nhoogland+chapter+4

toc ** 1. Chapter 4**

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 What Do You Think? ===== 2/28/11 The second that you drop at a high height is what produces the loudest scream on a roller-coaster. This is because you are going the fastest and you are the highest up.

Physics Talk Summary 3/1/11 ﻿A scaler quantity can be measure with a flexible piece of string or a metric tape measured placed along a path. Displacement is a measured distance with a direction included. Displacement depends on only the two endpoints, not on the detailed path. A vector has magnitude. Speed is the distance traveled by the time elapsed. Velocity is the displacement divided by the time elapsed. Velocity is a vector. Acceleration is the change in velocity divided by the time elapsed.

Checking Up Questions 3/1/11 ﻿1. Distance is not measured with direction and displacement is measured with direction. 2. 0 because your final position and your initial position are identical. 3. Speed is distance traveled and velocity is displacement traveled, both of them divided by the time elapsed. 4. Divide the change in velocity by the time elapsed.

Physics To Go 3/1/11 1.  2. The biggest thrill would be the drop because that is when the highest velocity and acceleration takes place. 3a) La Paz, Bolivia because they make the same revolution and they have a larger circumference so they have to be faster than the one with the smaller circumference. b) v=d/t v=40000/24 v=40/86400 v=4.63 m/s c) Because you are not going up or down, you are just going horizontal. 4. a= v/t a= 16-4/3 a= 4 m/s^2 5a) velocity b) displacement c) displacement d) displacement e) displacement 6. s=d/t s= 10/2 speed is 5 m/s 7. s=d/t 5= 5/t speed is 1 m/s 8. a=v/t a= 25-0/10 a= 2.5 m/s^2 10a) I would get rid of the flip and make the drops much lower because they are little and small and they aren't at the poper height and weight for those kinds of roller coasters and aren't mentally ready for that either. b)

What Do You Think Now 3/2/11

The drops and the loops of a roller coaster will create the biggest thrills. This is because that is when the highest velocity and acceleration takes place. When you are moving at a constant speed and going horizontally and not up or downwards is the most boring parts. When you are going vertically, like up or down you will get the biggest thrills. Thrills also come from changes in acceleration and going fast over sharp curves.

** Section 2 **
What Do You Think? 3/3/11 The second roller coaster would give a bigger thrill because it is less of an inline which means it is a steeper hill so you would be accelerating a lot faster as opposed to the first roller coaster where there is a smaller acceleration.

Physics Talk Summary
3/3/11 Gravitational potential energy is the energy an object has as a result of its position in a gravitational field. A moving ball has kinetic energy, kinetic energy is the energy of an object possessed because of its motion due to its speed. GPE is dependent on the height of the ball above the ground. The KE dependent depends on the speed of the ball. They also both depend on the mass of the ball. When the ball goes down the GPE decreases and the KE increases. THe unit for energy is a joule. GPE and KE are measured in joules. Mechanical energy is the sum of GPE and KE. The sum of GPE and KE only remain the same if there are no losses of energy due to friction, sound, or other outside sources and no additional energy from motors. At the braking point of the roller coaster KE is converted into thermal energy, sound, and some light. The sum of GPE and KE is constant.

Checking Up Questions 3/3/11 ﻿1. Changing the inline the higher up it goes the quicker it will reach the ground but it will have the same velocity as a lower incline ramp. 2. The higher the height and mass the larger the GPE will be. 3. The higher the height and mass the larger the KE will be. 4. As a car rolls down a hill the GPE decreases and the KE increases. 5. GPE= KE mgh=40,000 40,000/4 10,0000 (3) 30,0000 J KE

