar d. Vector 5.It is easier to look at a roller coaster as an energy ride when trying to find speed. It is easier as a force ride when trying to find acceleration. 6ab. c.It is easier to look at roller coaster two as a force ride because at each point of the track, force is equal. 7a. b. At each of these three points, the total energy is equal c. At each of these three points, the KE is equal because it has the same height d. You can ignore all of the other points because no matter what point you choose, KE+GPE are always going to equal the same amount
 * PTG**

The parts of the snake that will create the biggest thrill is when there is an acceleration involved. An acceleration is involved when the track turns left and right. Acceleration is a vector that causes a thrill during the ride. For this case the track has magnitude and direction causing the greatest thrill. Even if the track remained the same speed throughout the roller coaster, it would still be fun because of the changes in direction.
 * What do you think now?**

Section 10
In this picture I see a roller coaster with many problems. There is even a gap between the tracks, also carts and people are even falling off the track. It also shows carts that have parachutes attached to them as they fall off. The knowledge can people can get hurt or die on the roller coaster does cause thrill, but not a good thrill. If one half of the riders on a roller coaster died, the answer would remain the same.
 * What do you see/think?**

- An acceleration greater than 4 G's is unsafe - A free fall is 1 G - When moving in a circle or vertical loop, acceleration is measured by squaring the velocity then dividing it by the radius - a=v^2/r - Decreasing the height of the hill will decrease GPE, thus decreasing KE, overall decreasing velocity in making a safer roller coaster - This can also be done by increasing the radius of the loop - In order to find how many G's, you divided the acceleration by 9.8 - The larger the centripetal acceleration, the larger the centripetal force - The force required to keep a cart on track is the combination of normal force and weight - When a cart is moving in a vertical loop, a centripetal force is required - Centripetal Force= Normal Force + Gravitational Force - F=mv^2/r - The speed at the top of the loop must be great enough to get around the loop
 * Physics Talk**

1. The max safe acceleration is 4 G's 2. Decreasing the initial height, which would decrease velocity or increasing the radius of the loop 3. Acceleration is greatest at the bottom of the loop 4. The normal force is the greatest at the bottom of the loop
 * Checking Up**

1. In order to make sure the roller coaster is safe, you would want to make calculations to ensure the acceleration does not exceed 4 G's. Also, you would want to make sure the cart gets enough velocity to make it all the way through the loop. 2a. GPE=KE mgh=1/2mv^2 (9.8)(h)=1/2(20)^2 h=20 m
 * PTG**

b. a=v^2/r a=20^2/12 a=33 m/s^2

c. 33/9.8=3.4 G's. The acceleration does not exceed the max of 4 G's so the roller coaster is safe.

d. 9.8(4)=39.2 m/s^2 39.2=v^2/12 v=22 m/s A speed of 22 m/s would create safety concerns for the roller coaster.

e. 39.2=v^2/7 v=17 m/s A speed of 17 m/s would cause a safety concern

3a. a c=v^2/r ac=25^2/10 ac=63 m/s^2

b.63/9=7 G's. This roller coaster is not safe because it exceeds 4 G's.

4a. GPE=KE mgh=1/2mv^2 (9.8)(50)=1/2v^2 v=31 m/s

b. ac=v^2/r ac=31^2/10 ac=96 m/s^2

c. ac=v^2/r 96=v^2/10 v=24 m/s

d. ac=v^2/r ac=24^2/10 ac=58 m/s^2

e.Yes, the roller coaster is safe because it does not exceed 4 G's at the top or bottom of the loop.

5a. ac=v^2/r 9.8=v^2/8 v=8.9 m/s

b.GPE=KE mgh=1/2mv^2 9.8h=1/2(8.9^2) h=20 m

6a. ac=v^2/r ac=12^2/18 ac=8 m/s^2

b. Fc=mv^2/r Fc=(900)(12)^2/18 Fc=7200 N

c. The centripetal force provided is the friction from the wheels on the tracks.

7a. ac=v^2/r ac=20^2/15 ac=26.7 m/s^2

b. Fc=mv^2/r Fc=(900)(20)^2/15 Fc=24000 N

c. Yes this track is safe because it does not exceed the max centripetal force of 25000 N.


 * Physics Plus**

If it was possible to die or get hurt on a roller coaster, it would increase the thrill of the roller coaster but in a very negative way. Riders would not want to go on a roller coaster where one half of the passengers die. In order to ensure the safety of the passengers while also maintaining a thrill, a few precautions must be taken into account. For instance, the acceleration must not exceed 4 G's. Especially at the bottom of a loop. This can be done by decreasing the height of the incline which would decrease speed or simply increasing the radius. This is because a=v^2/r. Therefore, the death of passengers creates a greater thrill but extremely negative.
 * What do you think now?**