Chapter+4

=Chapter 4:=

Section 1toc :
What do you see? The man is thinking about a roller coaster and the woman is pushing him around in a wheely chair, changing his velocity and direction. What do you think? When the roller coaster makes a big drop along with a sharp turn is when most people scream.

Homework: Look up roller coaster design on the Internet and list at least two roller coasters mentioned. Describe their most important features. Kingda Ka at Six Flags Great Adventure in New Jersey: is 556 feet tall. The train is launched by hydraulic launch mechanism to 128 miles per hour in 3.5 seconds. Has an accelerator coaster design. Millennium Force at Cedar Point in Ohio: It is a steel roller coaster. It is 310 feet tall. It has a Giga coaster design- complete circuit coaster with a height from 300-399 feet.

Physics talk: Acceleration: The change in velocity divided by the time elapsed; acceleration is a vector quantity, it has magnitude (size) and direction. Speed is the distance traveled divided by the time elapsed. Velocity is the displacement divided by the time elapsed. It is also a vector it has MAGNITUDE and DIRECTION. Displacement is a measured distance with a direction included. scalar: a quantity that has magnitude (size/amount), but no direction. A vector is displacement divided by the time elapsed; velocity is a vector quantity, it has size and magnitude. Checking up: 1. Explain the difference between distance and displacement. Displacement is distance but with direction included. Distance does not pertain to direction. 2. You went to school and back home a total distance of 2 km. What is you displacement? Your displacement is zero because you end up back where you started. 3. what is the difference between speed and velocity? Speed is the distance traveled by the time elapsed. It has no direction. Velocity is a displacement divided by the time elapsed; velocity is a quantity vector and it has magnitude and size. 4. How can you find the acceleration of an object? Acceleration can be found by dividing the change in velocity by the time elapsed.

physics to go: 10. make the radius of the turns bigger. make the drops shorter. make the angle more gradual.
 * 1) [[image:depolroller.jpg width="192" height="144"]]
 * 2) The biggest thrill in the Terminator Express would be the drops because you feel like you are weightless and you are going so fast.
 * 3) a) They both have the same speed b) 40000km/24h = 1667 km/h c) You get a thrill because your body is not used to it so it is surprising and exciting
 * 4) (16-4)/3 = 4 m/s^2
 * 5) a) speed b) velocity c) velocity d) velocity e) displacement
 * 6) -v=d/t 10/2= 5
 * 7) v=d/t 5/t v= 1
 * 8) 25-0/10

What do you think now? The part of the roller coaster that has the greatest acceleration is where the most scream will occur. The turns will the the scariest because there is where there is the greatest amount of acceleration and change in velocity.

Section 2:
What do you see? On cart is going slow and the riders are sleeping and bored. The other roller coaster is going fast with a greater acceleration. What do you think? The second cart will give the bigger thrill because its track is steeper. The track with the 90 degree angle will provide the greatest thrill because it will have the greatest acceleration. Physics Talk: The speed of the ball or roller coaster is determind by the initial height of the track. Gravitational potential energy: The energy a body possesses as a result of its position in a gravitational field. Kinetic energy: the energy an object possesses because of its speed. When a ball comes down an incline the GPE decreases because the height above the ground level is decreasing. When the ball travels down the incline the speed increases and so does its KE. GPE= mass of object x strength of gravitational field x height GPE=mgh. Joule is the SI unit for all forms of energy; equivalent units for the joule are kg x m^2/s^2 or N x m. Mechanical energy is the sum of kinetic energy and potential energy. Checking up: 1. What effect does changing the length of the incline have on the speed of the ball when it rolls to the bottom? The higher the initial height the faster the ball will travel. 2. How does the gravitational potential energy of an object change with its height? with its mass? When the ground level height of the object is changing the GPE decreases. If the mass is heavier the GPE is going to be greater. 3. How does the kinetic energy of an object change with its speed? its mass?KE gets greater while the speed of the object gets greater. The greater the mass the greater the KE. 4. As a roller -coaster car rolls down a hill, what happens to the gravitational potential energy it loses? The GPE 5. If a roller -coaster has 40,000 J of gravitational potential energy when at rest on the top of a hill, how much kinetic energy does it have when it is 3/4 of the way down? 30,000 J PTG: 1. Both cars will have the same speed at the bottom of the incline because they are both released at the same initial height. 3.
 * Height || GPE || KE || Total (Gpe + KE ||  ||
 * top(30) || 60000 || 0 || 60000 ||  ||
 * Bottom (0) || 0 || 60000 || 60000 ||  ||
 * halfway (15 m) || 30000 || 30000 || 60000 ||  ||
 * 3/4 down (7.5 m) || 15000 || 45000 || 60000 ||