Physics To Go 3/7/11 1) They will both have the same speed at the bottom. 3)Mass of car = 200 kg g=10 N/kg or 10 m/s^2 60,000 J || 0 || 60,000 || 0 J || 60,000-0= 60,000 J || 60,000 || 30,000J || 60,000-30,000= 30,000 J || 60,000 || 15,000J || 60,000-15,000= 45,000 J || 60,000 || 4) 5) 6) 7a) GPE= mgh GPE= (9.8)(.20)(.75) GPE= 1.47 J b) KE= 1/2 mv^2 1.47= 1/2 (.2)v^2 14.7=v^2 v= 8.83 m/s 8.) The roller coasters velocity will decrease as the mass increases because it will need the same kinetic energy and the mass and velocity both directly increase the kinetic energy 9a) It will be going fastest from point a to b. b) C and F have the same speeds because they have the same height. c) It is going faster at point D. 10b) The roller coaster won't reach point H because it doesn't have enough acceleration in order to make it up to that point. 11)
 * Position of car (height) || GPE (Joules) || KE (Joules) || GPE+KE ||
 * Top (30 m) || 200(10)(30)= 60,000
 * Bottom (0 m) || 200(10)(0)= 0 J
 * Halfway (15 m) || (15)(10)(200)=
 * Three quarters (7.5 m) || (200)(7.5)(10)=15,000J
 * Postion of Car (height in meters || GPE (J) || KE (J) || GPE+KE ||
 * Top (25 m) || 75,000 || 0 || 75,000 ||
 * Bottom 0m || 0 || 75,000 || 75,000 ||
 * Halfway down 12.5 m || 37,500 || 37,500 || 75,000 ||
 * Further down 5 m || 15000 || 60,000 || 75,000 ||
 * Position of car || Height (m) || GPE (J) || KE (J) || GPE+KE (J) ||
 * Bottom || 0 || 0 || 50,000 || 50,000 ||
 * Top || 25 || 50,000 || 0 || 50,000 ||
 * Top of loop || 15 || 30,000 || 20,000 || 50,000 ||
 * Horizontal loop || 0 || 0 || 50,000 || 50,000 ||

What Do You Think Now? 3/10/11 If you ignored friction, the both of the carts will have the same speed because they both have the same initial height. If you did not ignore friction then B would have the bigger speed. Cart B has the bigger three because you are changing speed in a shorter amount of time other than from Cart A.

Section 3
What Do You Think? 3/3/11 ﻿Nowadays a roller coaster gets to its highest point by the chain and track that the roller coaster is riding on. It does cost more to lift the roller coaster if it is full of people because the mass will be heavier therefore the velocity needs to be greater.

Physics Talk Summary 3/3/11 Spring potential energy is the energy stored in a spring due to its compression or stretch. In some systems, energy is lost. Energies in a system include electrical energy, light energy, nuclear energy, sound energy, heat energy, chemical energy, and others. Each one is calculated using measurements. If you count all the energy, the total number of joules must remain the same. The total energy is conserved. On a roller coaster, the roller coaster has all it's energy as GPE at its highest point. As it is released, most of the energy becomes kinetic energy. Some small amount of the energy is converted to thermal energy and a smaller part to sound energy. The energy to pull up the roller coaster is usually electric. The equation for spring potential energy is 1/2kx^2. x is the amount of stretch or compression of the spring. The total GPE and KE are the same as the cart pulls up to the top of the hill.

Physics To Go 3/16/11 5. Because the roller coaster loses energy from the first hill so it will not have enough GPE be able to make it up the hill. 6. A roller coaster does not do this because energy is lost every time is goes up and down a hill, so by the time it gets to the end of the ride there is little to no energy left. 7. mgh (300)(.98)(15)= 44,100 J 8a) KE=1/2mv^2 KE=(1/2)(400)(15)^2 KE= 45,000 J b) KE=GPE 45,000 J c) KE=GPE 45,000=(400)(9.8)h 45000=3920h h=11.48 m 9. GPE is increasing because of the height in increasing, the GPE has to be increasing as well. 10. They all gain the same amount of potential energy because even though they took different paths, they all started and ended at the same point so it is the same height. 11a) THey should have the same values because they are equivalent. b) SPE=KE SPE= 1/2mv^2 SPE= (1/2)(.020)(2.7^2) SPE= .0729 J c) KE=GPE 1/2mv^2=mgh 1/2(.006)(2.7^2)=(.006)(9.8)h .02187=.0588h h= .37 m 12a) SPE=1/2kx^2 52,920=1/2k4^2 52,920=1/2k14 k=6,615 N m/s b) GPE=SPE GPE=mgh GPE=70,560 J 70,560=1/2kx^2 70,560=1/2(6,615)x^2 x= 4.62 m 13. KE=SPE KE=1/2kx^2 KE= 1/2(40)(.3)^2 KE= 1.8 J

What Do You Think Now? 3/16/11 A roller coaster gets to its highest point by the tracks, but electricity and motors. It costs more for a roller coaster to bring up more because because since it would have a larger mass it would need more work to be done which needs more electricity which costs money. More electrical energy would be needed for a roller coaster with a heavier mass because it needs more electricity. The more mass the less high the pop-up toy bounced because it was heavier.

