Ch4_FlaggR

= = Chapter (4) Section (1) toc This image shows the path of a child who is blindfolded sitting in a wheelchair. He is blindfolded and can not tell where he is going. The person pushing him knows the path they are going to cover.
 * What Do You See?**

The point of the roller coaster that creates the most screams is the beginning of the decline. The velocity rapidly climbs. Also loops may create excitement because the person may not see it coming then all of a sudden be upside down.
 * What Do You Think?**

The speed os something is the distance is traveled divided by the time that it took. Velocity is displacement divided by the time elapsed. Acceleration is the change in velocity divided by the time elapsed. A scalar a quantity that has magnitude however no direction. A vector is a quantity that had both magnitude and direction. Displacement is the difference in position, it depends only on the endpoints not on the path.
 * Physics Talk**

1) Displacement is the distance traveled with a direction, however distance and scalar don't include direction. 2) The displacement is 0 km. It was 2 km to the school and 2 km to get back home. This means that they would cancel each other and make 0. 3) Speed is scalar and it is calculated by the distance traveled divided by the time it took. Velocity is the displacement and it is divided by elapsed time. 4) Acceleration can be found with Acceleration = the change is velocity divided by the elapsed time.
 * Checking Up**

1) See Above 2) The largest thrill would come from the first hill because it is the tallest and would result in the highest velocity. The cart would slowly climbing the hill and as soon as it went over the top of the hill it would quickly accelerate giving the person a thrill. There are other sections of the coster though that would create screams as well including the sharp turns. 3) La Paz, Bolivia moves with the greatest velocity resulting from the largest radius in a 24 hour period. 3b) Velocity = Distance / TIme V= 4000 km / 4 hr V = 1667 hm/hr 3c) The speed is the largest however it is constant so their is no acceleration so you would not notice. 4) A = change in velocity / elapsed time A = 16 m/s - 4 m/s / 3s A = 4 m/s^2 5a) Car traveling ar 50 km/hr = speed 5b) Student riding bike 4 m/s going home = velocity 5c) Coaster whips around left turn at 5 m/s = acceleration 5d) Coaster going up 12 meters at 3 m/s = displacement and velocity 5e) train ride going NW at 150 km = displacement 6) Velocity = distance / time V= .1 m / 2 s V = .05 m/s 7) Velocity = distance / time .05 m/s = .05 time 1s = time 8) Acceleration = change in Velocity / change in time A = 25 m/s / 10 s A = 2.5 m/s^2 10a) If i had to make 2 changes to the roller coaster to make it more for young children I would decrease the height of the hill and its angle of decline and I would make the radius of the turn wider resulting in less force when the cart goes around it. 10b) see picture
 * PTG**

When there are large changes in the direction and acceleration it creates a large thrill for the riders. The large declines and turns creates the screams.
 * What Do You Think Now?**

= **Chapter (4) Section (2)** =

People riding a rollercoster down a steep decline and they are enjoying themselves. Then there are people on a very small decline part of the rollercoster and they seem to be having no fun.
 * What Do You See?**

The steeper rollercoster will provide the greater thrill because the steeper decline results in a higher velocity.
 * What Do You Think?**

Kinetic Energy is the energy an object has relating to its motion, GPE is the potential energy that something can have but it largely depends on its position in the gravitational field. Both of these energy forces depend on the objects mass. They have to equal each other. The units used for measuring both there is Joules. GPE and KE are both constant so when one goes down the other has to go up.
 * Physics Talk**

1. The greater the height is when the ball is released, the greater the speed will be at the bottom 2. When the height or mass increases or decreases than so does the GPE because mass and height affect the have a direct relationship with GPE. 3. KE increases when the velocity increases or when the mass increases. 4. As the cart goes down the hill the GPE decreases because the velocity is increasing which makes the KE increase. 5. 30,000 Joules of Kinetic Energy 3/4 of the way down.
 * Checking Up Questions**

