Thrills+and+Chills-Chapter+4

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 * Nichole Formicola's Wikilog - Period 8 CP Physics - E. Burns - 2010 **

SECTION 1
There are two people. A girl is pushing a guy in a wheely chair. He has a blind fold on and he feels like he is on a roller coaster. Since the blind fold is on, the turns and the motions he is moving in are surprising just like a roller coaster might be, because he does not know what is going to come next.
 * WHAT DO YOU SEE? **

When going up the hill not many screams are let out, but when going down the hill the loudest screams are let out. Going down the hill many people get scared because your stomach goes to your throat and that where a lot of the thrill is. The first drop and falling is the worst part, because you have to get used to the roller coaster.
 * WHAT DO YOU THINK NOW? **

Displacement is a measured distance with a direction included. Displacement depends only on the endpoints, not on the actual distance of the path. Speed is the distance traveled by the time elapsed. Velocity is the displacement divided by the time elapsed. Acceleration is the change in velocity divided by the time elapsed.
 * PHYSICS TALK SUMMARY: **

1) Distance is the actual measurement of an entire path and is a scalar quantity. On the other hand, displacement is a measured distance a direction included, but only depends on the endpoints not the distance of the whole path.
 * CHECKING UP QUESTIONS: **

2) You displacement is 0, because you started out at your house and came back to it, so the endpoints are the same.

3) Speed is the distance traveled divided by the time elapsed and is scalar, which means it has no direction. Velocity is the displacement divided by the time elapsed and included magnitude and direction.

4) You can find the acceleration of an object by finding the change in velocity by the time elapsed.

1) DRAW PICTURE
 * PHYSICS TO GO: **

2) The first hill on the Terminator is the most thrilling and is where the most screams are heard, because its anticipated and is the most suspenseful. It is also the steepest. 3a) 3b) v=d/t

3c) There is no change in velocity or direction, because it is a constant speed that everyone is traveling at. 4a) a = v/t a = 8/3 a = 2.6 m/s^2 5a) speed 5b) velocity 5c) acceleration 5d) displacement and velocity 5e) displacement 6) v=d/t v=10/2 v= 5 cm/s 7) v=d/t 5=5/t t=1s 8) 2.5 10) I would change the steepness of the hills and the drops, this would decrease the velocity. Not make the hills that long, so the acceleration and speed would decrease. Make the turns more gradual, so the diameter is bigger, so the turns are not scary. Also, take the loop out.

The steepest and largest drop is the part of the roller coaster that produces the loudest screams. This produces the loudest screams, because this is what is anticipated the most and this is when you feel the lightest. This part has the most increases velocity and the change in acceleration from top to bottom makes the riders stomachs go to their throats.
 * WHAT DO YOU THINK NOW: **

SECTION 2:
There is a roller coaster with two different carts. One cart is on a flat part of the roller coaster and they passengers in the car are sleeping. The other cart is going down a hill drop and everyone in the cart is screaming with their arms up in the air.
 * WHAT DO YOU SEE? **

Since the types of roller coasters are different you may get a different thrill. Wooden roller coasters and a bit less sturdy, so you feel everything. The steel roller coaster will probably be faster. Since the drop is 90 degrees you will be in a bucket seat with a seat belt that comes down, but in the wooden, its just a bar. It depends on what the rider thinks is more thrilling.
 * WHAT DO YOU THINK NOW? **

The final velocity is directly related to the height where the object is placed. The steel ball at the top of the incline has GPE and a moving ball has KE. GPE=mgh and KE=1/2mv^2. Mechanical energy is the sum of GPE and KE. The sum of GPE and KE only remains the same if there are no losses of energy due to friction, sound, or other outside sources and no additions of energy from motors. The total mechanical energy stays the same KEb+GPEb=KEt+GPEt.
 * PHYSICS TALK SUMMARY: **

1. By changing the length of the incline the speed of the ball will gradually increase, because there will be a greater distance and period of time for the ball to accelerate as it rolls down the ramps towards the bottom. 2. GPE will change when the height changes. If the height is greater then the GPE will be greater as well. The same will happen for the mass of an object, but when doing an experiment mass is usually canceled out. 3. The kinetic energy will increase if the speed increases, because it is directly related to the velocity. This will also happen with the mass when it is not canceled out. If the mass gets larger or smaller the Kinetic Energy will change accordingly. 4. As a roller coaster rolls down a hill, the GPE that the roller-coaster loses will be transfered to the people, it will be lost as heat energy. 5. It is 30,000 joules of kinetic energy; refer to the chart below.
 * CHECKING UP QUESTIONS: **