4. 5.
 * height (m) || GPE (J) || KE (J) || total (GPE+ KE ||
 * top (25) || 75000 || 0 || 75000 ||
 * bottom (0) || 0 || 75000 || 75000 ||
 * halfway (12.5) || 37500 || 37500 || 75000 ||
 * further down (5) || 15000 || 60000 || 75000 ||

6. 7. (0.2)(9.8)(.75) = 1.47 J 8. No because the mass cancels out when you do GPE=KE 9a. B because that is the lowest point so it has the least GPE and the most KE 9b. The cart with be traveling the same speed at point C and E 9c. The roller coaster is traveling faster at point D because it comes right after that large drop. 10b.There isnt enough kinetic energy for the cart to make it all the way up the second hill. 11. 11. What do you think now?
 * || height || GPE || KE || total ||
 * bottom || 0 || 0 || 50000 || 50000 ||
 * top || 25 || 50000 || 0 || 50000 ||
 * top of loop || 15 || 30000 || 20000 || 50000 ||
 * horizontal loop || 0 || 0 || 50000 || 50000 ||

The roller coasters will both have the same speed because mgh= .5mv^2 and since the masses cancel out the heigh is what determines the speed, and in the picture they both start from the same height.

Section 3: What do you see? Students are measuring how high the frog pop up toy travels through the photogate timer. Another student is collecting the data and another is holding the photogate in place. What do you think? They travel at a certain speed and built up their momentum in order to make it up its highest peak. It shouldn't cost more to send a roller coaster full of people because it goes a certain speed regardless of how many people in the cart. Physics Talk: Spring potential energy: the energy stored in a spring due to its compression or stretch. GPE=KE=SPE. All energies are measured in Joules. The total number of Joules must stay the same if energy is stored. If there is less, than the system lost energy. The larger mass has a smaller height and the smaller mass has a larger height. Electric energy from a power plant brings the roller coaster to its highest speak. When the cart is highest point the total GPE and KE of the roller coaster remains the same. SPE= 1/2kx^2 k is the constant, x is the amount of stretch or compression of the spring. GPE+KE+SPE=constant mgh+1/2kx= constant Checking up: 1.What happens to the spring potential energy of a pop up toy after it leaps off the table? The spring potential energy turns into both kinetic and gravitational potential energy as it bounces off the table .2. A pop up toy has 2 J of spring potential energy before popping. How musch kinetic energy will the toy have just after leaving the table? 2 J because it is all equal. 3. A pop up toy has 2 J of potential energy before popping. How much gravitational potential energy will it have at the top? It has 2 J of potential energy. 4.What two factors determine the amount of SPE that is stored in a spring? The spring constant and the compression of the spring. PTG: 5. The second hill on a roller coaster cannot be higher than the first because there is not enough SPE to get up the second hill.There will not be enough energy to make it up the second hill. It can only have the max height of the first hill. 6. The cart will eventually will slow down due to friction. It doesnt have enough momentum to make it up. friction is a force that creates work and work takes away from the other forms of energy. 7. GPE= mgh (300)(10)15=4500 J 8.KE= (1/2)mv^2 (1/2)400(15^2) 45000 J b.GPE=mgh 400*9.8*15= 45000 c. How high can this roller coaster go with these speeds? GPE=KE 10h=(1/2)15^2

9.The GPE is increases to the KE 10.same 11. GPE mgh .02*9.8*4 .078 KE= (1/2)mv^2 1/2*0.02*27^2 0.073 b. Yes GPE= KE .13m 12. GPE = EPE mgh=1/2kx^2 300*9.8*18=1/2k4^2 6600 N/m, 300*9.8*18=1/2*6600x^2 4.62 13. KE= EPE =1/2kx^2 1.85 What do you think now? How does a roller coaster get up to its height point? A motor brings the roller coaster up the hill. There is more GPE and work being used so you need more electrical energy so it is more expensive if the roller coaster is full.

