Chapter+4

Section 1
toc 2/28/11 A girl is pushing a blindfolded boy in a chair. He is changing velocities and directions which makes it more fun. He wont know where he is going because he is blind folded.
 * What do you See?**

I think that the part of the roller coaster that produces the loudest screams is when you begin to fall down the biggest drop because it causes excitement and fear.
 * What do you Think?**

**Roller Coaster Design Homework** One roller coaster design is the Wooden Roller coaster. These roller coasters don't travel as quickly as the ones made out of steel and they are usually older. The Texas Giant is one example. It has a 137 ft drop and can go up to 62 mph which is really quick for a wooden roller coaster. The Raven is also a famous wooden coaster that travels at the speed of 51 mph and contains a serious of big drops like most wooden roller coasters because they can't be built so the car goes upside down.

3/1/11 A scalar quantity is a quantity that has magnitude so it has size and amount but no direction. The displacement of an object is the difference in the position of it between the ending position and the starting position. Displacement only uses the endpoints, not the path in the middle. It is a vector quantity so it has size and direction. The speed of something like a roller coaster is the distance traveled over the time it was traveling. It doesn't is scalar. Velocity is the same thing but has direction so it is a vector quantity. v= change in d/ change in t. Acceleration is the change in velocity over the time. It is a vector quantity.
 * Physics Talk Summary**

**Checking Up Questions** 1.) Distance is a scalar quantity unlike displacement which is a vector quantity. The distance is the total amount traveled but displacement is only the difference of the starting point and the ending point. The path in the middle doesn't matter. 2.) Your total displacement is zero because you end where you started. 3.) Speed is a scalar quantity and velocity is a vector quantity. They are the same thing but velocity deals with direction and speed doesn't. 4.) The acceleration of an object is the change in velocity over the elapsed time. The change in velocity is the final velocity minus the initial velocity.

**Physics Talk** 1.) 2.) The biggest thrill occurs during the acceleration parts of the ride like when the rider is going down a huge drop. This produces thrill because the person has both fear and excitement. 3a.) La Paz, Bolivia is traveling faster because in the same amount of time, Bolivia is traveling a much larger distance. 3b.) v= d/t v= 40,000 km/24 v= 1666.7 m/s 3c.) You don't get a big thrill going at that high constant speed because you are going so fast that it is hard to realize it. There is also no acceleration 4.) a= change in velocity/ t  a= 16-4 / 3 a= 12/3 a= 4 m/s^2 5a.) speed 5b.) velocity 5c.) velocity 5d.) displacement and speed 5e.) displacement 6.) v=d/t v= .1/2 v=.05 m/s 7.) .05= 5/t .05t=5  t=1 m/s  8.) a= change in velocity/ time a= 25-0/ 10s a= 25/10 a=2.5 m/s^2 10a.) If i was designing a roller coaster for younger children, I would take away all the horizontal loops because in order to go over the loops you would need to accelerate a lot in order to make it over and to much acceleration would probably scare the children. I would also make the hills less high so it doesn't accelerate to much when going down. I would also make the radius smaller so there would be less force. I would make sure it was safe for them while also being fun. 10b.)

The biggest thrill is when there is an acceleration or a big change in speed. Mostly likely when you are going down a drop because that causes the most acceleration. This is because it is where there is the most excitement and fear.
 * What do you Think Now?**

Section 2
3/3/11

The people who are going down a steeper drop accelerating a lot and having a good time, but the people who arent accelerating and are on a flat part are having a boring time.
 * What do you See?**

The 90 degree steel roller coaster will give a bigger thrill because the riders will go straight down without a slope. The steeper it is the more of the thrill.
 * What do you Think?**

**Physics Talk** The speed of something is determined by the height of the incline not the length. Gravitational Potential Energy is the energy something posses when it is in a position in the gravitational field. It deals with height. Kinetic energy is the energy of an object in motion. It deals with speed. Both of them depend on mass as well. The unit of energy is joules (J). Mechanical energy is the sum of GPE and KE in a situation.