1) They have the same speed because they both have the same initial height 3)
 * PHYSICS TO GO:**
 * **Position of Car (height m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE +KE (J)** ||
 * top (30 m) || 60,000 || 0 || 60,000 ||
 * bottom (0 m) || 0 || 60,000 || 60,000 ||
 * halfway down (15 m) || 30,000 || 30,000 || 60,000 ||
 * three-quarters way down (7.5 m) || 15,000 || 45,000 || 60,000 ||

4) 5)
 * **Position of car (height m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE + KE (J)** ||
 * top (25 m) || 75,000 || 0 || 75,000 ||
 * bottom (0 m) || 0 || 75,000 || 75,000 ||
 * halfway down (12.5m) || 37,500 || 37,5000 || 75,000 ||
 * three-quarters way down (5 m) || 15,000 || 60,000 || 75,000 ||

6) 7)height: .75m mass:.2kg a) mgh= .2(9.8)(.75) GPE= 1.47J b) 1.47J same as GPE at top c) halfway, because it is half of the total GPE+KE .735J 8) No because the mass of the cart will not affect the speed of the roller coaster, because it cancels out in GPE=KE 9) a) B--> because it has the lowest height. b) At C and F--> they have the same height. c) D because it has more KE than GPE 10) At b,d, and f there will be no GPE but will be kinetic. At c and e there will be GPE but no KE. It will not reach point H, because it is so much higher than point A and all the other points of the roller coaster. By the time you are halfway through going up to point H you will run out of KE and you will start rolling backwards. 11) WHAT DO YOU THINK NOW: Roller coasters today are usually made with a spring or a cable at the beginning of the roller coaster to launch the roller coaster up the first hill. The part of the roller coaster with the greatest acceleration is going to give the riders the biggest thrill, because its not expected. Also, the mass of the people on the roller coaster is not a factor because in the equation GPE=KE the masses cancel out. Since both of the tracks have the same initial height, they will have the same thrill because height is the only factor that matters. The GPE and KE will be the same at the bottom, top, and middle in both of these roller coasters.
 * **Position of car** || **Height (m)** || **GPE (J) = mgh** || **KE (J) + 1/2mv^2** || **GPE + KE (J)** ||
 * bottom of hill || 0 || 0 || 50,000 || 50,000 ||
 * top of hill || 25 || 50,000 || 0 || 50,000 ||
 * top of loop || 15 || 30,000 || 20,000 || 50,000 ||
 * horizontal loop || 0 || 0 || 50,000 || 50,000 ||

SECTION 3:
Most roller-coasters today start with a chain or a cable or even a spring that pulls the roller coaster up to the first hill/drop. It does not coast more to life the roller coaster if it weighs more because of the people in it, because the mass is not a factor and it cancels out. GPE=KE
 * WHAT DO YOU THINK? **

Spring potential energy is the energy stored in a spring due to its compression or stretch. The spring potential energy becomes the kinetic energy of the pop up toy, which then becomes the gravitational potential energy of the pop up toy. The total GPE and the total KE of the roller coaster remains the same except for losses due to thermal and sound energy. The energy that pulls a roller coaster up is usually electric. SPE=1/2kx^2 a spring that is difficult to compress or stretch will have a large spring constant. The total SPE+GPE+KE= the same every time
 * PHYSICS TALK **:

1) The spring potential energy increases when the pop up toy leaps of the table, and than the SPE turns into KE. 2) The Pop Up toy will have 2Joules of kinetic energy, since the SPE=2j it has to remain the same at all times. 3) The GPE will be 2Joules when it reaches max height 4)
 * CHECKING UP QUESTIONS: **