Section 4: What do you see? There are two pictures one there is a roller coaster on Jupiter and one on the moon. The children riding the coaster on the moon are sleeping and bored. The one on Jupiter they are having fun. There are different gravities on both the moon and Jupiter. You would feel heavy on Jupiter becasue there is a lot of gravity. What do you think? No gravity does not have direction. Gravity is pushing the people in Australia in the opposite direction which holds them down.

Physics talk: gravitational lfiels: 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. Newtons 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 distances between the two bodies increases. Gravity: the force of attraction between two bodies due to their masses. 1.What is the direction of the gravitational field in your classroom? the gravitational field points inward towards the center of the earth. 2. Using the idea of field lines, where is the gravitational field the strongest? the fields are the strongest where the lines are the closest together. The farther away from the earth the less gravity. 3. If you triple the distance between two masses what happens to the force of gravity between the two masses. It triples as well because its directly proportional. 4. What is the force that holds the Moon in its orbit around the earth? Gravity holds the moon in its orbit 5. Approximately what is the shape of the orbit of the planets around the sun? The plants move in an ellipses.

PTG:

1 . If the gravitational force between the two asteroids doubles, the force would be 125 N. 2a. The gravitational force would be 1/4 of original. 2b. The gravitational force would be 1/9 of the original. 2c. The gravitational force would be 1/16 the original. 3. Everyone trusts gravity because it keeps our bodies down the Earth and always will. Also, nothing can float around in the air because to do gravity of Earth, what goes up must come down. We have always had gravity. 4. They are basically the same because the difference is so tiny 5a. The water on the side of Earth facing the moon is closer to the moon than the center of Earth. The water is attracted to the moon 5b. There are high tides on the side of earth facing the moon because the water moves independently to the Earth. Also, the water is a much less mass than the moon. The gravitational field around the moon attracts the water so it rises up with the force. There is an attraction to the moon so that is why water is dispersed. 5c. There is an an uneven distribution of water on Earth's surface because there is land on the other parts. Also, the water is at different distances from the moon so the gravitational force is different. They are inverse-square relation. Therefore, there are some points that the water is not closer to the moon because the waves do not reach as high. 6a. A fish's life would be different without gravity because it would not be pulled down into the water and would be flopping around in the air. They would die. 6b. Gravity holds a fish "down" on Earth because the mass of a fish is much less than the mass of the Earth. Masses are attracted, so the larger mass of the Earth attracts the fish. 7. a) 1/4 b) 1/9 c) 1/16 d) 4x 8. a) 2x b) 3x c) 4x d) 1/2x 9. a)4x b) 9x c) 16x d) 1/16x 10. a) 2x b) 9x c) 6x

Physics Plus: 1. a = v^2 / r 2. v=(2* pi)(3.84*10^6/2440800  v=998.505 m/s  3. a=v^2/r  a= 998.505^2/3.04*10^8  a= 0.0025 m/s

What do you think now? 1. Gravity does have a direction,it points towards the largest mass, which is the center of the earth. 2. People in Australia is attracted to the center of the earth, therefore it is held up. Gravity attracts the mass of people with the mass of the earth.

Section 5:
What do you see? There are two different scenes both weighing meat but they are weighing the meat different ways.

1.Can you use the same scale to weigh a canary and an elephant. No, you cannot use the same scale because their different sizes are not comparable. 2. A bathroom scale calculates your mass and then multiples it by gravity.