**Checking Up Questions** 1.) The length doesn't have an affect on the final speed, height affects it. 2.) As the height decreases so does the GPE. The mass affects it the same way. As the mass gets smaller so does the GPE. 3.) As the speed of an object gets faster, the kinetic energy increases. The same thing happens as the mass gets bigger. 4.) As a roller coaster goes down an incline it loses gravitational potential energy with its height, and the energy is converted into Kinetic energy because its velocity increases as it accelerates and kinetic energy deals with motion. 5.) GPE= KE mgh=40,000  40,000/4  10,0000 (3)  30,0000 J KE


 * Physics To Go**

1.) The speed is the same at the bottom. 3.)Mass of car = 200 kg g=10 N/kg or 10 m/s^2 60,000 J || 0 || 60,000 || 0 J || 60,000-0= 60,000 J || 60,000 || 30,000J || 60,000-30,000= 30,000 J || 60,000 || 15,000J || 60,000-15,000= 45,000 J || 60,000 || 4.)
 * Position of car (height) || GPE (Joules) || KE (Joules) || GPE+KE ||
 * Top (30 m) || 200(10)(30)= 60,000
 * bottom (0 m) || 200(10)(0)= 0 J
 * Halfway (15 m) || (15)(10)(200)=
 * Three quarters (7.5 m) || (200)(7.5)(10)=15,000J

5.) mass- 300 kg gravity- 10m/s^2 velocity at beginning- 0 m/s  6.) 7a.) GPE= mgh GPE= (9.8)(.20)(.75)  GPE= 1.47 J  7b.) KE= 1/2 mv^2 1.47= 1/2 (.2)v^2 14.7=v^2 v= 8.83 m/s 7c.) When the bob is halfway it will be equal 8.) The mass won't affect the ride, the ride will keep the same speed because the mass in GPE and KE cancel out. 9a.) From point a to b it will be going the fastest. 9b.) C and F have the same speeds because they have the same height. 9c.) At point D it is going faster because it has less GPE because it is lower and so the KE must be higher. 10b.) The roller coaster won't reach point H because it doesn't have enough acceleration in order to make it up to that point. 11.) Mass 200 kg
 * Postion of Car (height in meters || GPE (J) || KE (J) || GPE+KE ||
 * Top (25 m) || 75,000 || 0 || 75,000 ||
 * Bottom 0m || 0 || 75,000 || 75,000 ||
 * Halfway down 12.5 m || 37,500 || 37,500 || 75,000 ||
 * Further down 5 m || 15000 || 60,000 || 75,000 ||
 * Position of car || Height (m) || GPE (J) || KE (J) || GPE+KE (J) ||
 * Bottom || 0 || 0 || 50,000 || 50,000 ||
 * Top || 25 || 50,000 || 0 || 50,000 ||
 * Top of loop || 15 || 30,000 || 20,000 || 50,000 ||
 * Horizontal loop || 0 || 0 || 50,000 || 50,000 ||

**What do you Think Now?** 3/9/11

The roller coaster that has the highest height will most likely provide the biggest thrill because it starts off with the most GPE. Because the rides start off at the same height, they will both have the same speed in the end. I still agree with my answer the first time that B will provide the biggest thrill because in order to have the same KE as GPE at the beginning it will need to accelerate more because it is steeper.

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

A roller coaster gets up to its highest point by being pulled on chains. In order to get up to the point though it needs to have a lot of velocity because the more velocity, the higher the height is able to be. I don't think it costs more to lift a roller coaster full of people because the mass cancels out and doesn't matter.
 * What do you Think?**

The energy in a system can vary from kinetic to gravitational to spring potential energy. Spring potential energy is found in a spring when it is compressed or stretched. It is also called EPE (elastic potential energy). Energy is never lost but sometimes it is changed into a different kind of energy like heat and sound energy. A ball for example doesn't always bounce to the same height. There are many types of energy like heat energy, light energy, sound energy, and nuclear energy but in a system the total amount of joules must always remain the same. A roller coaster for example has its highest GPE at the highest point but it transfers into KE and thermal and sound energy as it goes down. EPE= 1/2 kx^2 k= spring constant x= stretch or compression
 * Physics Talk Summary**

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

5.) It can't be higher than the first because it won't have enough GPE to get to the top of the higher second hill. 6.) The roller coaster doesn't travel forever because as the roller coaster keeps going, it loses its kinetic energy and because of the friction, the KE and GPE is turned into work which stops the ride.0 7.) (300)(9.8)(15)= 44,100 J 8a.) KE= 1/2 mv^2 KE= 1/2 (400) (15)^2 = 45,000J 8b.) KE=GPE 45,000 J  8c.) 45,000= (400)(h)(9.8) 11.48 meters high 9.) As a ball is thrown upwards, its gravitational potential energy is increasing because its height is increasing and they are directly proportional. 10.) The gain is the same for each path because they are all going up to the same height so they will all have the same gravitational potential energy at the end. 11a.) They should have about the same values because they are equivalent. 11b.) SPE=KE SPE= 1/2 mv^2 SPE= 1/2 (0.020)(2.7)^2 SPE= 0.0729 J 11c.) KE=GPE  1/2mv^2= mgh  1/2 (.006)(2.7)^2= (.006)(9.8)h  .02187= .006(9.8)h  h= .13 m  12a.) SPE= 1/2 kx^2 52,920= 1/2k(4)^2 52,920=1/2k(16) x= 6,615 N m/s 12b.)GPE= SPE GPE= mgh  GPE= 70,560 J  70,560= 1/2 kx^2  70,560= 1/2 (6,615)x^2  x= 4.62 m  13.) KE= SPE KE= 1/2kx^2 KE=1/2 40(.3)^2 KE= 1.8 J
 * Physics to Go**