5. The second hill cannot be higher than the first because if it is the roller coaster wont have enough GPE to reach the top of the second hill. The first hill is always the highest. 6. Work due to friction creates heat--> thermal energy takes away GPE, which makes it less accessible for KE 7. GPE = electric energy (300)(9.8)(15) = electric energy 44,100 J = electric energy 8a. KE = 1/2mv^2 KE = 1/2(400)(15^2) KE = 45,000 J 8b. GPE = KE GPE = 45,000 J  8c. 45,000 = 400(9.8)h h = 11.48 meters 9. The GPE increases as the height of the ball is increases when thrown up in the air 10. They both gain an equal amount, because they are all going up to the same height, therefore the GPE will be equal at the end. 11a. The results are very similar (.078 vs. .073) 11b. KE = EPE 1/2mv^2 = EPE 1.2(.020)(2.7^2) = EPE .0729 J = EPE 11c. .4/3 = .13 m 12a. EPE = 1/2kx^2 52,920 J = 1/2k(4)^2 6,615 Nm/s = x 12b. GPE = SPE GPE = mgh GPE = 70,560 J 1/2(6,615)x^2 = 70,560 x = 4.62 m 13. KE = SPE KE = 1/2kx^2 KE = 1/2(40)(.3)^2 KE = 1.8 J
 * PHYSICS TO GO **

Yes, because even though the mass cancels out, the GPE will increase since the weight increases. When the GPE increases the more work is involved to get the roller coaster up the first hill. Therefore, the SPE will be bigger and since electrical energy is used to get the roller coaster up, the more money it will be with more people riding the roller coaster at once.
 * WHAT DO YOU THINK NOW: **

SECTION 4
The more gravity a roller coaster has the faster you go Gravity contains a direction that pushes objects towards the core of the earth. Because gravity is always pushing inwards towards the center, people living in Australia are able to be held on earth, because the gravity pushing inwards is always keeping them on the ground.
 * WHAT DO YOU THINK? **

__**Gravitational field**:__ the gravitational influence in the space around a massive object Gravitational field lines show:
 * PHYSICS TALK SUMMARY: **
 * Earth's gravitational Field**
 * It needs a source of the field and another object to interact with the field. This is called the response object.
 * direction in which the gravitational field is going
 * the field is stronger when the lines are close together and weaker when the lines are further apart
 * some points of the field
 * that the field extends to infinity

__**Inverse-Square Relationship**__: is the force of gravity between two objects decreased by the square of the distance between them. (Newton's Law of Universal Gravitation describes the gravitational attraction between objects)
 * explains how electrostatic forces depend on the distance from an electrical charge
 * __Newton's law of universal gravitation:__ all objects with mass attract all other objects with mass
 * force is proportional to the product of the two masses and gets stronger as masses increase
 * equation:[[image:kirnumwikilog:Screen_shot_2011-03-21_at_5.16.13_PM.png caption="Screen_shot_2011-03-21_at_5.16.13_PM.png"]]
 * Fg= force between the bodies
 * r= distance between their centers
 * m1 and m2= the masses of the bodies
 * G= universal constant that = 6.67x10 -11 N*m^2/kg^2

1) towards the center 2) closer you are to, the stronger the field will be 3) force of gravity triples 4) gravitational pull 5) circular
 * CHECKING UP QUESTIONS: **

PHYSICS TO GO: 1) 1/4 of 500 --> 125 N 3) Because we have never not had gravity. Gravity has always been present on earth as long as mass exists. 4) Acceleration due to gravity is less at the top than it is when at the bottom 5a) The side of the earth with water is closer to the moon 5b) When a body of water faces the moon the tides are higher 5c) lower tides are present when the water on earth is facing away from the moon 6a) The fish would break the water bubble, because they would swim in and than it would result in all the fish dying 6b) Gravity presses down on the water so the fish can swim in it and stay in it. 7a) divided by 4 7b) divided by 9 7c) divided by 16 7d) multiplied by 4 8a) x2 the force 8b) x3 the force 8c) x4 the force 8d) Half the force 9a) Force increases by 4 9b) Force increases by 9 9c) Force increases by 16 9d) Force decreases by 1/4 10a) Force doubles 10b) Force increases by 9 10c) Force increases by 6

FG = 1/(3.84x10^8) FG = 2.60916x10 ^-9 C = 2πr Time = 2415793158/2440800 v = 988.505 m/s a = 988.505^2/3.84 x 10^2 a = .0025 m/s^2
 * PHYSICS PLUS: **

Gravity's direction is pointing inwards toward the center of the earth. Australians can be held on the earth even though they are "upside down" because since gravity is pushing towards the center of the earth at all times it allows Australians to stay on the ground.
 * WHAT DO YOU THINK NOW: **

SECTION 5:
You cannot because the elephant is so much bigger than a canary that it would probably not fit on the scale and it would probably break the scale because of how heavy it is. A bathroom scales is simple, you just step up onto it and it in return pushes back with force that is equal to your weight.
 * WHAT DO YOU THINK NOW? **