Section 4
What Do You Think? 3/17/11 Gravity does not have direction. Gravity points to the center of the mass that it is on. People in Australia are still on Earth because of gravity. It pushes them the opposite direction.

Physics Talk Summary 3/17/11 a gravitational field is an influence that one object sets up in the space around it. The first object is called the source of the field. Earth is the source of its gravitational field. A second object interacts with this field. The second object is called the response object or the test object. It responds to the field and you can use it to test for the existence of the field and map it. Gravitational field lines show you: the direction of the gravitational field is the direction of the force on a mass. The gravitational field is stronger where the lines are close together and weaker where the lines are further apart. The field is present everywhere and extends out to infinity. The inverse-square relationship says that the force of gravity between two objects decreases by the square of the distance between them. Newton's law of gravitation describes the gravitational attraction of objects for one another. The strength of gravity is small. This law states that all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger either mass gets larger; the force decreases as the square of the distances between the two bodies increases. Gravity is the force of attraction between two bodies due to their masses.

Checking Up Questions 3/17/11 1. The gravitational field in our classroom is everywhere and it points to the center of the room. 2. The field is the strongest when the force lines are close together. 3. The force of gravity is cubed when the distance is tripled. 4. The force of the gravity holds the moon in place. 5. The shape is a circle.

Physics To Go 3/17/11 1) If the distance was doubled then the force would be 125 Newtons. 2a) 1/4 b) 1/9 c) 1/16 3) People trust gravity because it keeps us on the ground and it is always acting on us. 4) There is more at the bottom because you're going faster and you have more gravity acting upon you. 5a) The water is close to the moon. b) There are high tides because water has less mass than the moon so there is less gravity acting on it. 6a) Fish would have to always move in a circle and they could never swim in a straight line. b) Yes because it keeps them in the water. 7a) 1/4 b) 1/9 c) 1/16 d) 4 8a) doubled b) tripled c) quadrupled d) halved. 9a) double b) tripled c) quadrupled d) halved 10) doubles, x9, x6

Physics Plus 3/17/11 1) a=V^2/R^3 2) v=2(pi)(3.84x10^8)(2440800) v=998.505 m/s

a=V^2/r a=998.505/3.84x10^8 a=.0025 m/s^2

What Do You Think Now? 3/17/11 Gravity has a direction. The direction is that it always points to the center of whatever mass the object is. People in Australia can be "upside down" because since gravity always points to the center of the earth, that gravity is keeping them on earth too even though they are "upside down".

Section 5
What Do You Think? 3/28/11 ﻿You cannot use the same scale because even though they will both weigh the canary and the elephant accurately, an elephant would not be able to fit on the same scale as a canary. A bathroom scale works by stepping on it and the weight comes from the mass coming down on it.

Physics Talk Summary 3/28/11 If you want to stretch a spring more, a larger force is required. Many springs have the property that the stretch of the spring is directly proportional to the force applied to it. If the spring is not moving, the spring exerts a restoring force equal in magnitude to the force that stretched the spring. Hooke's law describes springs that behave in this way. The law explains very simply what storing force a spring exerts if it is stretched. The more you stretch a spring, the larger the restoring force of the spring. the equation for Hooke's law is force exerted by the spring=-spring constantxspring stretch (or compression). Fs=-kx. F is the force exerted by the spring, x is the stretch of the spring and k is the constant. The negative sign in the equation indicated that the pull by the spring is opposite to the direction it is stretched or compressed. Stretch a spring down and it pulls up, stretch a spring to the right and it pulls to the left. Compress a spring to the left and it pushes to the right. The spring constant is an indication of how easy or difficult it is to stretch or compress a spring. A stiff spring will have a large value for k and a soft spring will have a small value for k. Weight is a force. When an object is moved from Earth to the Moon, its mass stays the same, but its weight changes due to the change in the gravitational field strengths of Earth and the Moon. Many bathroom scales work by compressing a spring. The spring compresses just enough to provide an upward force equal to your weight. The more weight, the more compression of the spring is required.