1. The speeds of both carts A and B have the same speed even though their inclines are different because they have the same initial height. 3. 4. 5. 6. 7a. GPE = mgh GPE = (.2) (9.8) (.75) GPE = 1.47 joules 7b. GPE = KE 1.47 GPE = 1.47 KE 7c. Height = .375 (half way down) 8. It doesn't matter how many passengers are in the car. The GPE at the top has to equal the KE at the bottom. Also the masses cancel. 9a. It's traveling the fastest during B because it is at the lowest position. Kinetic Energy is at it's highest point when GPE is at its lowest point. 9b. At points C and F the coasters are traveling at the same speed because the heights of both are the same. 9c. The coasters traveling the fastest at point D because it has more Kinetic Energy than Gravitational Potential Energy. 10b. It is impossible for the coaster to reach point H because it is higher than the original hill. The GPE can not gain energy and there is not enough KE. 11.
 * PTG**
 * height (m) || KE=1/2mv^2 || GPE=mgh || GPE and KE combined ||
 * top (30) || 0 || 60,000 || 60,000 ||
 * bottom (0) || 60,000 || 0 || 60,000 ||
 * half (15) || 30,000 || 30,000 || 60,000 ||
 * 3/4 down (7.5) || 45,000 || 15,000 || 60,000 ||
 * height (m) || KE || GPE || combined GPE and KE ||
 * top (25) || 0 || 75,000 || 75,000 ||
 * bottom (0) || 75,000 || 0 || 75,000 ||
 * half (12.5) || 37,500 || 37,500 || 75,000 ||
 * 3/4 of the way down (5) || 60,000 || 15,000 || 75,000 ||
 * Position || Height (m) || GPE || KE || Combined ||
 * bottom hill || 0 || 0 || 50,000 || 50,000 ||
 * top hill || 25 || 50,000 || 0 || 50,000 ||
 * top loop || 15 || 30,000 || 20,000 || 50,000 ||
 * horiz. loop || 0 || 0 || 50,000 || 50,000 ||

The initial heights for both the coasters is the same. The greater the initial height than the greater the velocity. Both velocities would be the same at the bottom. However B would give you a better thrill because of the more rapid change in slope resulting in greater acceleration.
 * What Do You Think Now?**

=Chapter (4) Section (3)=

One of the kids launches a frog toy into the air. The other kid uses a ruler to see how high the toy reaches. At the bottom here is a photo gate time to get the frogs velocity at the beginning of its jump. Another kid is ready to launch another frog toy.
 * What Do You See? **

For the coaster to reach the highest point it slowly climbs the large hill. It doesn't cost more to lift people on the roller coaster. It doesn't matter how many passengers are on the cart it will make it to the highest point.
 * What Do You Think? **

Conservation of Energy, energy cannot be lost or destroyed. Energy in a system can vary between KE GPE and EPE. Spring potential energy is the energy stored in a spring due to its compression or stretch. The sum of all the energies is always the same. When using the table, the total number all the way to the right must be the same throughout in joules. A pop toy with a greater mass won't go as a high as one with lower mass, but SPE is the same. For a pop-up toy, GPE at the bottom and KE & GPE = KE & GPE and GPE. They have to balance out and equal each other. gpe = mgh
 * Physics Talk**

1. As it bounces off of the table, all of the SPE transfers into gravitational potential energy and kinetic energy. 2. Because it has 2 Joules of potential energy, the kinetic energy will be 2 Joules as well. 3. When reaching maximum height, the GPE will be 2 Joules. 4. EPE=1/2kx^2. K is the spring constant and x is the distance compressed.
 * Checking Up Questions**

5. The second hill can not be higher than the first because you can not gain energy, at the most you would be able to reach the same height however this is most likely not possible because of friction. 6. The second roller coaster wont travel forever as it moves it will lose KE and GPE which changes into heat and sound energy. Work due to the friction changes into thermal energy. This means you have less energy for KE and GPE. 7. GPE = electric energy (300)(9.8)(15)= electric energy electric energy = 44,100 Joules 8a. KE = 1/2 mv^2 KE=1/2(400)(15)^2 KE = 45,000 Joules 8b. GPE = KE GPE = 45,000 Joules 8c. 45,000= (400)(9.8)(h) height = 11.5 meters 9. As a ball is thrown upwards, the height is increasing, which means that the GPE also increases because GPE is directly related to height. 10. It is the same because it is independent. 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 similar results because they are the same. 1/2mv^2=mgh. Should be about the same as the GPE and GPE = (0.02)(9.8)(.4) GPE = .078 Joules 11b. SPE=KE SPE= 1/2 mv^2 SPE= 1/2 (0.020)(2.7)^2 SPE= 0.0729 Joules 11c. KE=GPE 1/2mv^2= mgh 1/2 (.006)(2.7)^2= (.006)(9.8)h (.02187) = (.006)(9.8)h h = .37 meters 12a. GPE = SPE mgh = 1/2kx^2 (300)(9.8)18 = 1/2k(4^2) k = 6615 N/m 12b. GPE= SPE GPE = mgh (400)(9.8)(18) 70,560= 1/2 kx^2 70,560= 1/2(6615)x^2 Joules x = 4.62 meters 13. KE= SPE KE= 1/2kx^2 KE=1/2 40(.3)^2 KE= 1.8 Joules
 * PTG **