If you want to stretch a spring more, a larger force is required. Hookes law: explains very simply what restoring force a spring exerts if it is stretched. The more you stretch a spring, the larger the restoring force of the spring. force exerted by the spring=-spring constant X spring stretch Fs=-kx the negative in the equation indicated that the pull by the spring is opposite to the direction it is stretched or compressed. weight=mg force=ma
 * PHYSICS TALK SUMMARY: **

1)The stretch of the spring increased five times 2)The spring constant increases with the spring stretch and the mass added. This is a constant increase. 3)The weight=m(9.8). This is the acceleration due to gravity 4)The force of compression of the spring is equal to your weight f=mg
 * CHECKING UP QUESTIONS: **

1a) w=mg w=(100kg)(9.8m/s^2)  w=980N  1b) w=mg w=(10kg)(9.8m/s^2) w =98 N 1c) w=mg  w=(60)(9.8)  w=588 N  2a) .25/130=1/x x=578.5 N
 * PHYSICS TO GO: **

2b) 4.45(1000) x= 4,450 N  2c) 4.45(50) x=222.5 N 3a)The slope of the graph above is 14.9 N/m 3b) 3c) 3d) 3e) 4) Fs=-kx 12=k(.03) k=400N/m 5) 6) 7) 8)

A canary and an elephant cannot use the same scale, because the scale that the elephant uses will not be able to change to the little mass of a small weighed canary. A bathroom scale uses the mass of a person multiplied with acceleration of gravity to give one their weight. The elephants weight is vast compared to the canary, so they need to use different scales. Also, if an elephant was to use a regular scale, the scale that a person uses is not able to register that big of a weight.
 * WHAT DO YOU THINK NOW: **

** SECTION 6: **
Your weight does not change on a roller coaster, but a scale would read different measurements and weights at different parts of the roller coaster. When you are at the top of a roller coaster going down the hill you feel as if you are floating, but your weight never actually changes it just feels that way.
 * WHAT DO YOU THINK NOW? **

When an object is at rest, the sum of the forces on that object equal zero. Newtons first law states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by a force. The object is at rest and no net force acts on it. Newtons second law states a=f/m. When an object is at a constant speed there is no net force acting on it, therefore the object has zero acceleration. This is the same for an object moving down with a constant speed. If you were sitting on a scale in a level roller-coaster cart, at rest or moving with a constant velocity, the reading on a scale would be equal to your weight. As the roller coaster starts moving up there is acceleration up. For your acceleration to be up the net force needs to be pushing you up. When going up the scale reading will be greater in magnitude than your weight. The magnitude of the force of the Earth pulling on you would be less than the magnitude of the force of the compressed spring within the bathroom scale. Fnet=ma Apparent weight: when the elevator is at rest or moving up or down at constant velocity, your weight readings are identical **. **
 * PHYSICS TALK SUMMARY: **

1) The sum is equal to zero 2) The scale reading is going to be greater than the actual weight. 3) The scale is accelerating more weight onto your body, which is going upwards, than the weight of your body motionless. 4) The scale reading is zero 5) Air resistance
 * CHECKING UP QUESTIONS: **

1) vf = vi + at 1a) vf = 0 + 9.8(2) vf = 19.6 m/s 1b) vf = 0 + 9.8(5) vf = 49 m/s 1c) vf = 0 + 9.8(10) vf = 98 m/s 2) vf = vi +at 2a) vf = 0 + 1.6(2) vf = 3.2 m/s 2b) vf = 0 +1.6(5) vf = 8 m/s 2c) vf = 0 +1.6(1) vf = 16 3a) Yes; the lines are both equal and oppositely pushing against the block 3b) Yes 3c) Yes 5) The elevator is accelerating downwards. Decreasing up or down 6) Their weight will be larger than 600 N. 7a) Decrease 7b) ∑F = ma N - w = ma N = ma + mg N = (50)(-1.5) + (50)(9.8) N = 415 J 8a) 50 kg - 490 N : N = w = mg 8b) ∑F = ma N - w = ma N = ma + mg N = 50(2) + (50)(9.8) N = 590 N 8c) 50 kg - 490 N 9) There is a different scale reading for the student in each elevator, because the acceleration of gravitation in each picture varies. If the weight and gravitation are equal the scale will read the students actual weight, but if the acceleration is down, the weight of the person will be zero. If it is accelerating upwards with more energy than there is gravitation, the scale reads a higher weight than the person actually weighs.
 * PHYSICS TO GO: **
 * **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 ||
 * Starting at Rest, Increasing Up || v^ a^ ∑F^ ||  || N>W ||
 * Continuing to move, Constant Up || v=0 a=0 ∑F=0 ||  || N=W ||
 * Slowing down to top floor, Decreasing Up || v^ a=down ∑F=down ||  || NW ||
 * Continuing to move, Constant Down || v=0 a=0 ∑F=0 ||  || N=W ||
 * Coming to a stop on the ground floor || v=down a=^ ∑F=^ ||  || N>W ||