Physics Talk: Hooke's Law: the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring. force exerted by the spring =spring constant X spring stretch. f=-kx. The negative sign in the equation indicates that the pull by the spring is opposite to the direction it is stretched or compressed. The spring constant (k) indicates how easy or difficult it is to compress the spring. 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. W= mg or F= ma. Weight is a force because there is no acceleration. Graphs give you the ability to predict points you have not measured. It also helps to see the relationship Checking up: 1. A spring obeys Hooke's Law. If the force on the spring is increased five times, how much does the stretch of the spring increase. 5 times because they are directly proportional. 2.What is it meant by the "spring constant" of a spring? The spring constant (k) indicates how easy or difficult it is to compress the spring. 3**.**How does the weight of an object in newtons compare to its mass in kilograms? since w=mg, the weight of an object is equal to its mass multimplied by gravity 4. When you stand on a bathroom scale, how does the force of compression of the spring compare to your weight? the scale reads the spring compression but then multiplies it by gravity 9.8, to give you your weight. Calibration. 1. a) w=mg w=100(9.8) w=980lb b) w=mg w=10(9.8) w=98lb c) w=mg w=60 (9.8) w= 588lbs 2. a) 25/130=1/x =520 b) 25/100=1/x 4000 c).25/50= 1/x 200 N 3. slope= 14.9 4. mg=kx 12 (9.8)= k(.03) 400 5. He wrote this because each are directly proportional to each other. As the force increases the strech will also increase 6. 15 because the larger the spring constant which makes it more difficult to pull. 7. 150 N/m 8. A spring scale works when a weight is hooked from a scale. As the spring stretches there is a displacement between the two distances. Using hookes law, you can figure out the weight of this object. 1.Can you use the same scale to weigh a canary and an elephant. No, you cannot use the same scale because their different sizes are not comparable.The canary would be weighted on a scale with a smaller spring constant opposed to a scale for an elephant that would have a large spring scale constant. 2. A bathroom scale calculates your mass and then multiples it by gravity. the scale reads the spring compression but then multiplies it by gravity 9.8, to give you your weight. Calibration. The spring converts the distance into weight.

Section 6
What do you see? There are two people in elevators one man and one boy. The man is dropping and his weight is zero. The boy is moving up and weighs more because there is a lot of force on him. Weight is a very relative value. What do you think? 1. Your weight does change when you are riding on a roller coaster. there is more force on you when you are on the roller coaster. You also feel heavier when you are going down. 2. If you were on a batherroom scale your weight would change on a roller coaster because there is more force on you. Physics talk: **When an object is at res the sum of the forces on that object equal zero. When it is at rest there is no acceleration or net force acting on it. If an object accelerates up there is an increase on the spring scale reading. If you were sitting on a scale on a roller coaster and were at rest or moving at constant speed your weight would be the same. If you are accelerating up the scale puts a force up on you. That force is responsible for the acceleration. The scale reading will be higher than you normally on because the force is pushing up on you. Newton's 1st Law: object at rest stays at rest, or in motion stays in motion, unless acted on by unbalanced force ** **Newton's 2nd Law: unbalanced force creates acceleration; the bigger force is in the same direction as acceleration & vice versa** **show this w/ motion map & FBDs. (increase in v & a same direction, decrease v & a opposite motion)** **Net Force = ma** **increasing speed: velocity and acceleration point in same direction** **decreasing speed: velocity and acceleration point in opposite directions** **Net Force and Acceleration point in the same direction** **the bigger force is in the same direction as net force** Checking up: 1.the net force is zero 2.the weight will be heavier 3.There is a force acting in the opposite direction on you. 4.zero because there is no force 5. Air resistance will affect the rain drops. PTG: 1. Vf = Vi(0) + at  a) (9.8)(2)  =19.6 m/s  b) vf=(9.8)(5) =49 m/s c) vf= (9.8)(10) =98 m/s  2.  (a. (1.6)(2) = 3.2 m/s (b. (1.6)(5) = 8 m/s  (c. (1.6)(10) = 16 m/s
 * **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 ||

increasing speed: velocity and acceleration point in the same direction. Decreasing speed: velocity adn acceleration point in opposite directions Net force and acceleration always point in the same direction. The bigger force is in the same direction as the net force.

5: increasing down and decreasing up Net Force = m a  Nscale - W = ma  6. v is up acceleration is up so the biggest force points up. N of the scale is greater than weight so he seems heavier. 7.When you start moving velocity is down so acceleration is down as well. Net force is down so the weight is greater than the normal force. b) N=ma+mg =(50*-1.5)+(50*9.8)  415N  8. a and c) w=mg 50*9.8 490N b) N-mg=ma N=50(2) +490  N=590 N  9. Drawing one: in sketch one, the elevator has no acceleration because the weight on the scale is the same as the persons actual weight. This means that the elevator is either at rest or moving with a constant speed.  Drawing two: in this picture the elevator is in free fall so that is why the person in the picture is lifted of the scale. the person is moving at the same rate as the scale with no force pushing up on him so the scale would read 0. the acceleration would be 9.8m/s^2  Drawing three: In this picture, the elevator is accelerating upward so the scale has a higher reading than the persons actual weight. The person would also feel heavier because of the force that the scale exerts up on the person.  10. They would find the loops exciting because they feel heavier when inside in the loop. A change between increasing upward/downward acceleration and decreasing upward/downward acceleration would also be a good idea. The increase acceleration upward would make them feel heavy and the increase down would change their feeling to light. The decrease upward would then keep them feeling light, but the decrease downward would have them feeling heavier.

