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=toc Section 1=

What Do You See
A person is pushing their blindfolded friend around and taking random turns. The person in the chair is pretending that he is on a roller coaster.

What Do You Think
The part when the people are going downhill is when most people scream on a roller coaster because that is when they are going the fastest. When you are going downhill on the coaster, it feels like a free fall, so some people get scared. This free fall feeling is what makes people scream on a roller coaster.

Roller Coasters
Two famous roller coasters are Kingda Ka at Six Flags and the Cyclone at Coney Island. Kingda Ka is famous because it is the tallest roller coaster in the world. Some parts of the ride are a horizontal launch that brings you to 128 mph from rest in 3.5 seconds. You will also shoot 90 degrees into a quarter-turn. Also, you will go 456 feet high, and then vertically plunge into a 270 degree spiral. Also, you will swoop down a valley and then up a 129 foot camel hump. The Cyclone is a very famous roller coaster that was built back in 1927. It was famous because it broke records in speed, height, and fright. Some famous parts are the 58.6 degree first drop, its top speed of 60 mph, and sharp turns that give riders the feeling that they will fall off of the track.

Physics Talk
-scalar: a quantity that has magnitude (size/amount), but no direction. -displacement- the difference in position between a final position and an initial position; it depends only on the endpoints, not the path; displacement is a vector quantity, it has magnitude (size) and direction. -vector- a quantity that has both magnitude (size/amount) and direction -speed- distance traveled divided by the time elapsed; speed is a scalar quantity, it has no direction -velocity- displacement divided by the time elapsed; velocity is a vector quantity, it has magnitude (size) and direction -Vav = d/t -if a person walks around the block, their displacement is 0 if the finish where they started, but their distance is not 0. -acceleration- the change in velocity divided by the time elapsed; acceleration is a vector quantity, it has magnitude (size) and direction -a=v/t

Checking Up
1. While distance is the measurement between two things, displacement is the distance with a direction included. 2. The displacement is 0 km. 3. Speed is the distance traveled divided by the time elapsed; speed is a scalar quantity, it has no direction. Velocity is displacement divided by the time elapsed; belocity is a vector quantity, it has magnitude (size) and direction. 4. You can find acceleration by using the equation a=v/t, where v is the change in velocity and t is time elapsed.

PTG
1. 2. The parts where there are changes of direction and acceleration are where most people get the biggest thrill. These are the parts with the biggest thrills because the changes of speed and direction can really surprise people, while sometimes going straight can bore riders. 3a. La Paz, Bolivia has the greater speed. 3b. 40000/24 = 1666.7 km/h 3c. There is no acceleration so we do not really notice the earth spinning. We are also very used to the world spinning, so we do not get a thrill out of it. 4. Vf-Vi / t = 16-4 / 3 = 4m/s^2 5a. speed 5b. velocity 5c. acceleration 5d. displacement, velocity 5e. displacement 6. v=d/t = .1m/2s = .05m/s 7. v=d/t .05m/s = .05/t t = 1s 8. a = v/t a = 25-0 / 10 a = 2.5m/s^2 10a. If I could change two things on the Terminator Express to make it so children could ride on it, I would take away the Clothoid Loop and also make the hills not as high. Children would get very scared on the loop and would most likely not be enjoyable for them. Also, many little children are afraid of heights, so smaller hills would also make the ride more enjoyable. 10b.

What Do You Think Now
The parts that produces the loudest screams are the parts with changes of direction and speed. The riders become surprised and maybe scared when these occur, so they usually scream. These changes in direction and speed is what makes riders have fun.

=Section 2=

What Do You Think
The steel roller coaster with the 90 degree angle will give the biggest thrill because that means on the way down you will have a much greater acceleration. Going downhill on a steep hill is much more thrilling to riders than going downhill on not a steep hill.