When riding a roller coaster your weight will never change. On the other hand the forces acting upon the rider changes. This causes the rider to feel lighter or heavier. If you were to carry a scaled on the ride you would be able to see these different forces at different points in the ride. Just because force changes does not mean weight does. The springs in the scale would read the amount of force that the rider is exerting on it and the scale will return an opposite force
 * WHAT DO YOU THINK NOW: **

** SECTION 7 **
There is not enough gravity to push you down when forces are acting upon you in a different way. The forces will than take over and the gravity will pull you down causing you to fall out of the ride.You do not fall out because the acceleration, normal, and weight are pointing towards the center of the circle, so there are force pressing against you
 * WHAT DO YOU THINK? **

the force towards the center in the normal force. In any circular motion when the object is moving at a constant speed, the force that keeps the object moving in a circle is called he centripetal force. The centripetal force is always directed toward the center. The centripetal force is not an additional force is the name given to a force like friction, tension, gravity, or the normal force. If there is a net force, an object must be accelerating. The acceleration must be towards the center, therefore this is called centripetal acceleration. In a vertical loop, this centripetal force can be either the gravitational force, the normal force of the track on the coaster car or a combination. When it is a combination of the two you much add the forces as vectors.
 * PHYSICS TALK SUMMARY: **

1) Centripetal Force 2) Yes; you are constantly changing direction 3) Weight and Normal 4) Normal force is whats responsible for apparent weight. 5) Mass increases--> Fc increases ; Velocity increases--> Fc increases ; Radius increases--> Fc decreases
 * CHECKING UP: **

1a) 1b) 2a) 2b) 6a. No 6b. Yes 6c. vf + -vi N20 + W20 sqrt(20^2+20^2) = 28.3, 45degress 7. v^2/R 20^2/200 =2 m/s^2 10.
 * PHYSICS TO GO: **
 * ~ Fast ||~ Moving ||~ Roller ||~ Coster ||
 * || Required Centripetal Force || Force of Gravity (weight) || Normal Force (track on car) ||
 * Top of Loop || 4000 N || 500 N || (4000-500) 3500 ||
 * Bottom of Loop || 6000 N || 500 N || (6000+500) 6500 ||


 * ~ Slow ||~ Moving ||~ Roller ||~ Coaster ||
 * || Required Centripetal Force || Force of Gravity (weight) || Normal Force (track on car) ||
 * Top of Loop || 800 N || 500 N || 300 ||
 * Bottom of Loop || 2800 N || 500 N || 3300 ||

13a. Light 13b. Heavy 13c. Light 13d. Uncertain 13e. Uncertain 14a. Zero 14b. Down 14c. Up 14d. Zero 14e. Zero 14f. Sideways 14g. Sideways

1a) Net Force decreases in an indirect relationship 1b) Velocity increases in a direct relationship 2) Track must be at least 4x stronger 3) Net Force decreases with the radius of the curve. 4) The bigger the radius for the curve, the bigger the force is required to keep the car moving along the curve. When the curve is tighter than a smaller force is needed 5) When more string was let out into the curve a smaller force was needed in order to complete the circle.
 * PHYSICS PLUS: **

**WHAT DO YOU THINK NOW?** There is a force that acts along with your normal force and the force of gravity which is called the centripetal force. This causes the passenger on a roller coaster to stay inside the ride at all times, because it is pushing against you. Centripetal force is a force that acts on a body moving in a circular path that directs all of the force towards the center around which the body is moving. Acceleration and Net force point to the center and always have to been in the same direction.