Checking Up Questions 3/28/11 1. The stretch of the spring increases five times as well. 2. Spring of constant is an indication of how easy or difficult it is to stretch or compress a spring. 3. Weight changes due to it's gravitational field and mass does not. 4. The spring compresses just enough to provide an upward force equal to your weight. The more weight, the more compression of the spring is required.

Physics To Go 3/29/11 1a) 100(9.8)= 980 lb b) 10(9.8)= 98 lb  c) 60(9.8) 588 lb  2a) 130(.25)= 32.5 N  b) 1000(.25)= 250 N  c) 50(.25)= 12.5 N  3a)   c) Y2-Y1/X2-X1 2.4-2/16.2-13= .4/.032  slope=12.5 d) The slope is the k value. The k value is the spring constant. e)   Since my slope is steeper, my k value is higher, which means more force would require it to stretch which makes it difficult to stretch. 4. Fs=kx k=Fs/x k=12/.03 k=400 N/m 5. Hooke means that the larger the force, the larger that it will stretch. The force and the stretch are directly proportional. 6. 15 N/m because the larger the spring constant, the larger the force so the more difficult it is to stretch. 7. k=Fs/x k=3/.02 k=150 N/m 8. A spring scale works by the spring that is inside. The spring compresses when a mass gets put on the scale. The upward force that the compress provides is the same weight that is put on the scale. The scale converts the compression into pounds when the object is placed on it. The larger the compression, the more weight is on it.

What Do You Think Now? 3/30/11 ﻿No, you cannot use the same scales to measure a canary and a elephant. To measure a canary you have to use a spring scale, and to measure an elephant you have to use a very big bathroom scale. A scale works because of the springs that are inside of it. When an object goes on the scale, it pushes down on the springs, and the springs provide an upward force back. The force is converted into pounds while taking into account the acceleration due to gravity.

Section 6
What Do You Think? 4/5/11 No, your weight does not change when you are riding a roller coaster, you just feel like you are lighter at some points of the ride than you actually are. No, because your weight does not depend on how high up in the air you are, it just depends on your mass and gravity.

Physics Talk Summary 4/5/11 When an object is at rest, the sum of the forces on that object is equal to zero. Newton's first law-the object is at rest and no net force acts on it. Newton's second law-you realize that the object is at rest and therefore has a zero acceleration and therefore no net force acting on it. Newton's first and second laws can once again be used to explain correctly that the sum of the forces on that object equals zero.The smaller the force, the more it accelerates down. Any larger the more it accelerates up. Newton's second law states that it is the net force acting on you that is responsible for your acceleration. According to a vector diagram, the force of the scale is larger than the force of gravity. The net force is, therefore, up and according to Newton's second law, the object will accelerate up, f=ma.If you accelerate up, the scale will read a higher weight than you really are. If you accelerate down, the scale would be lower your actual weight. If you are constant or at rest, your weight readings are identical. That's because constant speed or at rest requires no net force. If an object accelerates, oyu know there must be a net force.

Checking Up Questions 4/5/11 1. There is no net force when an object is moving at constant speed. 2. The scale reading will be higher than the person's actual weight. 3. Because you feel your weight because of the contact forces between your body and other objects. 4. The scale wouldn't push up at all and the reading would be 0 N. 5. Gravity is the force that slows a falling raindrop.