Roller Coasters today are lifted to their highest points by motors and cables. It does cost more to life a roller coaster that if full because there is a greater mass which results in a greater GPE. The greater GPE requires greater work to lift the coaster which is results in more electricity too lift the coaster.
 * What Do You Think Now?**

=Chapter (4) Section (4)=

The person on on the left seems bored because their coaster's initial drop is not large which generates a small thrill. It is not a very steep drop and it is on the moon. The other picture shows a coaster which gives a greater thrill because of a larger initial drop and they are on jupiter which has greater gravity which results in more coaster speed.
 * What Do You See?**

Gravity does have direction and it is directed towards the core of the earth. This means that it equally pushes down on all people even Australians who may be upside down at some points. The large mass of earth results in this gravity.
 * What Do You Think?**

The gravitational influence in the space around a massive object with large mass. Earth of the source of its gravitational field because it is the first object that sets up in the space around it. A second object interacts with this field (moon). Acceleration due to gravity becomes less as an object moves further from the surface of Earth. The relationship between the magnitude of a gravitational force and the distance from the mass. this also describes how electrostatic forces depend on the distance from an electrical charge. The force of gravity between 2 objects decreases by the square of the distance between both objects. All bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bogies increases. The force of attraction between two bodies due to their masses
 * Physics Talk**

1. The direction of the gravitational field in the classroom is points towards the ground. 2. The field lines are the greatest neath earths core because that is where gravity points to. 3. If you triple the distance than the force is only one ninth of the original. 4. Gravity holds the moon in its orbit around the earth. 5. The path that the planets follow around the sun is an elliptical path or a circular path.
 * Checking Up Questions**

1. .The original force is 500 N if the distance is doubled the force would be 125 N. 2a. Fg would be 1/4 of the original 2b. Fg is 1/9 original 2c. Fg is 1/16 original 3. Gravity is always there. As long as Earth maintains itself as the largest mass than gravity will stay. 4. Acceleration due to gravity is less at the top, than the bottom. 5a. Water on the Earth's side facing the moon is closer to the moon than the center of Earth. This is where there is high tide, and on the opposite side of Earth away from the moon is low tide. 5b. Water moves independently from earth as there is high and low tides. The moon is attracted to the water causing high and low tides. 5c.Water is not evenly distributed over earth because of land mass. All bodies of water are different distances from the moon and therefore, have different forces of the gravitational field of the moon. This is the inverse-square relationship. The further away from the moon, the smaller the waves and tide. 6a. If a fish was not impacted by gravity, it would be moved away from the water and into the air. 6b. Gravity holds the water down so the fish can swim in the water. Gravity holds the fish in the water because the mass of a fish is much less than the mass of the Earth. The fishes small mass attracts it to the earth. 7a. 1/4 the force 7b. 1/9 the force 7c. 1/16 the force 7d. 4 times the force 8a. 2 times the force 8b. 3 times the force 8c. 4 times the force 8d. 1/2 times the force 9a. 4 times the force 9b. 9 times the force 9c. 16 times the force 9d. 1/4 the force 10a. 2 times the force 10b. 9 times the force 10c. 6 times ** the force **
 * PTG**


 * Physics Plus**
 * 1. a = v^2 / r **
 * 2. v = d/t **
 * 2 x (3.14) x [3.84x10^8) / 2440800 **
 * v = 998.505 m/s **
 * 3. a = v^2 / r **
 * a = 998.505^2 / 3.84x10^8 **
 * a= 0.0025 m/s^2 **

Gravity has a downward direction pointing towards the core of the earth. This is due to the huge mass of the earth. The earths gravity is acting upon all people the same weather they be in the U.S or in Australia. Peoples mass is so small compared to that of the earth which is why they are attracted to it.
 * What Do You Think Now?**

=Chapter (4) Section (5)=

A man using a normal scale to weigh a type of food. The scale pushed down to measure weight. THe other man is using a spring scale in a laboratory and it looks a lot more precise.
 * What Do You See?**