**SECTION 8**
It takes more work and energy to pull a roller coaster up a steep incline, because it takes more power and energy to get up. When going up a gentle incline it does not take that much energy to get up the incline.
 * WHAT DO YOU THINK? **


 * PHYSICS TALK SUMMARY: **

1. Work turns into GPE 2. From the work done to pull it up the incline 3. Work is less when using a ramp because it changes the distance moved 4. It escapes through the heat 5. Watt or J/s
 * CHECKING UP QUESTIONS: **

1a) GPE will be bigger at the top, where it will equal 0 at the bottom depending on how high the roller coaster is off the ground 1b) W = Fd  W = lx  1c) w = lx  1d) .5lx^2 1e) all of the energy is built up in the spring so all of the work and GPE and SPE are in the spring constant 1f) As it reaches the top of the incline it will gradually slow down 2a) W = Fd 150 x 7  w = 1050 J  2b) W = Fd  60 x .5 30 J 2c) W = Fd  40 x 75  3000 J  2d) W = Fd  500 x .7 350 J 3) Instead of conserving energy you should be consistent with the amount of energy that you use at one point.  4) The force exerted on the cart changes which causes the forces given off by the track to change. 5a) W = Fd 10000 x 20  200000 J  5b) P = F/∆t 200000/150 1333.33 W  6) There is work needed to go up the first and second incline. GPE is at the top. During the first drop GPE turns in to KE. The vertical loop has GPE and KE. The final curve of our coaster has a little GPE and mostly KE because of all the built up energy before. At the end there is work due to friction. This causes the coaster to stop.
 * PHYSICS TO GO: **


 * WHAT DO YOU THINK NOW: **

SECTION 9:
kids are taking a test. One knows what there doing and the other does not. One of the kids is using energy to solve and the other is using force to solve. The boy does not know what he is doing because energy is more apparent when talking about roller coasters. Energy affects the roller coaster more than the force does. Also, it is easier to measure energy than it is to measure the acceleration or the force of the track, because you can gather the variable to find energy easier than the variable needed to find the force. The turns of the snake will be the most thrilling, because since you are changing direction you are accelerating which gives a thrill to the rides. Even though the snake may be going the same speed at all times, since you change direction you are accelerating which makes it feel as if the roller coaster changed speed.
 * WHAT DO YOU THINK/SEE? **

If a description includes both a number and a direction it is a vector. There are some descriptions that include a number but no direction. Force is a quantity that always has directions. A quantity with a number and no direction is a scalar. The scalar quantity is called distance. Speed is also scalar. Displacement is described by a vector. To add vector you must draw them and use vector additions. When the two vectors are perpendicular to each other use the phytagorean theorem. Energy is a scalar. After a roller coaster begins moving downhill the sum of the GPE and KE remain the same. The roller coaster starts with GPE and as the cart moves it converts to KE. If two points on the roller coaster have the same height they must have the same GPE, which they also have the same KE. __Energy considerations tell you three things:__ 1) The total mechanical energy (GPE+KE) is the same at every point (no friction) 2) The GPE depends only on the height from a reference position since the mass and the gravitational force remain the same. 3) If two points on a roller coaster have the same height the roller coaster is moving at the same speed at those two points. The steeper the sloop the larger the gravitational force down the incline and the quicker it is to get to the bottom. Shifting directions add thrill. Your speed changed as you move to different heights. As you move closer to the ground, your speed increases. The force of gravity does work on the roller coaster and increases its KE. Changes in energy require work by a force.
 * PHYSICS TALK: **

1) Pythagorean theorem 2) energy is scalar; force is a vector 3) mechanical energy is the same at every point; the GPE depends only on the height; two points on the roller coaster with the same height have the same GPE and the same KE. 4) Yes because energy depends on the height that the roller reaches along with the speed. 5) Requires work
 * CHECKING UP QUESTIONS: **


 * PHYSICS TO GO **

1) 2) they provide the same change in speed, because since they start from the same height they have the sam GPE. Since they have the same GPE they have the same KE, which means they have the same speed. 3a) scalar 3b) vector 3c) scalar 3d) vector 3e) vector 3f) vector 3g) scalar 3h) scalar 3i) scalar 4a) scalar 4b) vector 4c) scalar 4d) vector 5) 6a) 6b) 6c) It is easier to examine the forces since there are no hills or loops at this point. 7a) 7b) All of the types of energies would be equal at these three points, since they are all of the same height 7c) Kinetic energy would be equal at all of these heights, since they are all at the same height 7d) Kinetic Energy and GPE changes as the roller coaster changes, but energy is never lost because it is impossible to kill energy.