Physics To Go 4/6/11 ** 1a)vf= vi+at ** ** 0 +9.8(2)= 19.6 m/s **  b)** vf= vi+at ** 0+9.8(5)= 49 m/s c)** vf= vi+at ** 0+9.8(10)= 98 m/s  ** 2a) **** vf= vi+at ** ** (1.6)(2)= 3.2 m/s ** ** b) **** vf= vi+at ** ** (1.6)(5)= 8 m/s **  ** c) **** vf= vi+at ** ** (1.6)(10)= 16 m/s ** 4) ** 5) f=ma ** ** 137-140=0 ** ** The elevator is either increasing down or decreasing up because he feels is lighter. ** 6) The persons will feel heavier because the normal force is bigger than the force of weight. His weight will continue going up as the elevator starts accelerating more.  7a) The scale will read lighter than their normal weight. b) a= F/m 1.5= 50/m  m= 33.3 kg  8a) The scale will read 50 kg.  b) a= F/m  2= 50/m  m=100 kg  9)In the first sketch the person on the elevator is moving at a constant speed. There is no change in acceleration and no change in velocity and therefore there is no change in the netforce. Because of that the persons apparent weight is equivalent to their original weight. In the second sketch, the person is increasing down. They are in freefall which means that they aren't in contact with the scale so their force exerted on it is zero. Their mass is zero. In the last sketch the person feels heavier because the elevator is accelerating upward. The floor is exerting 100 N more mass than the person is on the scale. Their normal force is higher than their weight and therefore their apparent weight is more than their normal weight. 10)
 * **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 equal W ||
 * Starting at Rest, Increasing Up || v=up, a=up, ∑F=up ||   || N greater than W ||
 * Continuing to move, Constant Up || v=0, a=0 ∑F=0 ||   || N equal W ||
 * Slowing down to top floor, Decreasing Up || v=up, a=down, ∑F=down ||   || N greater than W ||
 * At rest, top floor || v=0,a=0,∑F=0 ||   || N equal W ||
 * Starting at rest, Increasing Down || v=down, a=down, ∑F=down ||   || N less than W ||
 * Continuing to move, Constant Down || v=0, a=0, ∑F=0 ||   || N equal W ||
 * Coming to a stop on the ground floor || v= down, a=up, ∑F=up ||   || N greater than W ||

What Do You Think Now? 4/6/11 No, your weight doesn't change when you are riding a roller coaster, but your apparent weight does. When you are at the top of the the roller coaster, you feel heavier than you would feel at the bottom of a roller coaster. This is because you are exerting more normal force weight at the top than at the bottom of a roller coaster.

Section 7
What Do You Think? 4/7/11 You don't fall out of a roller coaster when the cart goes upside down during a loop because of the pressure that is opposite of you. It is pushing you down in your seat. The cart of the roller coaster has a force acting on it that keeps it moving in a circle.

Physics Talk Summary 4/7/11 Centripetal force- force that keeps an object moving in a circle. It would be one of the forces like Normal, Weight, tension. If there's a force then there's an acceleration. Tangental speed remains constant, there is acceleration only because you are changing direction. Equation for centripetal acceleration is Ac=V^2/R. Fc=mv^2/R. If you increase mass, the force gets mass. This is a direct relationship. Increase speed, force increases. This is a direct relationship. If you increase radius, decrease force. This is indirect relationship. They are all to the center always.

Checking Up Questions 4/7/11 1. Centripetal force is required to keep an object moving in a circle. 2. There is centripetal acceleration present. 3. Normal force and weight. 4. Normal force is responsible. 5. As the mass increases, the centripetal force increases as well. As the speed of the object increases, so does the centripetal force. They are both directly proportional. Velocity is directly squared. As the radius gets smaller the centripetal force increases. They are inversely proportional.

Physics To Go 4/10/11 1a) In a circle. b) A tangent (straight) line. 2a) Friction b) Leave the circle 6a) No, the speed did not change. b) v=vf+(-vi) 2-^2+20^2=square root of c 28.3 m/s c) inversetan=20/20=40 degrees. 7) a=v^2/R 20^2/200 2- m/s^2 10)
 * **Fast Roller Coaster** || Required Centripetal Force || Force of Gravity (weight) || Normal Force (force of track on car) ||
 * Top of Loop || 4000 N || 500 N || 3,500 N ||
 * Bottom of Loop || 6000 N || 500 N || 6,500 N ||

13a) Heavier b) Uncertain c) Heavier d) Heavier e) Normal 14a) Up  b) Down  c) Up  d) Up  e) Zero f) Sideways g) Sideways
 * **Slow-Moving Roller Coaster** || Required Centripetal Force || Force of Gravity (weight) || Normal Force (force of track on car) ||
 * Top of Loop || 800 N || 500 N || 300 N ||
 * Bottom of Loop || 2800 N || 500 N || 3300 N ||