Physics Talk
GPE- the energy a body possesses as a results of its position in a gravitational field. KE - the energy an object possesses because of its speed. -by changing the slope of the incline and measuring speeds, we found out that the speed of the ball is affected by the initial height of the ball. -GPE is dependent on the ball's height and KE is dependent on the ball's speed -both GPE and KE depend on the mass of the ball -GPE=mgh -KE = .5mv^2 -m is mass of ball -g is strength of gravity = 9.8m/s^2 -h is height of ball -v is velocity of ball -the unit for energy is the Joule -the sum of GPE and KE is constant -the total energy of a roller coaster always stays the same

Checking Up
1. Changing the incline has no effect, what has an effect is what height you drop the ball from. 2. the GPE of an object changes when the height changes because GPE is dependent on height, considering the formula is GPE=mgh, h being height. The higher the height, the greater the GPE. It also changes when the mass changes because it is also dependent on mass. The heavier the mass, the greater the GPE, considering m is mass in GPE=mgh. 3. Since KE is dependent on mass and speed, the greater the mass or speed, the greater the KE is. KE=.5mv^2, so a greater mass or speed will result in a greater KE. 4. As a roller coaster rolls downhill, the GPE it loses is turned into kinetic energy. While the height of the coaster becomes lower and lower, the speed of it increases. 5. 30,000J

**PTG**
1. The speeds are exactly the same at the bottom. 3. 4.   5.  6.   7a. GPE = mgh = (.2)(9.8)(.75) = 1.47J 7b. KE = .5mv^2 = .5(.2)(.75/7.35)^2 = .00104 J  7c. The GPE and KE will be equal at the middle of the ramp. When it is higher on the ramp, the bob has more GPE. When it is lower on the ramp, the bob has more KE. So if the bob is at the middle, it will have an equal GPE and KE. 8. The speed of the roller coaster will slow down because now it has more mass. The heavier the mass, the slower the object usually moves. 9a. It is traveling the fastest from A-B because it started the highest and has the most time to accelerate downwards. 9b. From C-D and from E-F. Though they take place at different heights, the length of the downhill track is the same. This means it takes the same time to get from the top to the bottom of the downhill part of the track. 9c. It is traveling faster at D because the coaster just finished accelerating after going downhill, while at E the coaster has less speed because it was going uphill. 10b. The roller coaster cannot reach point H because it will not have enough energy to make it up to the top of the hill. The energy from point E will not be enough to bring the coaster up to point H. 11.
 * PositionOfCar-->height(m) || GPE=mgh || KE=.5mv^2 || GPE+KE ||
 * top (30m) || 60000 || 0 || 60000 ||
 * bottom (0m) || 0 || 60000 || 60000 ||
 * halfway down (15m) || 30000 || 30000 || 60000 ||
 * further down (7.5m) || 15000 || 45000 || 60000 ||
 * Position of Car--> Height (m) || GPE (J)=mgh || KE (J)=.5(mv^2) || GPE+KE (J) ||
 * top (25 m) || 75000 || 0 || 75000 ||
 * Bottom (0m) || 0 || 75000 || 75000 ||
 * Halfway (12.5 m) || 37500 || 37500 || 75000 ||
 * 3/4 way down (5m) || 15000 || 60000 || 75000 ||
 * PositionOfCar || height (m) || GPE(J)=mgh || KE(J)=.5mv^2 || GPE+KE (J) ||
 * bottom of hill || 0 || 0 || 50000 || 50000 ||
 * top of hill || 25 || 50000 || 0 || 50000 ||
 * top of loop || 15 || 30000 || 20000 || 50000 ||
 * horizontal loop || 0 || 0 || 50000 || 50000 ||

What Do You Think Now
Roller coasters with steeper hills usually thrill the riders more than coaster with hills that are not as steep. When the hills are steeper, the coaster will go faster because it is closer to free falling than a not steep hill. The thing that directly affects speed is how high the top of the hill is to the bottom of the hill. It does not matter what the track is like; it could be curved or straight, but if the starting height is the same then the speed at the bottom will also be the same.

= = =Section 3=

What Do You Think
A roller gets to the peak of the track by using its kinetic energy. It does not cost more to lift the roller coaster if it is full of people. Even if the coaster is full of passengers, it will still make it to the top of the hill.