What do you think now?What do you think now? no your weight would not change, just your apparent weight would change if you were on a roller coaster because there is a force on you that makes you feel heavier, especially when you are going down. Your weight would be inaccurate if you were to be on a scale when riding a roller coaster. You actual weight does not change though. increasing speed: velocity and acceleration point in the same direction. Decreasing speed: velocity and acceleration point in opposite directions. Net force and acceleration always point in the same direction. The bigger force is in the same direction as the net force.

Section 7:
What do you see? there are people riding down a roller coaster that is leaning off the track. there are other roller coasters going around clothoid loops What do you think:The weight is bigger than the normal force so it is keeping you inside the cart. physics talk: centripital force is any force that points to the middle of the circle. centripital acceleration always points to the center as well tangental velocity - speed is usaually constant but there is always acceleration if ac is = to 0 then you are moving in a straight line. equation is EFc=mv^2/R= Ac increases radius makes centripial foce go down when increase the mass force increases increase velocity force is increased as well. to find apparent weight- identify the acceleration find the force and that equals the bigger force. less than 4gs are safe for acceleration clothoid loop- at the top the radius is smaller and bigger at the bottom. 1. centripital force 2. yes you are accelerating 3. normal and weight 4. Normal force is responsible. 5 on the mass its direct relationship and radius is inverse and velocity is direct square

PTG: 1.

2.a) The force of friction acts as the centripetal force on a car. Friction makes you travel in a circle. b

6.No the speed doesnt change. the velocity changed because the direction changed. v2-vi=change in v 20^2+20^2=28.7 m/s tan=20/20 =45 degrees 7.v^2/r=a 20^2/200=2 10. 500N 3500N 6500 N  13. a) C-heavier b)D-cant tell both acceleration and net force point down c)E-heavier normal is bigger d)F- heavier normal is greater than weight e) Lift- you should feel normal 14.  a. Bottom of hill #1- up b. Top of vertical loop- down  c. Bottom of vertical loop- up  d. Bottom of hill #2- up  e. Lift hill (going up at constant speed)- zero  f. Horizontal loop- to center  g. Back curve- to center  Physics Plus:  1. a) The other side of the equation gets larger.As the mass increases the net force increases as well b) The velocity increases Fnet also increases by a lot because it has a square relationship. 2. The track's force must be quadrupled.  3.The force gets smaller as well 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 then a smaller force is required.  5. No force is required because it would continue in a straight line without any force.  What do you think now?  Inertia presses you into your seat. Centripetal force pushes towards the center. Normal force pushes towards the center of the roller coaster when your on ton.

section 8
What do you see? There is a roller coaster with a large hill and people doing work to pull a cart up. They are sweating, carrying the cart up the hill. Once at the top of a hill, the cart flies down the incline really fast.

What do you think? It takes more energy to pull the roller coaster up a steep incline than a gentle incline because the height is higher. It is less difficult to walk up a gentle incline because the steepness is not as hard on our muscles and force we need to use to get us up the hill is decreased.

Physics Talk --work: the product of displacement and the force in the direction of the displacement; the energy transferred to an object W = force (parallel to the displacement) x displacement W is the same regardless to the angle of the incline Force is larger on a steeper incline ; but the distance along the incline was smaller the work done by a force on an object is the energy transferred to the object work is needed to bring the coaster to the top of hill work increases the energy of the system work to lift cart up the ramp is = work to lift it vertically to that height when you lift vertically, the force = in magnitude to weight of the cart vertical displacement is the height that it must be lifted W = F x d W = weight x height W = mgh More Roller Coaster Energy *cart is raised with electrical energy supplied by a motor electrical energy calculated by measuring voltage, current, and time steam also could raise it work is done by the spring (by electricity or by heat) coaster system gains that amount of energy & GPE is increased by that amount work is also done by friction and air resistance which for example will become heat energy and dissipate into the air Braking the Roller Coaster brakes use friction to convert KE into thermal energy (heart: friction (brakes) need back-up too = large spring that could compress, as it compresses, KE is stored as SPE  make a final hill  power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred  P = work done / time elapsed  watts: the SI unit for power; 1 W = 1 J/s