Physics Plus 4/11/11 1a) Since the mass gets larger, the force will decrease because it is an indirect relationship.  b) Since the velocity gets larger, the force will too. This is because of the equation f=mv^2/r. If you were to make the velocity larger, the force will have to get larger to, to stay equal. 2) If the speed is doubled, then the force required is quadrupled. 3) The force net will decrease as well with the radius of the curve. 4) The larger the radius for the curve, the **larger** the force is required to keep the car moving along the curve is tight then a **smaller** force is required. 5. The more string that was let out, the less force was needed. Sample Problem: v- 12 m/s, r=20 m, m= 300 kg a=v^2/r 12^2/20= 7.2 m/s f=ma =(300)(7.2) =2200 N

What Do You Think Now? 4/12/11 You do not fall out of the roller coaster when it goes upside down during a loop because of the the centripetal force that keeps you up against your seat. Inertia makes you feel pushed into your seat. Net force is always pointing to the center and pushes you in the opposite direction, you accelerate downward.

Section 8
What Do You Think? 4/12/11 No, it doesn't take more energy to pull up the roller coaster up a steep incline than a gentle incline. This is because both of the inclines have the same distance. It is more difficult to walk up a steep incline than a gentle incline because

Physics Talk Summary 4/12/11 The product of force multiplied by distance is called work. The work done by a force on an object is a measure of the energy transferred to the object. The work done on a roller coaster is measured by mgh. The roller coaster car is usually raised with electrical energy supplied by a motor. Electrical energy can be calculated by measuring the voltage, current, and time. The brakes of a roller coaster use friction to convert the KE of the car's motion into thermal energy. Power is the dividing the work done by the time elapsed. Watts is the unit for power; joules per second. W stand for watts.

Checking Up Questions 4/12/11 1. The energy has gone to the top. 2. The roller coaster gets it from the height of the roller coaster. 3. Because of the height and the weight. 4. It turns into thermal energy. 5. Watts.

Physics To Go 4/12/11 1a) The cart only has GPE at the top before it is moving but at the bottom of the ramp there is no GPE. b) All the work is done by gravity. c) All the work is done by the spring. d) 1/2 kx^2 e) The energy is kinetic and GPE. f) The cart begins to slow down as it starts compressing the spring 2a) Zero because it is perpendicular work not parallel b) w=fd w= 60(.5) w=30 J c) w=fd  w= 75(40)  w= 3,000 J  d) w=fd w= 500(.7) w= 350 J 3) A better way of saying conserving energy is saying don't waste it. The law of conservation of energy says to convert it into different forms os that it is never wasted.  4) The mass on the cart would have changed because of the clay people so it would need more force to bring the cart up. There would be more work done as well as the GPE would be more. 5a) w=fd w= 10,000(20)  w= 200,000 J  b) Power= W/t power= 20,000/150 power= 133.3 W (J/s) 6) Up the first incline, there is work which changes to GPE at the top. Down the hill there is KE which is changed into KE and GPE when going through a loop. It changes to KE when you are going through the horizontal loop. WHen you get to the second hill there is GPE and KE, and finally there is work done at the end to stop the cart.

What Do You Think Now? 4/14/11 It doesn't take more energy to pull up the roller coaster up a steep incline than a gentle incline because the inclines are both the same distance. It it more difficult to walk up a steep incline than a gentle incline because you need more force. A steeper incline goes up a shorter distance so you need more force to reach the equal amount of weight.

What Do You Think Now?
4/25/11 The parts of the snake that will be the most thrilling would be the turns that move quickly and shortly. The snake will still be fun even if the speed is the same because since there is a change in direction there will still be a change in direction.

Physics Talk Summary 4/25/11 A number with both quantity and direction is called a vector quantity. Distance and speed are scalar quantities. Displacement is a vector because it has magnitude and direction. To solve for a vector you use pythagorean theorem. Energy is a scalar quantity because to find the total energy you just add all the energies of the system together. All the total energy in a roller coaster for example is constant through the entire ride. Gravity and mass are constant so the GPE is dependent on the height. A roller coaster cart at the same heights will have the same speed. Force is a vector. Weight on a coaster always remains the same pointing down, and normal points perpendicular to the track. To find the time that a cart would reach the bottom of a hill you would need to look at the forces. The steeper the slope, the more gravitational force pointing down and so the bigger the acceleration is. On a straight incline, the normal and weight force are constant and so is the acceleration. On a curved ramp the normal force is always changing. There is more acceleration and bigger thrills. When the heights are the same, the GPE is the same, and the kinetic energy is the same so the carts are going at different speeds. Energy conservation involves simple addition and force requires vector addition. Energy conservation is easier to solve. Energy and force are related.