Physics Talk
-spring potential energy: the energy stored in a spring due to its compression or stretch -bungee cords, trampolines, bent poles, etc. have spring potential energy -Kaitlin's loss in money would have resulted in the money being somewhere else -in some systems, energy can be lost - in the pop up toy and roller coaster, the total energy can be GPE, KE or SPE, but the sum of the energies must be be the same -scientists look for electrical, light, nuclear, sound, heat, chemical, and other energies -energy is measured in Joules -each energy can be calculated using measurements -the total energy is conserved. -the pics below show a pop up toy's behavior after doubling its mass -the toy with the larger mass didn't jump as high -the SPE for both toys were equal -both of their energies were equal -the larger mass had smaller height and smaller mass had larger height -a roller coaster has the most GPE on top of the hill -when it goes downhill, it turns into KE -electrical energy usually pulls the coaster to the top of the hill -GPE and KE remain the same other than the loss of thermal and sound energy -when the roller coaster comes to a stop, the KE turns into thermal energy -SPE=.5kx^2 -k is spring constant, x is the stretching amount of the spring

Checking Up
1. After popping up, the SPE turns into GPE and KE. 2. SPE = KE 2J = 2J KE = 2J 3. SPE = GPE 2J = 2J GPE = 2J 4. The two factors that determine the amount of SPE that is stored in a spring are shown in the equation SPE = .5kx^2. k is the spring constant and x is the amount of stretch or compression of the spring.

PTG
5. It cannot be higher than the first hill because the roller coaster will not have enough kinetic energy to make it over the second hill. 6. If the ride went on forever, the friction between the roller coaster and the track would eventually bring the ride to a stop. Also, the ride would get very boring to keep on going up and down the same hills over and over again. 7. GPE = mgh (300)(9.8)(15) GPE = 44100J 8a. KE = .5mv^2 .5(400)(15)^2 KE = 45000J 8b. KE = GPE GPE = 45000J 8c. KE = GPE .5mv^2 = mgh .5(15)^2 = 9.8h h = 11.48m 9. Its GPE is increasing because it is going higher. 10. Their gains are the same because they are all going to the same height. 11a. GPE = mgh (.020)(9.8)(.4) .784J KE = .5mv^2 (.020)(2.7)^2 .1458J They do not give the same values. 11b. KE=SPE .1458=.2458 SPE = .1458J 11c. GPE=mgh (.06)(9.8)h=.1458 h = .25m 12a. .5kx^2 52920J = .5k(4)^2 k = 6615Nm/s 12b. GPE = SPE mgh = GPE GPE = 70560J .5(6615)(x)^2 = 70560 x = 4.62m 13. KE = SPE KE=.5kx^2 KE = .5(40)(.3)^2 KE = 1.8J

What Do You Think Now
Roller coasters get up to its highest point by using its kinetic energy. The faster it moves, the higher it will be able to go, which means if it has enough kinetic energy it will be able to reach the top of the hills. It does cost more with a coaster full of people because the coaster needs to do more work to reach the top of hills, which cost the makers more money. When the mass is greater, the GPE and KE are also greater.'

=Section 4=

What Do You Think
Gravity has a direction, but not a specific direction. Gravity is directed towards the ground, but since the world is a sphere, gravity pushes down if you are at the north pole, and up if you are at the south pole. People in Australia are held on earth because gravity keeps them on the ground. Though they are upside down, gravity pushes to the ground, and since the ground is technically above them, gravity pushes them up, keeping them on Earth.

Physics Talk
-A "field" is an influence that one object sets up in the space around it. -1st object is called the source of the field -Earth is the source of its gravitational field -The second object is called the response object or test object, which can be examples of my body, or the moon -the second object responds to the field -the direction of the gravitational field is towards Earth's ground. -gravity is everywhere and extends to infinity -gravitational field: the gravitational influence in the space around a massive object. -inverse-square relationship: 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. -if you triple the distance, the force is 1/9 of the original force -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 either mass gets larger; the force decreases as the square of the distance between the two bodies increases. -gravity: the force of attraction between two bodies due to their masses. -All objects have mass and Earth attracts all objects -all bodies with mass attract each other -Newton's Universal Law of gravitation: -all bodies with mass attract each other -force is proportional to the product of 2 masses. it gets stronger as mass increases -force decreases as distance between the 2 bodies becomes farther -Fg =(Gm1m2)/r^2 -Fg is distance between bodies -r is distance between their centers -m1 and m2 are the masses of the bodies -G = 6.67x10^-11N x m^2/kg^2 -using newton's laws you can figure out that the moon orbits the earth which orbits the sun like the other planets -this law can accurately describe the forces