No you can not use the same scale to weigh a canary and an elephant because their eight varies too much for a scale to accurately weigh each one. A bathroom scale works by you stepping on the scale and it pushes down on a meter that reads your weight in pounds.
 * What Do You Think?**

Hooke's law is a law that states that the restoring force exerted by a spring is directly proportional to the distance of the stretch and or the compression. If there is a negative it indicates the opposite of the direction of the compression or stretching. If there is a large spring constant that means the the spring is stiff and does not stretch easily. If the spring constant is small that means the spring will stretch easily. Weight = mass*gravity. Weight changes depending upon gravity however somethings mass always stays the same. In a bathroom scale there is a spring that is compressed and the meter goes to whatever your weight is by providing an equal force equal to your weight.
 * Physics Talk**

**Checking Up** 1) If there is a force on the spring and it is increased by 5 times the stretch of the spring will increase by 5 times also because of their direct relationship. 2) The spring constant will show the stiffness of a spring. If K is larger than the spring is stiffer if K is lower than the spring is more flexible. 3) Mass is a needed part in the equation for weight. K = kg*m/s^2. The mass is part of the weight. 4) The more weight that is used on the scale than the more compression this will be. This will make the reading weight on the scale go up.

**PTG** 1a. Weight = mass*gravity weight = 100 * 9.8 weight = 980 Newtons 1b. Weight = mass*gravity Weight = 10*9.8 Weight = 98 Newtons 1c. Weight = mass*gravity Weight = 60*9.8 Weight = 588 Newtons 2a. .25/130 = 1/x 520 = 1/x x = 520 Newtons 2b. .25/1000 = 1/x 4000 = 1/x x = 4000 Newtons 2c. .25/50 = 1/x 200 = 1/x x = 200 Newtons 4. Fs = -Kx 12 = -K*(.03) 12/(.03) = -K K = 400 N/m 5. If the force of a spring increases than the stretch distance will increase too because they are a direct relationship. The greater the spring constant than the more stiff the spring will be. Adding weight to the spring will increase the stretch distance but not as much as changing the spring constant. The negative before the K means that the force goes the opposite way as the spring. 6. The greater that the K is than the more stiff the spring it. This means that a 15 N/m spring would be more difficult to stretch because the constant is bigger. 7. The slope = 150 N/m F = kx 3 = k(.02) K = 150 N/m 8. A spring will show someones weight in Newtons. This is based on Hooke's law and the spring is directly proportional to the force pulling on it. These scales can be read by using the mass added and the stretch distance of the spring that is created by the weight of the object. This creates F = -kx

**What Do You Think Now?** 1) You can not use the same scale to measure the weight of a canary and an elephant. This is because scales work by compressing a spring. The spring needed to measure the weight of an elephant would be much more stiff and have a much higher spring constant than one needed to measure the weight on a canary. 2) Bathroom scales work by by compressing a spring. The weight of the human provides a force to push down on the spring and is balanced by a spring in the scale. The more force the spring has to use to equal out the humans weight the more the person weighs.

= Chapter (4) Section (6) =

There is a man in one elevator that looks like he weighs a lot. His weight is causing the elevator to drop. There is no tension on the rope holding up the elevator. He is traveling down so there is 0 force. THere is another elevator that a little boy is in. It is going up so the rope is taught and the scale is reading a force because there is more force pulling up.
 * What Do You See? **

No your weight does not change while you are on a roller coaster. This is because gravity is always acting on you and your mass always stays the same. However your apparent weight does change at different parts of the roller coaster because of the direction of the acceleration. Yes because when you are going downward there would be very little force acting on the scale but when the roller coaster was going up there would be a much larger force on the scale.
 * What Do You Think? **


 * Physics Talk**
 * According to Newton's first law, an object at rest has no net force acting on it. According to the second law, an object at rest has zero acceleration and no net force acting on it. The same goes for an object in constant velocity. When sitting on a scale on a leveled roller coaster, the scale reading would be equal to the actual weight of the person. When accelerating up, there is a net force pushing you up. When moving up on the scale, the magnitude reading is greater than weight. The magnitude of the force of Earth would be less tahn the force of the compressed spring in the scale. The net force of a person is down if an elevator/person are accelerating downward. Weight readings are identical when the elevator is in constant motion or at rest. When accelerating up, the person accelerates up. The Earth pulls down on you with a smaller force than the scale goes upward, therefore, the scale reads a larger force. The forces make weight feel greater/less (force hold stomach in place against gravitational forces.) When elevators accelerate down, the reading is smaller force than originally because the force of the scale is up on the person and less than the force of weight down. Air resistance can't be ignored on a roller coaster. A roller coaster in a free fall accelerates 9.8m/s^2. **