A roller coaster gets to the highest point by using electricity and motors to pull it up to the highest point. It costs more money for a roller coaster full of people because a lot of work has to be done to get people through the ride and more mass means more electrical energy. The roller coaster's cost is based on electricity. Before I said that it wouldn't cost more which is wrong.
 * What do you think now?**

Section 4
3/16/11

Two different roller coasters are set in space. One is on the moon and one is on jupiter. The kids who are on Jupiter seem to be having a really good time but the ones on the moon are not having a good time. Jupiter has more gravity than the moon so that is affecting the ride.
 * What do you See?**

I think gravity doesn't have a direction. Gravity points to the center of whatever mass it is on. People can be in australia "upside down" because the gravity is holding them to the earth. Gravity pushes on them in the opposite direction as it points towards us.
 * What do you Think?**

The gravitational field is the gravitational influence in a space around an object. Earth is the source of its gravitational field. The object inside earth is the response object. The field is all around the massive object and points to the center. The field is stronger when the lines pointing to the center are closer. It is present everywhere and extends to infinity. The inverse square relationship is the relationship between the magnitude of the gravitational force and the distance from the mass. This shows how electric static forces depend on distance for electric charge. Newtons law of universal gravitation states that all bodies of mass attract all other bodies of mass. Force is proportional to the product of two masses. As the mass gets larger so does the strength of the force. Gravity is the attraction between two objects with mass. The equation for force of gravity is Fg= (Gm1)(Gm2)/ r^2. Gm- universal constant equal to 6.67x10^-11 n(m^2/kg^2) r= distance between centers m1 and 2 are the mass of the bodies
 * Physics Talk**

**Checking Up Questions** 1.) The gravitation field is all around our classroom and it is all pointing towards the center of the room. 2.) The field is the strongest when the force lines are close together. 3.) The force of gravity is cubed when the distance is tripled. 4.) The force of gravity holds the moon in place. 5.) The shape is a circle.

**Physics to Go**

1.) 1/2^2=1/4 of 500 = The force would be 125 newtons 2a.) It would be 1/4 2b.) It would be 1/9 2c.) It would be 1/16 3.) People trust gravity because it is acting on us at all times, it keeps us on the ground. If there is mass there is gravity. 4.) The acceleration due to gravity is the same. Even though at the top of the roller coaster, the acceleration due to gravity is lower, there is really an insignificant difference so they are essentially the same. 5a.) The water is closer to the moon, the water is pulled to the move. 5b.) Because the water has less mass than the moon does, gravity doesn't affect it that much which is why there are high tides. The water is attracted to the moon. 6a.) They fish wouldn't be able to stay in the water because gravity wouldn't hold them down. 6b.) It holds fish down on earth because it keeps them in the water. 7a.) doubled- 1/4 7b.) tripled- 1/9 7c.) quadrupled- 1/16 7d.) halved- 4 8a.) doubled- x4 8b.) tripled- x9  8c.) quadrupled- x16  8d.) halved- x(1/4) 9a.) doubled - doubled 9b.) tripled- multiplied by 9 9c.) quadrupled- multiplied by 6 9d.) halved- halved 10.) doubled, x9, x6

**Physics Plus** 1.) a= V^2/ R^3 2.) v=2(pi)(3.84x10^8)(2440800) v=998.505 m/s

a=V^2/r a= 998.505/ 3.84x10^8 a= 0.0025 m/s^2

**What do you Think Now?** Gravity has a direction, it always points towards the center of the earth because it always points to the object with the largest mass which is the center. People in Australia can stand "upside down" because gravity is always pointed to the center to the earth and therefore the gravity is keeping them on the earth to. It is keeping them on the ground even though they are upside down.

Section 5
3/28/11

**What do you See?** In the first picture a man is weighing a piece of meat on a scale. He is showing the meats weight. In the second picture a main is weighing the meat on a spring scale using Newtons. He is calculating the mass. They are both being weighed though so they are similar.