Checking Up
1. The gravitational field is towards the ground, which is why people stay on the ground 2. It is the strongest when you are on the ground, not in the air. 3. It becomes 1/9 of what it originally was. 4. The inverse square relationship shows how the moon orbits around earth. 5. The shape of the orbit is an oval.

PTG
1. 1/4 2a. Fg would be 1/4 of original 2b. Fg would be 1/9 of original 2c. Fg would be 1/16 of original 3. Gravity is trusted because it keeps people from falling off of the earth; it keeps people on the ground. 4. The acceleration due to gravity is higher at the bottom of the coaster compared to the top of it, but it is relatively not high so it can be rounded off to 9.8m/s^2 at any height of the ride. 5a. The water on Earth's side is closer to the moon. 5b. The gravitational field of the moon attracts the water that is closest to it, causing high tides. 5c. Since there is land in different places on earth, water cannot be there. Therefore, water is unevenly distributed because wherever land is not there, water is. 6a. Without gravity, the fish would not stay in the water. They would just float out of the water and into the air, so they would suffocate and die. 6b. Gravity holds the fish in the water. It holds the fish in water since masses attract and fish weigh less than earth, fish stay in the water. 7a. 1/4 7b. 1/9 7c. 1/16 7d 4 times 8a. 2x 8b. 3x 8c. 4x 8d. 1/2 9a. 4x 9b. 9x 9c. 16x 9d. 1/4 10a. 2x 10b. 9x 10c. 6x

Physics Plus
1. 1/60^2 = 1/3600 of the original force 9.8/3600 .0027m/s^2

2. v=d/t v= (2 * pi * (3.84 x 10^8) / 2440800 v= 988.51m/s 3. a=v^2/r a = 998.512^2 / (3.84x10^8) a = .0026m/s^2 4. Both of these methods are valid considering that they both ended up giving very close answers. One was .0027, and the other was .0026, so that is close enough to say that both methods are acceptable. 1. 1 year / 365 days / 3600 seconds = 1,314,000 seconds per year t^2/r^3 1,314,000^2 / (7.5x10^10)^3 4.092672E-21 2.
 * || Mercury || Venus || Earth || Mars || Jupiter || Saturn || Uranus || Neptune ||
 * Mean distance from the sun (AU) || .3871 || .7233 || 1 || 1.524 || 5.203 || 9.539 || 19.19 || 30.06 ||
 * Sidereal period of orbit (years) || .24 || .62 || 1 || 1.88 || 11.86 || 29.46 || 84.01 || 164.79 ||
 * t^2/r^3= || 7.94 || 8.13 || 8.00 || 7.99 || 7.99 || 8.00 || 7.99 || 8.00 ||

What Do You Think Now
Since my answers from What Do You Think are the same, my answers will not really change. Gravity's direction is towards the earth's ground, not up, down, left, or right. If you are on top of the world, technically gravity's direction is down considering the ground is below. If you are on the bottom of the world, technically gravity's direction is up considering the ground is above. People in Australia stay on the ground because gravity's direction is towards the ground. Gravity keeps people on the ground, so even though they are upside down, they are kept on the ground because the gravity's direction is upwards since the ground is technically above them.

=Section 5=

What Do You Think
You most likely cannot use the same scale for both a canary and elephant because of the huge weight difference. A scale that can weigh a bird would probably break if an elephant was on it. A scale that can weight an elephant would probably not even register a weight if a canary was on it. A bathroom scale works by simply finding your mass and multiplying it by the force of gravity, 9.8. The unit for this would be pounds.