1. The sum of all the forces acting on an object when it is moving up at constant speed is zero.  2. When accelerating up on a bathroom scale on a roller coaster, the reading on the scale will be greater than your weight in magnitude.  3. You feel as if you weight more when you accelerate upward because of contact forces and stretching stomach tissues, and forces are holding your stomach in place  4. If the elevator cable were to break, you would only have the force of your weight pulling you down & nothing pushing you up. The force reading on the scale would be zero and you'd feel weightless.  5. Air resistance slows a falling raindrop.
 * Checking Up**


 * PTG**
 * 1a. vf=vi+at **
 * =0+(9.8)(2) **
 * = 19.6 m/s **
 * 1b. vf=vi+at **
 * (9.8)(5) **
 * = 49 m/s **
 * 1c. vf=vi+at **
 * =(9.8)(10) **
 * =98 m/s **
 * 2a. vf=vi+at **
 * =(1.6)(2) **
 * =3.2 m/s **
 * 2b. vf=vi+at **
 * =(1.6)(5) **
 * =7.5 m/s **
 * 2c.vf=vi+at **
 * =(1.6)(10) **
 * =16 m/s **

5. Because you feel lighter, it means that it is increasing down. Acceleration must be negative because if the reading is less than what it is at rest, than acceleration and force are down. Decreasing up is also an option. Normal force is less than weight. 6. Velocity and acceleration are both pointing up. Net force points in the direction of acceleration. The force is pointing up. The normal force has to be bigger. 7a. Once the elevator begins, the scale reading will go down. That is the direction of velocity and acceleration. The 1.5 acceleration becomes negative. Force points to the weight in this case. 7b. ∑f=ma N-w=ma N=ma+mg; 50(-1.5)+50(9.8)=415 N 8a. The forces are equal. The reading on the scale will remain 50 kg because it is at rest. The weight will be 490 N. 8b. V and A go up, and ∑f go up as well. The normal force is greater than weight. N=590. 8c. As the elevator travels up at constant speed, the reading on the scale will remain the same because all forces are equal. Normal is equal to weight. 9. In the first picture the elevator is at rest/constant velocity. The scale is going to read 113 lb because that is home much the person weighs. The forces are equal because acceleration is 0. In the second picture the elevator is in free fall. The reading on the scale is 0 because there is no force keeping him down, the only force is gravity and there is nothing to balance that out. In the third picture the elevator is accelerating upward. The reading on the scale is going to be greater because when you are accelerating upward that force is greater so it is going to make your weight seem heavier. 10. Our roller coaster is designed for teenagers. It has an steep initial drop into a vertical loop. Than it has a few sharp turns into a triple horizontal loop. THe constant changes in velocity would make our riders feel heavy at certain points and light during others. This would make the ride more enjoyable. = = Your actual weight does not change when you are riding on a roller coaster because your true weight is gravity, only your apparent weight changes. If you were sitting on a bathroom scale, the scale would give different readings for different places on the roller coaster. This is due to the direction of acceleration and the direction of the net force. If the bigger force is pointing up, then your apparent weight is greater. If the bigger force is pointing down, then your apparent weight is less. When you are almost at the top of a hill and the cart is decreasing up, your weight would read less that it actually is because the force pushing you up the hill is less than that of your body. = = =Chapter (4) Section (7)=
 * Section 6, PTG #4 **
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || zero ||  || equal ||
 * Starting at Rest, Increasing Up || up ||  || greater ||
 * Continuing to move, Constant Up || zero ||  || equal ||
 * Slowing down to top floor, Decreasing Up || down ||  || less ||
 * At rest, top floor || zero ||  || equal ||
 * Starting at rest, Increasing Down || down ||  || less ||
 * Continuing to move, Constant Down || zero ||  || equal ||
 * Coming to a stop on the ground floor || up ||  || greater ||
 * What do you think now?**

People look like they are about to fall off the track because they took a turn going to quick.
 * What Do You See?**


 * What Do You Think?**
 * You don't fall out of the cart when it goes upside down during a loop because gravity is keeping you in place in the seat. Acceleration and force are pointing toward the center of the loop. **