**What do you Think?** I think you can't use the same scale that you use on an elephant because their weights aren't comparable. The elephant weighs a lot more so it needs to be weighed on a bigger scale that is meant for heavier things. A bathroom scale works by calculating your mass and also multiplying gravity to it because weight is mass times gravity.

**Physics Talk Summary** To stretch something like a string you need a force. The larger the force the more it is stretched. The force for a stretch has a linear relationship. A graph would show a straight line. Robert Hooke made this discovery of the spring. Hookes law states that the restoring force exerted by the spring is directly proportional to the compression or stretch of the spring. The equation is F(force)= -k (spring constant)*x(compression or stretch). The negative shows that the stretch is in the opposite direction as the force. The spring constant is how hard it is to stretch or compress the spring. A stiff spring has a larger K value. Weight is in Newtons. It is 9.8 times the mass. Weight is a force and it changes between the earth and the moon for example because of the gravity. Scales measure weight by a spring being compressed. A net force equals the mass times the acceleration. Weight=kx

**Checking Up Questions** 1.) The spring is stretched 5 times more if the force is 5 times higher. 2.) The string constant is how hard or easy it is to compress or stretch a spring. The harder it is, the higher the spring constant value. 3.) An objects weight is newtons is its mass times 9.8 4.) The more you weight, the more the spring is compressed, and the more upward force the spring must provide.

**Physics to Go** 1a.) w=mg w=100(9.8)  w=980 N  1b.) w=mg w=10(9.8) w= 98 N 1c.) w=60(9.8)  w= 588 N  2a.) 1/4 lb= 1 N  130(4)= 520 N  2b.) 1000(4)= 4000 N  2c.) 50(4)= 200 N  3a and b.) ﻿  3c.) (0,0) (.3,2) m= (2-0)/ (.3-0) m= 1.47 3d.) The slope is the spring constant value. It is the k value. 3e.) My slope is steeper which shows that the slope or the k value is higher. It would be more difficult to stretch because more force is required to stretch it. 4.) F=kx 12=k(.03)  k=400 N/m  5.) Hooke meant that when there is a force acting on something, there will be a stretch or a compression. If you are putting a force on a spring and pulling on it, the spring will stretch. 6.) The one with a spring constant of 15 N/m will be harder to stretch. 7.) (0,0) and (2,3) m= (3-0)/(2-0) m= 3/2 k= 3/2 or 1.5 N/cm 150 N/m 8.) A spring scale works with springs on the inside. When someone or something is put on the scale, the springs compressed. The amount that the compress also provides an upward force of the same weight that is put on the scale. The scale is able to convert the compression to pounds so when you put weight on it, the arrow automatically moves. The more compression, the more weight.

**What do you think Now?** You shouldn't use the same scale to weigh a canary and an elephant because an elephant weighs a lot more than a canary does. You need a bigger scale with more stiff springs to measure an elephant. A scale works because there are springs on the inside of it. When someone steps on the scale, they push down on the springs. The springs provide an upward force back. The force is then converted into pounds at it takes into account the acceleration of gravity. The arrow moves according the the amount of pressure on the springs.

Section 6
Two people are on the elevator. The man who weighs a lot more is dropping on the elevator while standing on a scale. His weight is zero because more weight is pushing him up than down. THe little boy is going up and he weighs 200 pounds because weight is pushing him down more than pushing him up.
 * What do you See?**

I think your weight changes while you are on a roller coaster. As you are going down a hill for example, you are lighter because there isn't as much force pushing you down as when you are on the top of the roller coaster.
 * What do you Think?**

**Notes** 4/5/11
 * Newtons first law: An object at rest stays at rest or an object in motion stays in motion unless acted on by an unbalanced force
 * Newtons Second law: Unbalanced force creates an acceleration. The bigger force is in the same direction as acceleration and vice versa. To do this, draw a motion map and a free body diagram. (Increasing v and a are same direction, decreasing v and a in opposite direction.
 * Net force= mass x acceleration.- Newtons second law. In a free body diagram, the one with the bigger net force is acceleration to the direction of the bigger force. If something is being pulled Tension is bigger than friction for example
 * If acceleration is down, weight is more than normal
 * increasing speed- acceleration and velocity are pointing in the same direction
 * net force and acceleration are always in the same direction
 * The bigger force is in the same direction as net force