Physics Talk
-stretching an object requires force -the more you stretch the object, the larger the force needed -Robert Hooke discovered this property of springs -stretch is directly proportional to force -force exerted by the spring = -spring constnat x spring stretch -Fs = -kx -Hooke's law: the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring -w=mg -m is in kilograms -f=ma -weight: the force exerted on a mass as a result of gravity; the weight force on an object due to Earth is downward, in the vertical direction. -a bathroom scale works by compressing a spring when you step on it

Checking Up
1. 5x 2. The spring constant indicates how easy or difficult it is to stretch or compress the spring. 3. The mass is multiplied by the force of gravity, 9.8 in order to find the weight of the object. 4. The compression of the spring provides an equal force to your weight.

PTG
1a. w=mg =100*9.8 = 980N 1b.w=mg=10*9.8=98N 1c. w=mg=60*9.8=588N 2a. 130*4.45=578.5N 2b. 1000*4.45=4450N 2c.50*4.45=222.5N 3a. 3b. 3c. (2-1.2)/(13-8) = .16 3d. 3e. 4. Fs=-kx 12=k(.03) 400N/m=k 5. Force is directly proportional to the spring's stretch. So as the force increases, the spring stretches or compresses more. 6. The 15N/m spring 7. Fs = -kx 3 = -k(2) -1.5=k 8. When you step on it, a spring compresses. The more you weigh, the more it compresses. The spring provides a force equal to your weight.

What Do You Think Now
You cannot use the same scale for both a canary and an elephant. If a canary's weight registered on a scale, an elephant would most likely break the scale because its weight is much more the the canary's. If the elephant's weight registered on a scale, the canary's probably would not register because it is so light compared to the elephant. A scale has a spring in it, and it compresses when someone stands on it. The heavier the person, the more it compresses. The spring provides a force equal to the person's weight, which is what is displayed on the scale.

=Section 6=

What Do You Think
Your weight does not change, the ride just gives you the feeling that your weight is changing when it goes downhill. When it goes downhill, it makes you feel like you are falling. Since you are going so fast, you actually rise out of your seat, which is what makes you feel that you are getting lighter. You also feel lighter because you do not feel gravity since you are traveling in the same direction as it's force; to the ground. When you go uphill, you feel heavier because you are moving in the opposite direction of gravity's force. Yes, the scale would read differently because you would feel heavier on the scale if you are going uphill and you feel lighter if you are going downhill.

Physics Talk
-when an object is at rest, the sum of the forces on the object equals 0 -Newton's 1st Law: an object at rest stays at rest and an object in motion stays in motion unless acted on by another force -Newton's 2nd Law: a=F/m -an object moving down at constant speed is identical to the object moving up at constant speed -when you are accelerating upwards, the scale will show a heavier reading -when you are accelerating downwards, the scale will show a lighter reading -a bathroom scale has to provide a force equal to your weight in order to make the net force on you zero -as the roller coaster starts moving up, there is acceleration up -the scale reading will be greater in magnitude than your weight -the force of the scale is larger than the force of gravity -Newton's second law states Fnet=ma -weight readings are identical when you are at rest or moving at a constant speed -when an object accelerates, there is a net force on the object

Checking Up
1. 0 2. It shows a heavier reading when moving upwards 3. You feel heavier because you are moving in the opposite direction of gravity's force 4. It shows a lighter reading because you are moving in the direction of gravity's force 5. The force that slows a raindrop is called air resistance.