 * Physics Talk**
 * Centripetal force can be any one of the four forces that makes an object move in a circular path. The centripetal force always points towards the center of the circle. The centripetal force is not an additional force, it is a combination of the forces that make the object move circularly. Centripetal acceleration is the acceleration pointed towards the center. If Ac = 0 then the object is moving in a straight line. Your apparent weight in a circle is always changing because the acceleration is always changing. To keep a roller coaster safe, the force needs to stay below 4 g's. Trained people like astronauts can handle up to 6 g's.The tangential speed is almost always constant.The equations to finding the centripetal force, acceleration, and net centripetal force are: Ac=V^2/R, Fc=ma, Net Fc= mv^2/R. **


 * Checking Up**
 * 1. Centripetal acceleration allows an object to stay in the motion of a circle. **
 * 2. If traveling in a circular motion and constant speed, you are centripetal acceleration. **
 * 3. The forces at the top of the loop are the gravitational force and normal force. **
 * 4. Normal force is responsible for apparent weight. **
 * 5. As mass increases, Fc increases. As velocity increases, Fc increases (direct-square relationship) and as radius increases, Fc decreases. **

1a. The path would be a circle 1b. If the string holding the car broke it would travel in a straight line tangent to the circle. 2a. THe friction of the tires replaces the string. 2b. If you hit a patch of ice while going in a circle you would travel in a straight line because of no friction. 6a) no, it is still 20 m/s b) yes, the direction did c) Change V = V2-V1 = SQRT(20^2 + 20^2)  = 28.3 m/s  tan@=20/20  @=45 degrees  28.3 m/s @ 45 degrees North West  0 m/s to 90 degrees north  7. Ac= v^2/r  =20^2/200  Ac= 2 m/s  10. A fast moving one  10b. Slow Moving one  13a. heavier  13b. uncertain  13c. heavier  13d. heavier  13e. normal  14a. up  14b. down  14c. up  14d. up  14e. zero  14f. sideways  14g. sideways
 * PTG**
 * || Required Fc (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 4000 || 500 || 3500 ||
 * bottom of the loop || 6000 || 500 || 6500 ||
 * || Required Fc (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 800 || 500 || 300 ||
 * bottom of loop || 2800 || 500 || 3300 ||

** Physics Plus ** 1a. The Fnet increases. As the mass increases, the velocity stays the same, the radius stays the same, this increases the net force. 1b. Iv the velocity increases, the Fnet also increases by a lot because it has a squared relationship (quadruples if velocity doubles). 2. The strength of the track (force) must be quadrupled. 3. The Fnet also gets smaller if the r gets larger (indirectly proportional) 4. The larger the radius for the curve, the smaller the force required to keep the car moving along the curve. If the curve is tight (r is very small) then a larger force is required. 5. If you were to let go of the stopper, it would continue in a straight line motion without any force.

When riding a roller coaster you stay in because of the inertia that wants to make you keep going straight. There is also centripetal force acting upon you and forces your body towards the center of the coaster. Also you are not upside down long enough to fall out of your seat.
 * What Do You Think Now?**

=Chapter (4) Section (8)=

People laboring really hard to bring the roller coaster to the top of the track. Once all the work is done the GPE takes over and brings it the rest of the way down.
 * What Do You See? **

** What Do You Think ** It does not take more energy to go up a steep incline than a gentle one as long as they are the same total height. As shown in the equation GPE = mgh, as long as the heights are the same, steepness does not matter. It is harder to walk up a steep incline because it feels like gravity is pushing on you harder if you go up a steep hill.

**Physics Talk** Roller coasters need to be at the top of the first hill to begin the ride. Work is the product of displacement and the force in the direction of the displacement; the energy transferred to an object. W = F*d. F is the part of the force parallel to the displacement. D is displacement. In our lab, a spring scale pulled the lab cart up the incline and the force was in the same direction as the displacement. F*d was always the same regardless of angle. The GPE of the cart increased as a result of the work done by the spring scale. Work must be applied to bring the coaster up the first hill. The vertical displacement is the height that the coaster must be lifted.

**Checking Up Questions** 1. The energy at the top is transferred into GPE. 2. The coaster gets its GPE from the work that the cart has while getting up the hill. 3. Truckers use a ramp because they need less force for a longer distance. 4. The roller coaster's kinetic energy is transferred into work because of the friction. 5. J/s, also known as watts.