An object at rest has zero net force. Newtons first and second law describe this because there is no acceleration so the force must be zero in the second law, and an object in motion stays in motion or an object at rest stays at rest unless acted upon by a force. It is the same as an object in constant speed. There is no net force because there is no acceleration. At constant speed or at rest, there is the same amount of force acting on you as the force of weight that you are providing. If you are accelerating, like accelerating up on a roller coaster for example, there is a net force acting on you. If you are accelerating up, the force of gravity isn't as strong on you so it appears that you weigh more. F=ma- to calculate acceleration Fscale= weight due to scale -ma When you are accelerating upward you feel you are heavier because of the drop of your stomach and your nerves. When an elevator is accelerating down, you feel that you weigh less. Everything on earth has an acceleration of 9.8 m/s squared in free fall but that is ignoring air resistance. Air resistance slows something down. It is always there are it is hard to ignore. Wind is an example of air resistance.
 * Physics Talk Summary**

3.) You feel like you weigh more because forces like the cart are pushing up on you. There needs to be enough force on you to keep you in your seat and to keep your stomach in place as well because it moves around. The force is stronger on you then the force you are exerting back. 4.) The scale would read zero in free fall because the contact force between the person and scale is zero. 5.) Air resistance slows it down.
 * Checking up Questions**
 * 1.) The net force is zero at constant speed. **
 * 2.) The persons normal is heavier when they are accelerating upward on a roller coaster. **

**Physics to Go** ** 1a.)vf= vi+at ** ** 0 +9.8(2)= 19.6 m/s **  1b.) ** vf= vi+at ** 0+9.8(5)= 49 m/s 1c.) ** vf= vi+at ** 0+9.8(10)= 98 m/s ** 2a.) ** ** vf= vi+at ** ** (1.6)(2)= 3.2 m/s ** ** 2b.) ** ** vf= vi+at ** ** (1.6)(5)= 8 m/s ** ** 2c.) ** ** vf= vi+at ** ** (1.6)(10)= 16 m/s ** ** 4.) ** ** 5.) f=ma ** ** 137-140=0 ** ** The elevator is either increasing down or decreasing up because he feels is lighter. ** 6.) The persons will feel heavier because the normal force is bigger than the force of weight. His weight will continue going up as the elevator starts accelerating more.  7a.) The scale will read lighter than their normal weight. 7b.) F= ma n- mg=ma  N=ma+mg  N= (50x-1.5)+(50x9.8)  N= 415 N  8a.) 1=mg W=(9.8)(50) w=490 N 8b.) N-W=ma  N=mg+ma  N=(50 x9.8) + (50x 2)  N=590 N  9.)In the first sketch the person on the elevator is moving at a constant speed. There is no change in acceleration and no change in velocity and therefore there is no change in the netforce. Because of that the persons apparent weight is equivalent to their original weight. In the second sketch, the person is increasing down. They are in freefall which means that they aren't in contact with the scale so their force exerted on it is zero. Their mass is zero. There is no normal force. In the last sketch the person feels heavier because the elevator is accelerating upward. The floor is exerting 100 N more mass than the person is on the scale. Their normal force is higher than their weight and therefore their apparent weight is more than their normal weight. 10.) Our roller coaster acceleration shouldn't be that high because it is made for children. The acceleration would probably have to be around 3 Gs because 6 Gs is the highest that a person can handle. Because they are young we need to be careful that the ride isn't dangerous.
 * **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 ||

Your weight on a roller coaster does not changed, but your apparent weight changes. Basically you feel like your weight is changing but it really isn't Your weight on a scale on a roller coaster would change though. When you are going up a hill for example, you feel heavier then when you are at the bottom of a hill, and you weight on a scale at the top of the hill would be heavier. This is because you are exerting more normal force that weight at the top compared to the bottom.
 * What do you Think Now?**

Section 7
A bunch of carts are going up and down hills and on clothoid loops on a roller coaster. One of the carts is going around on a curve and it is falling off the track. There is nothing keeping the roller coaster on the track. The ride has inertia and the car wants to keep going straight.
 * What do you See?**

A ride going around a loop on a roller coaster is able to go upside down because of the centripetal force pointing towards the center of the loop. The cart has a force acting on it that keeps it going around in a circle.
 * What do you Think Now?**

An object that is spinning in circles must have a force pointing towards the center of the circle to keep it moving. Whenever something is spinning in a circle it is accelerating. On a roller coaster, the track provides a force to keep the ride on the track. One a roller coaster, if the cart tilts while going around a horizontal curve, the force keeping the ride on the track is normal force. Centripetal force is present when something is moving in a circle at constant speed. Centripetal force can be a combination of gravity, friction, and tension. As the speed increases, the mass increases and/or the radius of the curve decreases, the centripetal force is larger. Tangential velocity is the direction the object is moving in. It is almost always constant. The equation: Fc= mv^2/ r Centripetal acceleration is the acceleration of an object as it is going around in a circle by an object traveling at constant speed. It points to the center as well. It is always present because you are changing direction. If there is none it means you are going in a straight line. The direction of the centripetal force is always changing because it is always pointing to the center, like on a vertical loop. In a loop the centripetal force can be gravitational, normal, or a combination (where you add the vectors together). At the top of the loop and bottom, your apparent weight changes. At the bottom you feel heavier and at the top you feel lighter. A ride in order to be safe can accelerate to much or it gets dangerous for the rider.
 * Physics Talk**