PTG
1a.Vf=Vi+at Vf=0+(9.8)(2) Vf=19.6m/s 1b.Vf=Vi+at Vf=(9.8)(5) Vf=49m/s 1c.Vf=Vi+at Vf=(9.8)(10) Vf=98m/s 2a. Vf=Vi+at Vf=0+(1.6)(2) Vf=3.2m/s 2b. Vf=Vi+at Vf=0+(1.6)(5) Vf=8m/s 2c. Vf=Vi+at Vf=0+(1.6)(10) Vf=16m/s 4. Section 6, PTG #4 5. The elevator was moving increasing down since it showed a lighter reading. It could have also been decreasing up to show a lighter reading. 6. The weight shown on the scale will be heavier than his actual weight. 7a. decrease 7b. ∑F=ma N-w=ma N=ma+mg =(50)(-1.5)+(50)(9.8) =-75+490  =415 8a. a=0 ∑F=0 N=w=mg=490N 8b. ∑F=ma N-w=ma N-490=50(2) N=590N 8c. 50kg because there is no acceleration 9. when the elevator moves upwards the weight is heavier because they are moving in the opposite direction of gravity, so the person gets pushed to the scale harder. when the elevator moves down the weight is light because they are moving in the same direction of gravity, so the person does not get pushed as hard to the scale, so the weight is shown as being lighter. The person and scale are actually both free falling so the scale reads 0 because they are both moving downwards. The one on the left shows the person's actual weight because there is no acceleration. 10. Rides are more exciting with greater acceleration because you gain or lose speed faster, which surprises the riders. A person could get injured or even die when there is a free fall on a roller coaster because they are very dangerous. In our coaster, the coaster steeply moves downwards at first but is not a free fall. It goes into a loop, then over a hill, then 3 horizontal loops, another hill, and then the ride ends. Our ride is very safe and would attract teenagers and adults seeking a thrilling ride.
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || v=0, a=0, ∑F=0 ||  || N=w equal ||
 * Starting at Rest, Increasing Up || v=up, a=up, ∑F=up ||  || N>w greater ||
 * Continuing to move, Constant Up || v=up, a=0,∑F=0 ||  || N=w equal ||
 * Slowing down to top floor, Decreasing Up || v=up a=down ∑F=down ||  || Nw greater ||

What Do You Think Now
Your weight does not actually change when you go up or down when you ride in an elevator, but a scale would not show your actual weight while accelerating in an elevator. If the elevator accelerates up, the scale will show a number heavier than your weight because you are moving in the opposite direction of gravity. If the elevator accelerates down, the scale will show a number lighter than your weight because you are moving in the same direction of gravity.

=Section 7=

What Do You Think
You do not fall when you are upside down because you are still moving on the track with the coaster and you are not upside down long enough to begin falling out of the coaster. If the coaster went much slower, you would most likely fall because you would be upside down long enough to begin falling.

Class Notes
Centripetal force centripetal acceleration apparent weight in circle safety equation

tangential speed of ten remains constant

∑Fc=MAc Ac = v^2 / r

∑Fc = mv^2 / R

increase m, increase Fc (direct) increase v, increase Fc (direct square) increase R, decrease Fc (indirect or inverse)

iD Ac - center ALWAYS iD ∑F - center ALWAYS bigger force ∑F - to center ALWAYS

Physics Talk
-if you attach a string to a straight-moving vehicle and hold the string in place, the car will move in circles around the point you are holding -if the object moves in circles, it must have a force towards the center of the circle -the most thrilling parts of roller coasters are parts with change of speed or direction -normal force: the force acting perpendicular to the surface -centripetal force: any force directed toward the center that causes an object to follow a circular path at constant speed -normal force is Fn -Earth moving around the Sun has a force of gravity toward the Sun -in our rubber stopper experiment, we experienced centripetal forces -the centripetal force got larger when the speed of the stopper increased -it also got larger when the radius of the circle became smaller -centripetal force equation: Fc = mv^2 / r -Fc is centripetal force, m is mass, v is velocity, and r is radius -when a roller coaster goes around a curve, you accelerate -centripetal acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed -when a roller coaster is in a loop, the direction of the centripetal force is always changing -in a vertical loop, the centripetal force can be either the gravitational force, the normal force, or both -you feel heavier at the bottom of the loop on a coaster -how much of the normal force required to keep a car moving depends on the mass and speed of the car -in an elevator, your weight shown on a scale changes when you accelerate -in order to not faint during acceleration, pilots and astronauts have to practice and get used to the conditions -safety on a roller coaster requires you to stay under 4g's during the ride

Checking Up
1. centripetal force 2. yes 3. weight and normal forces 4. normal force 5. the centripetal force becomes greater when mass increases. It increases when the radius decreases. Speed does not matter for centripetal force.