The most thrilling part of the roller coaster will be the turns. Throughout these turns you are changing acceleration since you are turning into a different direction. The turns can be sharp and sudden, so that the riders get scared and even anticipated. The change in speed makes it more thrilling, since you are not going the same speed throughout the entire ride. If the speed remained the same throughout the ride the acceleration is still changing which makes it thrilling.
 * WHAT DO YOU THINK NOW: **

CHAPTER 10
Knowing that people can get hurt of even die on a roller coaster can change the thrill of the ride. By knowing this the roller coaster can loose its riders and can even be shut down. Yes, many roller coasters do have safety hazards and people still ride the roller coaster, because they do not believe they will be that one person to die. If the roller coaster was constantly being talked about its safety measures than more and more people would drift away from the roller coasters thrill. If it was true that about half of all roller coaster rides would result in the death of its passengers than there probably would not be roller coasters. Even though knowing there are safety measures and things have happened and people still ride roller coasters after, if it was a fact that half of roller coasters would actually result in passengers deaths than roller coaster would be ridden less frequently.
 * WHAT DO YOU THINK? **

A roller coaster will not be safe if its acceleration is greater than 4g. A free fall provided an acceleration of 1g. a=v^2/r Qualitative(no numbers): decreasing the speed at that point will lower the acceleration. This can be accomplished by changing the height from which the roller coaster descends. The largest centripetal acceleration also requires the largest centripetal force. The force acting on the coaster car is a combination of its weight and the normal force from the track The normal force required when the coaster is moving in a circle at the bottom of the loop is greater than the normal force that would support the care the the bottom of an incline. Car at rest has no net force. Normal force up must equal the gravitational force down. When the car is moving in a vertical circle the sum of the normal and gravitational force must equal the centripetal force required. SInce the gravitational force is down the normal force at the bottom of the loop is greater. F=ma F-mv^2/r
 * PHYSICS TALK SUMMARY: **

1) 4g 2) -decreasing the speed at that point -changing the height -less gravitational potential energy, will result in less KE. 3) At the bottom of the loop 4) At the bottom of the loop
 * CHECKING UP QUESTIONS: **

1) I would check the force at each point of the roller coaster, (GPE and KE), I would make sure all acceleration at each point is under 4g, I would check the sturdiness of the track and the roller coaster. 2a) mgh = 1/2mv^2 9.8(h) = 1/2(20)^2 = 20 m 2b) a = v^2/r a = 20^2/12 a = 33 m/s^2 2c)Yes 2d) v^2/12 = 39.2 v = 21.6 m/s 2e) v^2/7 = v =17 m/s 3a) a = v^2/r a = 62.5 m/s^2 3b) No because it is over 6 g's. It is supposed to be under 4 g's 4a) mgh = 1/2mv^2 9.8(5) = 1/2v^2 = 31 m/s 4b) a = v^2/r a = 31^2/10 a = 96.1 m/s^2 4c) Ac = v^2/r 96 = v^2/10 v = 24 m/s 4d) 58 m/s 4e) The acceleration is safe at the top and bottom of the loop 5a) mgh = 1/2mv^2 9.8(16) = 1/2v^2 v = 8.9 m/s 5b) mgh = 1/2mv^2 9.8h = 1/2(8.9^2) h = 20 m 6a) a = v^2/r a = 8 m/s^2 6b) mv^2/R 900(12)^2/18 = 7200 N 6c) The force of the track on the wheels 7a) a = v^2/r a = 26.6 m/s^2 7b) mv^2/R 900(20)^2/15 = 24,000 N 8a) No mass is not a factor in finding centripetal acceleration. the equation is a=v^2/r 8b) Same speed 8c) Yes it will, because the normal force from the track needs to be bigger.
 * PHYSICS TO GO: **

Knowing that people can get hurt or die on a roller coaster does change the thrill of the ride. If people knew that deaths were occurring because of a ride I would believe no one would ever ride that roller coaster again. That roller coaster would probably be taken down if this was true. If riders found out that one half of all roller coaster rides ended in the death of its passengers than no one would be riding roller coasters. Roller coasters would not be stated to be safe anymore therefore people would not trust them to keep them safe. So my answer would not change
 * WHAT DO YOU THINK NOW: **