1.) Centripetal force is required to keep an object moving in a circle. 2.) There is centripetal acceleration present. 3.) Normal force and weight 4.) Normal force is responsible. 5.) As the mass increases, the centripetal force increases as well. As the speed of the object increases, so does the centripetal force. They are both directly proportional. Velocity is directly squared though. As the radius gets smaller the centripetal force increases. They are inversely proportional.
 * Checking up Questions**

**Physics Talk** 1a.) 1b.) It is tangent to the circle 2a.) Centripetal Force is what keeps the car moving in a circle. 2b.) 6a.) The roller coasters speed would stay at 20 m/s 6b.) The velocity changed because the car changed direction 6c.) 20^2+20^2= c^2 20 sqrt 2 m/s North West  7.) Ac= v^2/r ac= 20^2/ 200 Ac= 2 m/s 10.) For a fast moving roller coaster For a Slow-moving roller coaster 13a.) Bottom of the hill- heavier 13b.) top of the vertical loop- don't know 13c.) bottom of ther vertical loop- heavier 13d.) bottom of second hill- heavier 13e.) Lift hill (constant speed)- normal 14a.) Bottom of first hill- up 14b.)top of vertical loop- down 14c.)bottom of vertical loop- up 14d.) bottom of second hill- up  14e.) Lift hill (constant speed)- zero  14f.) Horizontal loop- up  14g.) Back curve- up
 * || Required Centripetal Force (N) || Force of gravity (N) || Normal force (N) ||
 * at the bottom of the loop || 4000N || 500 N || 3500 N ||
 * at the bottom of the loop || 6000 N || 500 N || 6500 N ||
 * || Required Centripetal Force(N) || Force of gravity (N) || Normal force (N) ||
 * at the top of the loop || 800 N || 500 N || 300 N ||
 * At the bottom of the loop || 2800 N || 500 N || 3300 N ||

**Physics Plus** 1a.) The other side of the equation gets bigger. It increases because as the mass increases net force increases. 1b.) There is a square relationship so it increases. The force is quadrupled. 2.) The tracks force must be quadrupled because as the velocity is doubled, there is a square relationship. 3.) The force gets smaller because the force and the radius are indirectly proportional. 4.) The larger the radius for the curve, the **smaller** the force required to keep the car moving along the curve. If the curve is tight then a **larger** force is required. 5.) If you were to let go of the stopper it would continue in a straight line path without any force.

You don't fall out of a roller coaster when you are upside down because the centripetal force is holding you in. You feel pressed into your seat because of inertia. Net force is always pointing towards the center. The force pushes you in the opposite direction. You accelerate downward.
 * What do you Think Now?**

Section 8
Kids are pulling up a roller coaster car up a steep hill. They are struggling to pull it up because it is heavy and a lot of work. Once they get to the top though it is easy to get the kids down. It is easier going down a hill than going up.
 * What do you See?**

It takes more energy to pull a roller coaster up a steep incline because you need to pull it over a farther distance. There needs to be more energy. It is harder to walk up a steep incline because you need more force to get yourself up. You need more energy.
 * What do you Think?**

Work is the product of force and distance The force must be parallel to the distance. When an incline is steeper, you need more force, but the distance along the incline is shorter. The product of the force and distance along an incline is always the same. Work is converted into GPE on a roller coaster going up an incline. Roller coasters usually use electrical energy, which is measured in voltage, to get up an incline. The Kinetic energy and GPE of a roller coaster are transferred to heat and sound energy as well. To stop a roller coaster, most have brakes, but some also use huge springs. The kinetic energy is transferred into Spring potential energy to stop the cart. The power is the work done divided by the time. It is basically the speed from which the work is transferred into energy. The unit for power is j/s which is called watts
 * Physics Talk**

1.) The energy at the top is transferred into GPE. 2.) The roller coaster gets its GPE from the Work that the cart has while getting up the hill. 3.) Truckers use a ramp because though the same amount of work is used, you need less force because the distance is longer. 4.) The coaster's kinetic energy is transferred into work because of the friction. 5.) J/s which is also called Watts.
 * Checking up Questions**