**Physics To Go**
1a &1b and 2b. 1a. It moves in a circular path 1b. It moves in a path tangent to the circular motion 2a. normal force 6a. no 6b. yes 6c. it traveled 40m west in 2s 7. a=v^2 / R = 20^2/200 = 2m/s^2 10. Fast Moving Coaster Slow Moving Coaster 13a. C = heavy 13b. D = light 13c. E = heavy 13d. F = heavy 13e. G = normal 14a. 0 14b. down 14c. up 14d. 0 14e. 0 14f. sideways 14g. sideways
 * || required centripetal force || force of gravity (w) || normal force ||  ||
 * At top of loop || 4000 || 500 || 3500 ||
 * bottom of loop || 6000 || 500 || 6500 ||
 * || required centripetal force || force of gravity (w) || normal force ||  ||
 * Top of loop || 800 || 500 || 300 ||
 * bottom of loop || 2800 || 500 || 3300 ||

**Physics Plus**
1a. As mass increases in the equation Fnet = MAc, Fnet also increases. 1b. In the equation Fnet = mv^2 / R, if velocity increases, Fnet will also increase. It will increase more than if mass was increased because velocity is squared while mass is not. If mass doubles, Fnet doubles. If velocity doubles, the Fnet quadruples. 2. If the speed doubles, then the track must be 4x as strong, as shown in the equation Fnet=mv^2 / R. If velocity doubles, then Fnet quadruples, so the track must be 4x as strong. 3. The Fnet decreases as the radius increases, as shown in the equation Fnet=mv^2 / R. If R increases, then the Fnet would decrease. 4. The larger the radius for the curve, the smaller the force required to keep the car moving along the curve. If the urve is tight (r is very small) then a larger force is required. 5. When the stopper was in a larger loop, it took less force to keep it moving in a circular motion. When it was in a smaller loop, it took more force to keep it moving in a circular motion. Since it would take no force to have the stopper move in a straight line, a larger radius would mean less force needed. 6a. Ac = v^2 / R Ac = 12^2 / 20 Ac= 7.2m/s^2 6b. Fc = mv^2 / R Fc = (300)(12^2) / 20 Fc = 2160N

What Do You Think Now
You do not fall out of a roller coaster when it goes upside down because you are moving so fast and you are not upside down for very long. There is not enough time for you to begin falling. You are accelerating downwards since your acceleration is towards the center.

= Section 8 =

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
-a roller coaster has to get to the top of the first hill to begin the ride -work: 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 -power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred -P = W/t

Checking Up
1.It is transferred into GPE 2. It gets its GPE from the work that the cart does while moving up the hill. 3. They use a ramp because they need less force, even though its a longer distance. 4. It's KE is transferred into work because of the coaster's friction. 5. Watts, or W/t

PTG
1a. The GPE is less at the bottom. GPE = mgh. if h is lower than GPE is lower. 1b. W=change in GPE 1c. W=GPE 1d. SPE = .5kx^2 1e. kinetic and a little GPE 1f. when it hits the spring 2a. W=F*d = 0 * 7 = 0J 2b. W = F*d = 60 * .5 = 30J 2c. W = F*d = 40 * 75 = 3000J 2d. W = F*d = 500 * .7 = 350J 3. Decrease energy consumption 4. It would be heavier, which would mean more force is needed, meaning more work, meaning more GPE. 5a. 10000N * 20m = 200000J 5b. Power = work done / time = 200000/150 = 1333.33 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 takes 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.

=Section 9=

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
-vectors include numbers and direction -scalars include numbers but no direction -scalars can be added, subtracted, multiplied, and divided -speed is a scalar - when vectors are in the same or opposite direction, you add or subtract them to find the displacement -when vectors are perpendicular to each other, you solve with the pythagorean theorem -energy is a scalar -all energies are in Joules -to find the total energy, you just add up all of the energies -the total energy always stays the same, but the types of energy may increase or decrease -the only thing that can change in GPE is the height, since mass and force of gravity stay the same -if 2 points on a roller coaster are at the same height, then the roller coaster is moving at the same speed at both points -as long as the beginning and ending heights are the same, all coasters, no matter what the steepness of the hill is, will reach the same velocity -the only difference is that they might get to the bottom of the hill at different times -the normal force is perpendicular to the track -on straight tracks, normal and gravitational forces stay in the same direction -on curved tracks, normal force changes since the direction of the track changes -Force in the direction of motion creates acceleration -Work done creates changes in energy