Checking Up 1. When a spring scale is used to do work pulling a cart to the top of an incline, the energy has turned into the GPE 2. The roller coaster gets its GPE at the top of the first hill from work done by the spring that gains that amount of energy 3. They use a ramp when loading a truck because the force is decreased so it is not as difficult to do. work to lift up the ramp is = work to lift it vertically to that height, when you lift vertically, the force = in magnitude to weight of the cart, vertical displacement is the height that it must be lifted 4. When the brakes stop a roller coaster, the KE is converted into thermal energy 5. unit for power is watts. 1 W = 1 J/s

PTG 1 a. The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline. b. As the cart went from the top to the bottom, all of the work is done by gravity. c. All of the work is don't by the spring as the spring compressed d. SPE = 1/2kx^2 e. The total energy just before it hits the spring is GPE. f. You begin to slow down just when you first touch the spring. 2.  a. W = F x d   work is zero because the force and distance are perpendicular, or not in the same direction. b. W = F x d W = 60 x .5 W = 30 N c. W = F x d  W = 75 x 40 W = 3000 N d. W = F x d  W = 500 x .7 W = 350 N 3. Instead of simply saying to "conserve energy," you could say "conserve energy within a system" because this relates directly to KE, SPE, GPE, and W. This energy is constantly being transferred and conserved except when it is lost to friction, heat energy, sound energy, etc. 4. If clay was added, the mass would increase, so the force would increase. Therefore, the distance it would travel would decrease to keep Work consistent. Then, the GPE and KE would increase. 5 a. W = F x d  W = 10,000 x 20 W = 200,000 N b. P = work / change in t  P = 200000 / 150 P = 1333 1/3 J/s 6. On the way up the ramp the roller coaster is gaining GPE and the motor is performing work on the roller coaster cart. The work from the motor increases the energy of the roller coaster. At the top, there is not more work by the motor, but there is some work by friction with the air and track. Up the first incline (W to GPE) down hill (GPE toKE) up loop at the top (KE and GPE) back curve (KE) up second hill (GPE and KE) horizontal loop (KE) braking which is (work).

What do you think now?

It takes more energy to pull the roller coaster up a steep incline than a gentle incline because the height is higher and W = GPE. and GPE is mass times gravity times height. It is less difficult to walk up a gentle incline because more force is needed to get up a shorter distance. It takes less force to get us up a longer distance.

section 9:
What do you see? A girl and and a boy thinking about a roller coaster. The girl is thinking about the energy and the boy is thinking about force. The girl has more equations written down because it is easier to use energy. What do you think? The top of the inside of the clothoid loop will be the most thrilling part. Even though the speed is the same because there are loops and turns where there is more force making it feel like you are going faster etc. Physics Talk: Vector measures direction and includes the size and energy, weight. Scaler quantities are speeds and distance, your age, time, a quantity, mass. ( whether you can draw an arrow towards it or not. If you can it would be vector). Scalier- regular arithmetic to add. Vector addition techniques - that take direction into account. same direction add- different direction subtract. right angles - Pythagorean and trig (inverse tan). Use energy when scalier quantity and forces when vector. Use energy if there is work involved. the easiest application of energy is when you have heights and velocity. when its going from one condition to another condition. or changing accelerations. The link between forces and energy is work. forces CAUSE work and work CREATES CHANGE IN energy.

checking up: 1. what process is needed to add vector quantities? pyagream 2. Energy is scaler and force is vector 3. (GPE +KE) are the same at every point as long as there is no friction. GPE depend only on the height from a reference point. two points on the track that have the same height will have the same speed. 4.no, energy considerations are path independent. Because you are not considering friction, the path does not affect the final speed.. 5. a force for example, work, would provide a change in energy.