1a.) The cart only has GPE at the top before it is moving but at the bottom of the ramp there is no GPE. 1b.) All the work is done by gravity. 1c.) All the work is done by the spring 1d.) 1/2 kx^2 1e.) The energy is kinetic and GPE. 1f.) The cart begins to slow down as it starts compressing the spring 2a.) zero because it is perpendicular work not parallel 2b.)w=fd w= 60(.5) w=30 J 2c.) w=FD  w= 75(40)  w= 3,000 J  2d.) w=FD w= 500(.7) w= 350 J 3.) A better way of saying conserving energy is saying don't waste it. The law of conservation of energy says to convert it into different forms. Energy is never wasted.  4.) The mass on the cart would have changed because of the clay people so it would need more force to bring the cart up. There would be more work done and the GPE would be more. 5a.) w=FD w= 10,000(20)  w= 200,000 J  5b.) Power= W/T power= 20,000/150 power= 133.3 W (J/s) 6.) Up the first incline, there is work which changes to GPE at the top. Down the hill there is KE which is changed into KE and GPE when going through a loop. It changes to KE when you are going through the horizontal loop. WHen you get to the second hill there is GPE and KE, and finally there is work done at the end to stop the cart.
 * Physics To Go**

**What do you Think Now?** It is harder to pull a roller coaster up a steeper incline. It takes more energy because you need more force. A steeper incline goes up a shorter distance so you need more force to reach the equal amount of weight. It is the same for walking up a hill. A steeper hill is harder to walk up.

Section 9
4/25/11

**What do you See?** In the picture there is a girl who is thinking about energy and she has a lot of calculations. The boy is thinking about force and there is nothing on the paper. They are both picturing a roller coaster.

The part of the Snake that will be the most thrilling will be when the roller coaster moves from left to right because it is a change in velocity due to the change in direction. If the speed always remains the same, it will be fun because the roller coaster is changing directions.
 * What do you Think?**

**Physics Talk Summary** A number with both quantity and direction is called a vector quantity. Distance and speed are scalar quantities. Displacement is a vector because it has magnitude and direction. To solve for a vector you use pythagorean theorem. Energy is a scalar quantity because to find the total energy you just add all the energies of the system together. All the total energy in a roller coaster for example is constant through the entire ride. On a roller coaster, when friction is insignificant, GPE+KE will always equal the same thing. Gravity and mass are constant so the GPE is dependent on the height. A roller coaster cart at the same heights will have the same speed. Force is a vector. Weight on a coaster always remains the same pointing down, and normal points perpendicular to the track. To find the time that a cart would reach the bottom of a hill you would need to look at the forces. The steeper the slope, the more gravitational force pointing down and so the bigger the acceleration is. On a straight incline, the normal and weight force are constant and so is the acceleration. On a curved ramp the normal force is always changing. There is more acceleration and bigger thrills. When the heights are the same, the GPE is the same, and the kinetic energy is the same so the carts are going at different speeds. Energy conservation involves simple addition and force requires vector addition. Energy conservation is easier to solve. Energy and force are related. When you have heights and velocities you use energy. Forces cause work to be done and work creates a change in energy.

**Checking up Questions** 1.) You need to use pythagorean theorem to solve a vector addition problem. 2.) Energy is a scalar quantity and force is a vector. 3.) It tells you that on a ride where friction is insignificant, KE+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. 4.) The path doesn't affect it  5.) A force like work is required.

**Physics Talk** 1a.) a^2+b^2=c^2  5 ^2 +5^2=c^2  50= c^2  c= rt 50 m/s south west  1b.) tan x= 5/5 x= 45 degrees 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. 3a.) distance- scalar 3b.) displacement- vector 3c.) speed- scalar 3d.) velocity- vector 3e.) acceleration- vector 3f.) force- vector 3g.) kinetic energy- scalar 3h) potential energy- scalar 3i.) work- vector 4a.) scalar 4b.) vector 4c.) scalar 4d.) 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.  6a.) 6b.) 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.) 7b.) The GPE at all these points are equal because they are at the same height. The cart has the same amount of energy. 7c.) The kinetic energy is equivalent because their GPE is the same. They are going at the same speed. 7d.) You are able to ignore the other points because they are at the same height. The mass and the gravity are always constant so the total GPE is controlled by the height. GPE +KE must always be equal at each point on the roller coaster so because their GPE is the same, the kinetic energy must also.