Checking Up
1. addition or the pythagorean theorem depending on the direction of the vectors 2. energy is a scalar, force is a vector 3. -The total energy remains the same -the GPE depends on the height -if 2 points on a roller coaster have the same height, the the speed is the same at both points 4. no because as GPE goes down, KE goes up, so the total energy always remains the same 5. work

PTG
1a. change of velocity = 7.07m/s. sin45 southwest 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 3a. scalar 3b. vector 3c. scalar 3d. vector 3e. vector 3f. vector 3g. scalar 3h. scalar 3i. scalar 4a. scalar because of no direction 4b. vector because there is direction 4c. scalar because it is energy 4d. vector because there is direction 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. 6b. 6c. It is easier since the forces are always in the same direction. Even though the direction of gravity is the same always in any situation, the direction of the normal force changes in the first one, and it does not change in the 2nd one since the track is straight the whole time. 7a. 7b. The total energy is equal at each point. 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 vice versa.

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.

=Section 10=

What Do You Think
When people know that people have gotten injured or died on a ride just makes the audience not want to go on the ride. There is no point of risking your life in order to get a thrill. That fact does not make it thrilling, it just makes it dangerous. If 1/2 of the passengers died, I would still think that the ride is dangerous and not more thrilling. No one would want to go on a ride that they would probably die on.

Physics Talk
-roller coasters have to be safe to be fun -coasters aren't safe if the acceleration is more than 4g -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 -decreasing the speed will lower the acceleration -the most centripetal force is required at the bottom of the loop -the force acting on the coaster is a combination of weight and normal force from the track -An at rest cart requires no net force -Normal force up must equal the gravitational force down -Centripetal force is required for a cart to move in circles -the sum of normal and gravitational forces must equal the centripetal force -centripetal force can be calculated with Fnet = ma or Fnet = mv^2 / r -1g feels normal on earth -2g feels 2x as heavy -your acceleration is 1g in a freefall -you need enough speed to make it around a loop, otherwise you will fall

Checking Up
1. 4g 2. lower the speed or make the loops larger 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.

Physics To Go
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 = .5mv^2 (9.8)h = .5(20)^2 h = 20m 2b. a = v^2 / r a = 20^2 / 12 a = 33.3 m/s^2 2c. 333m/s^2 / 9.8m/s^2= 3.4g This is safe since it is less than 4g. When the acceleration is more than 4g, the ride is not safe. 2d. 9.8 * 4 = 39.2m/s^2 39.2 = v^2 / 12 v = 21.7m/s. there are safety concerns at this speed. 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 4a. GPE = KE mgh = .5mv^2 (9.8)(50) = .5v^2 v = 31.3m/s. This is the speed at the bottom 4b. a = v^2 / r a = 31.3^2 / 10 a = 97.9m/s at the top 4c. Ac = v^2 / R 96 = v^2 / 10 v = 24m/s 4d. Ac = v^2 / R Ac = 24^2 / 10 Ac = 58m/s^2 4e. Since the acceleration never exceeds 4g at the top or bottom of the loop, the ride is safe. 5a. GPE = KE mgh = .5mv^2 (9.8)(16) = .5v^2 v = 8.9m/s 5b. GPE = KE mgh = .5mv^2 (9.8)(16) = .5v^2 v = 8.9m/s 6a. Ac = v^2 / r = 12^2 / 18 = 8m/s^2 6b. Fc = mv^2 / r = (900)(12)^2 / 18 = 7200N 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 will go the same speed since it is only the mass changing, which does not affect centripetal acceleration. 8c. Since weight is increasing, it will need better material since the normal force of the track will be greater.

What Do You Think Now
When a ride has a high rate of death, it does not make it thrilling, it makes it intimidating. 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. Rides are fun when they are safe and thrilling, not when they can take your life away.

Physics Plus