PTG: 1.a^2+b^2=c^2 5 ^2 +5^2=c^2 50= c^2 c= 50 m/s south west b) tan x= 5/5 x= 45 degrees  2. Both roller coasters start at the same height so even if they have different slopes they will have the same change in speed and reach the bottom at the same time. The only thing that will be different is that they will get there at different times.  3. a) distance- scalar b) displacement- vector c) speed- scalar d) velocity-vector e)acceleration-vector f) force-vector g) kinetic energy - scalar h) potential energy- scalar i) work- vector 4. a) scalar b) vector c)scalar d)vector 5. energy: As you move up the first hill you gain GPE, then when traveling down it the GPE turns into KE. At the top of the clothiod loop there is both GPE and KE. Force: the force of gravity does work which keeps the roller coaster moving (increases its KE) 6. c) it is easier to analize the forces because the tract is just a straight line and the normal force is always perpendicular to the track.  7.   b) they all have the same energy because they all have the same height. c) ITs all the same d) you can ignore all the other points's energy because its all based on GPE, its height. GPE+KE must always be the same.

What do you think now? The most thrilling part of "The Snake" will be when it changes directions. When it turns left or right there will also be a change in velocity but not a change in speed. Even if the speed stays the same it will still be fun because there is still changes in velocity throughout the ride.

Section 10
What do you see? There are a lot of roller coasters. There is a gap in the tracks, people are falling off and there are carts going way to fast. What do you think? Yes people arent going to want to go on the ride if there is a great chance that they wont survive. Most people want a big thrill but not a near death experience. no my answer would not change because people want to have fun on these rides, not die. There is a difference between a fun ride and one that could injure you. Physics talk: Roller coaster safety Acceleration safe values- up to four gs ac=v^2/R to decrease the values if they were greater than four gs you could increase the radius, lower the velocity, reduce the height of the start, or increase the height of the position. Forces: fc=mv^2/R N+W=mv^2/R N-mv^2/R-mg W=1gs 2gs you would feel twice as heavy. The speed at the top of the loop has to be great enough to make it around the loop Checking up 1.4 gs is the maximum safe acceleration for a roller coaster. 2. You can make the acceleration safe by varying (decreasing) the speeds and increasing radius of the circle. 3.The largest acceleration is at the bottom of the loop. 4. At the bottom of the loop the normal force is the greatest because normal is pointing towards the middle of the center. PTG: 1. To ensure that the roller coaster is safe, these engineers must make sure that its acceleration does not exceed 4 gs, the track must be able to exert a certain amount of force on the coaster so it does not break, and the speed at the top of the loop must be great enough in order for it to be able to complete the loop. 2. a) 20m b. a=v^2/r  144/12  a=12m/s^2  c. no there is no safety concern  d. 84=v^2  22m/s  e) (17) 3.a= 25^2/10 625/10=62.5 m/s^2 62.3/9.8= 6.3 b. no this is not a safe acceleration because it exceeds 4gs. 4 a.) GPE= MGH  mgh= mv^2  9.8(50)= v^2  490=v^2  v= 31 m/s  b.) a= v^2/r a= 22.14 ^2/ 10 a= 96 m/s^2 c.) v= sqrt(a*r) v= sqrt(49.02*10)  v= 22.14 m/s  d.) 58 m/s e.) This roller coaster is safe because the acceleration isn't too high. 5  a.) mgh= mv^2 9.8(16)=v^2 v= 8.9 m/s b.) GPE= KE mgh=1/2mv^2  9.8h= 1/2(12.52)^2  h= 20 m  a.) a= v^2/r a= 12^2/18 a= 8 m/s^2 b.) F=mv^2/r F= 900(12)^2 / 18  F= 7,200 N  c.) The normal force on the track and the weight will provide the centripetal force. 7 a.) a= v^2/r  a= 20^2/15  a= 26.67 m/s^2  b.)F= mv^2/r F= 900(20)^2/15 F= 24,000 N c.) The ride is safe because the cart exerts 24,000N and the ride can exert 25,000N.  8  a.) It will not change because the mass doesn't affect the centripetal acceleration. b.) It will be going the same because the mass doesn't affect it. c.) It could need a stronger material to hold more people. What do you think now? Physics plus:







What do you think now? The aspects that could be the most dangerous if the roller coaster was poorly designed would be the top of the loop. If there isnt enough normal force than you could fall out of the roller coaster. There needs to be enough speed to make it around the top of the loop. Also the acceleration cannot exceed 4gs.