**PTG** 1a. The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline.  1b. As the cart went from the top to the bottom, all of the work is done by gravity.  1c. All of the work is don't by the spring as the spring compressed  1d. SPE = 1/2kx^2  1e. The total energy just before it hits the spring is GPE.  1f. You begin to slow down just when you first touch the spring. 2a) 0, there is no acceleration. <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> b) W=fd <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W = 60 * .5 <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W= 30 <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> c) W= fd <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W=40*75 <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W=3000 <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> d) W=fd <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W= 500 * .7 <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;"> W=350 3. Decrease energy consumption, don't waste energy. Don't use it when it isn't useful. 4. Mass would increase, which would require more force which would mean more work which would mean more GPE. 5a. W=F*d =(10,000)(20) =200,000 J  5b. P=W/t =20,000/150 =1,333.33 W 6. GPE is increasing and doing work, at the top it is all GPE. As you go down, GPE turns into KE. ON top of the vertical loop, you got KE and GPE. At the bottom of the loop, you got all KE. At the back curve, you have KE and some GPE. At the horizontal loop, you have KE. In the end, work is done in order to bring the coaster to rest.


 * What Do You Think Now?**
 * It requires the same amount of energy to pull a coaster up a steep incline than a gentle incline as long as both reach the same height. The gentle incline is less steep, but will be a longer track. Since W=GPE and both have the same height, the work needed for both are the same. It is more difficult to go up a steep incline because more force is needed if both inclines are the same length. When it is steeper, that means you will have a higher max height, meaning higher GPE, meaning more work needed to climb the steeper slope. **

=**Chapter(4) Section (9)**=

There are two people one is taking a test about energy and one about force. The one thinking about force is having a hard time thinking of what to write but the person taking the test on force is having an easy time. Energy is easy to measure unlike other forces.
 * What Do You See?**


 * What Do You Think?**
 * The parts where the Snake is changing direction are the parts that will be the most thrilling for riders. Even though the ride stays the same speed, it is still thrilling. Since your direction changes, your velocity changes by positively accelerating on the turns. **


 * Physics Talk**
 * Something with both a number and a direction is called a vector. A quantity with magnitude and no direction is a scalar. Displacement is taken into account with vectors. Vectors need to make a triangle and do Pythagorean theorem to get the hypotenuse because vectors need direction along with size. Energy is a scalar. The total mechanical energy is equal at all points of the roller coaster ignoring friction. Force on the other hand is a vector quantity. Force of gravity is always down. The normal force is always perpendicular to the track. The changes in acceleration in size and direction create the bouncy feelings. Force and energy are related. Weight does work on the roller coaster and increases its KE. **


 * Checking Up**
 * 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 **

** 3a. scalar ** ** 3b. vector ** ** 3c. scalar ** ** 3d. vector ** ** 3e. vector ** ** 3f. vector ** ** 3g. scalar ** ** 3h. scalar ** ** 3i. scalar ** ** 6b. ** ** 6c. The forces are the same everywhere. There is an x-component of weight. It is constant and the same at all four points. ** 7b. The total energy is equal at each point because of the same heights. 7c. The KE is equal at each point since they all have the same velocity 7d. You can ignore the other points because GPE + KE is equal at every point on the coaster. As GPE goes down, KE goes up and as GPE goes up KE goes down.
 * PTG**
 * 1a. change of velocity = 7.07m/s. sin(45) SW **
 * 1b. a^2 + b^2 = c^2 **
 * 5^2 + 5^2 = c^2 **
 * 50 = c^2 **
 * c = 7.07m/s SW **
 * 2. They provide the same change in speed because they are all dropped from the same height, so they start out with the same GPE. This means that they have the same KE and velocity **
 * 4a. Scalar **
 * b. Vector because weight has a direction **
 * c. Scalar **
 * d. Vector **
 * 5. It is seen as an energy ride when you are trying to find speeds and you know the heights of the coaster. It is seen as a force ride when you want to find normal force or acceleration. **
 * 6a.[[image:Photo_on_2011-05-02_at_13.02.jpg]] **
 * 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 **
 * 7a.[[image:Photo_on_2011-05-02_at_13.03.jpg]] **


 * What Do You Think Now?**
 * On The Snake, the most thrilling parts are the parts that change direction. Since the ride does not have any loops because the ride is always ground level, the riders will get their thrill from going left and right. Straight rides are very boring for riders, so that is why the turns are a part of this ground level ride. Even though the speed never changes, the velocity positively increases as it whips around turns. Overall, though the Snake never leaves the ground nor does it ever change speed, the ride is still very enjoyable for riders. **