**What do you Think Now?** I think that when the snakes switches direction from left to right, the ride will be most thrilling. This provides a change in direction which also changes the velocity. If the speed remains the same, the ride will still be fun because the velocity is changing. Since the direction is changing, the velocity is too.

Section 10
4/28/11

In the picture there are a lot of different carts going down a bunch of different ramps. There are a lot of safety problems. People are falling off and the tracks are broken. The acceleration is to high for some parts and they are going way to fast.
 * What do you See?**

The knowledge that a person could get hurt of die doesn't make the coaster more thrilling, it makes people not want to go on it. It has no appeal. If I found out that half the riders died or got hurt, I wouldn't change my answer, i wouldn't go on a roller coaster if I knew death was a possibility.
 * What do you Think?**

**Physics Talk Summary** Safety is important on a roller coaster. To be save a roller coaster cannot exceed an acceleration of 4 gs. An object in free fall has an acceleration of 1 g and a ride on a straight incline has an acceleration of less than 1 g. Centripetal acceleration occurs when the car is inside a loop. It always points towards the center of the circle. Centripetal acceleration = v^2/r. To get less acceleration, you can either change the velocity by making the height of the initial starting position smaller, or the height of the loop higher, or you can make the radius bigger. You can use qualitative data to decide how to fix it. This kind of data doesn't use numbers. Quantitative is with numbers. The largest acceleration needs the biggest force. There is always normal force and weight acting on a cart. A cart at rest or at constant speed with always have a net force of zero. When it is moving in a vertical circle, the normal force will be bigger than weight. centripetal force= ma. Fc= mv^2/r. You feel heavier as the number of g's increase because there is more normal force on you. At 1 g you feel normal. A cart with low speed will not make it all the way up a loop because of the force of gravity.

1.) 4 gs is the maximum safe acceleration. 2.) You can decrease the height of the coaster which will decrease the GPE as well as the kinetic energy. The velocity with get smaller, or you can make the radius of the loop bigger. 3.) At the end of the loop. 4.) At the top of the loop.
 * Checking up Questions**

**Physics To Go** 1.) I would check the accelerations at each of the points to make sure that it is under 4 gs. This will ensure that the people wont be killed or knocked unconscious. I would also check to make sure that the cart is going fast enough around the loop. If it isn't, the cart won't be able to make it over the loop. 2a.) mgh+1/mv^2 20 m 2b.) a= v^2/ r  a = 20^2/ 12  a= 400/12  a= 33.33 m/s^2  2c.) No it is over 4 gs  2d.) 4g= 39.2 m/s  39.2= v^2/12  470.4= v^2  v= 21.69 m/s  2e.) 39.2=v^2/ 7 274.4=v^2 v= 16.57 m/s 3a.) a= v^2/r a= 25^2/ 10  a= 62.5 m/s^2  3b.) yes it is a safe acceleration 4a.) GPE= MGH mgh= mv^2  9.8(50)= v^2  490=v^2  v= 31 m/s  4b.) a= v^2/r a= 22.14 ^2/ 10 a= 96 m/s^2 4c.) v= sqrt(a*r) v= sqrt(49.02*10)  v= 22.14 m/s  4d.) 58 m/s 4e.) This roller coaster is safe because the acceleration isn't too high. 5a.) mgh= mv^2 9.8(16)=v^2 v= 8.9 m/s 5b.) GPE= KE mgh=1/2mv^2  9.8h= 1/2(12.52)^2  h= 20 m  6a.) a= v^2/r a= 12^2/18 a= 8 m/s^2 6b.) F=mv^2/r F= 900(12)^2 / 18  F= 7,200 N  6c.) The normal force on the track and the weight will provide the centripetal force. 7a.) a= v^2/r a= 20^2/15  a= 26.67 m/s^2  7b.)F= mv^2/r F= 900(20)^2/15 F= 24,000 N 7c.) The ride is safe because the cart exerts 24,000 and the ride can exert 25,000.  8a.) It will not change because the mass doesn't affect the centripetal acceleration. . 8b.) It will be going the same because the mass doesn't affect it.  8c.) It might need a stronger material to hold the extra people.


 * Active Physics Plus**

If I knew that a roller coaster could cause injury or death I wouldn't go on the roller coaster. I wouldn't want my life to be in danger. If i knew half the riders died i would definitely not go on the roller coaster. A roller coaster is most dangerous around a loop. If the acceleration is to high, it can be lifethreathening. If the velocity isn't big enough though, the roller coaster cart wouldn't be able to make it all the way around the loop. To increase the safety of our roller coaster, we can make sure the acceleration is under 4gs and make sure the cart is fast enough around the loop.
 * What do you Think Now?**