=**Chapter(4) Section (10)**=


 * What Do You See?**
 * In this picture, there is a very large roller coaster with many turns, loops, and large heights. It looks very dangerous as you can see many people falling off of the track, and could easily die. This ride could be too dangerous to ride because there are too many spots that can cause serious injury. **


 * What Do You Think?**
 * 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. **


 * Physics Talk**
 * Roller coasters have to be safe to be fun so that no one gets hurt. Coasters aren't safe if the acceleration is more than 4g's because thats where the human body is comfortable. Acceleration is usually less than 1g on straight inclines. When a coaster goes around a turn, its acceleration can be much more than 1g. a=v^2/r. To find the amount of g's, you take the acceleration of the point and divide it by 9.8. The largest centripetal acceleration requires the larges centripetal force. The sum of the normal force from the track and the weight must equal the required net force. Fnet=mv^2/r. Another safety feature is that the cart needs enough speed to complete the loop. Normal is 5gs at the bottom of the curve and 3 g's at the top of the curve. Acceleration has to be greater than 9.8 m/s^2 at the top of a loop. **

1. The maximum safe acceleration on a roller coaster is 4 g's. 2. Two ways too keep the acceleration low are to make the radii larger and lower the velocity. Also, if you make the height smaller, the GPE becomes smaller, which decreases the KE.
 * Checking Up**
 * 3. the acceleration is the greatest at the bottom of the loop. **
 * 4. the normal force is the greatest at the bottom of the loop. **

1. You will check to make sure that the acceleration is no more than 4g at any point. Also, if there is any loops you have to make sure that the coaster will have enough acceleration to make it around the loop fast enough so riders do not fall out. 2a.GPE=KE mgh=1/2mv^2 (9 .8)(h)=1/2(20)^2 h=20 m 2b. a=v^2/r =20^2/12 =33.3 m/s^2 2c. 33.3 m/s^2 / 9.8=3.4 g's. This is safe because the maximum amount of g's considered safe is 4. 2d. 9.8*4=39.2 m/s^2 39.2=v^2/12 v=21.7m/s. This is not safe. 2e. 39.2 = v^2 / 7 v = 16.57m/s there are safety concerns at this speed 3a. Ac = v^2 / r = 25^2 / 10 = 62.5m/s^2 3b. 62.5/9.8 not safe because its more than 4g's 4a.GPE=KE mgh=1/2mv^2 (9.8)(50)=1/2(V^2) v=31.3m/s. The speed will be this at the bottom 4b. a=v^2/r a= 96m/s^2 at the top. 4c. Ac=v^2/r 96=v^2/10 v=24m/s 4d. 58m/s^2 4e. no 5a. GPE = KE mgh = .5mv^2 (9.8)(16) = .5v^2 v = 8.9m/s 5b.GPE=KE mgh=1/2mv^2 9.8h=1/2(8.9^2) h=20m 6a. Ac=v^2/r =12^2/18 =8m/s^2 6b. Fc=mv^2/r =(900)(12)^2/18 =7,200 N   6c. The normal force of the track and weight provide the centripetal force. 7a. Ac = v^2 / r = 20^2 / 15 = 26.7m/s^2 7b. Fc = mv^2 / r = (900)(20)^2 / 15 =24000N 7c. The roller coaster is safe since the centripetal force is 24000N while the maximum is 25000N. Since the force is less than the max, it is safe. 8a. The centripetal acceleration will not change as mass changes since mass has nothing to do with centripetal acceleration, as seen in the equation Ac = v^2 / r  8b. It is the same speed because only mass is being added. 8c. Yes it will require a stronger material because the normal force from the track will need to be greater because weight is increasing.
 * PTG **


 * Physics Plus**




 * What Do You Think Now**
 * Knowing that a person can die or get seriously injured creates tremendous negative thrill, to the point where it will not attract people to the ride. If I knew that a certain ride had a caution sign of death, I would not go on it because it is not worth it. People will not want to risk their lives to go on a ride, so the ride will not make any money. This would end up hurting the park's business and could force them to shut down if no one comes to the rides. To ensure the ride is safe, one must be sure that the person is strapped in at all times, and when there are very sharp turns, the cart stays on the track. Also, when going around a loop vertically, the coaster must have enough speed to complete the loop, or the passengers will fall and die. Also the maximum acceleration a roller coaster can reach and still be safe if 39.2 m/s^2 or 4 G's . **