Checking Up Questions 4/25/11 1) You need to use pythagorean theorem to solve a vector addition problem.  2) Energy is a scalar quantity and force is a vector. 3) It tells you that on a ride where friction is insignificant, KE+GPE will always equal the same thing, gravity and mass are constant so the GPE is depended on its height, and if the roller coasters are at the same height, they will be going at the same speed too. 4) The path doesn't affect it  5) A force like friction is required.

Physics To Go 4/26/11 1a) b) tanx=5/5 x=45 degrees 2) Since you have the same GPE, you have the same KE, so you have the same velocity. 3a) scalar b) vector c) scalar d) vector e) vector f) vector g) scalar h) scalar i)scalar 4a) Scalar because there's no direction. b) Vector because weight is down. c) Scalar because it's energy. d) Vector because it has a direction. 5) As an energy it is easier when you're moving, and when you're trying to find speeds, and you know the heights. As a force when you're trying to find the normal force or acceleration. 6a) b)  c) It;s easier to measure the force in roller coaster 2 because it is a straight track. This is because normal force is always perpendicular to the track. 7a)  b) The GPE at all these parts are equal because they're all at the same height. The cart has the same amount of energy. c) The kinetic energy is equivalent because their GPE is equal and they're going the same speed. d) You're able to ignore the other points because they're the same height. The mass and the gravity are always constant so the total GPE is controlled by the height. GPE+KE must always be equal at each point on the roller coaster so because their GPE is the same, the kinetic energy must also.

What Do You Think Now? I think the roller coaster will be most thrilling when it switches direction. With the change of direction, you also change the velocity. The speed may remain the same, but it will still be thrilling because the velocity is changing since the direction is changing.

Section 10
What Do You Think? 4/28/11 I think that the knowledge that people can get hurt or die in a roller coaster changes the thrill of the ride. It changes the thrill because knowing that you are doing something dangerous will raise your anticipation. The thrill would still be the same if one-half of all roller coaster rides end up in death of its passengers, because it will be even more dangerous so your anticipation will raise, but I don't think many people would continue going on roller coasters if that information was true, and they knew about it.

Physics Talk Summary 4/28/11 Since safety is very important for a roller coaster, a roller coaster cannot exceed an acceleration of 4 gs. An object in free fall has an acceleration of 1 g and a ride on a straight incline has an acceleration of less than 1 g. Centripetal acceleration occurs when the car is inside a loop. Centripetal acceleration = v^2/r. To get less acceleration, you can either change the velocity by making the height smaller or you can make the radius bigger. You can use qualitative data to decide how to fix it. The largest acceleration needs the biggest force. There is always normal force and weight acting on a cart. A cart at rest or at constant speed with always have a net force of zero. When it is moving in a vertical circle, the normal force will be bigger than weight. centripetal force= ma. Fc= mv^2/r. You feel heavier as the number of g's increase because there is more normal force on you. At 1 g you feel normal. A cart with low speed will not make it all the way up a loop because of the force of gravity.

Checking Up Questions 4/28/11 1) 4 gs is the maximum safe acceleration.  2) You can decrease the speed of the coaster which will decrease the GPE as well as the kinetic energy. The velocity with get smaller, or you can make the radius of the loop bigger. 3) At the bottom of the loop. 4) At the bottom of the loop.

Physics To Go 5/1/11 1) I would check the accelerations at each of the points to make sure that it is under 4 gs. This will ensure that the people wont be killed or knocked unconscious. I would also check to make sure that the cart is going fast enough around the loop. If it isn't, the cart won't be able to make it over the loop. 2a) mgh+1/mv^2 20 m b) a= v^2/ r  a = 20^2/ 12  a= 400/12  a= 33.33 m/s^2  c) No it is over 4 gs  d) 4g= 39.2 m/s  39.2= v^2/12  470.4= v^2  v= 21.69 m/s  e) 39.2=v^2/ 7 274.4=v^2 v= 16.57 m/s 3a) a= v^2/r a= 25^2/ 10  a= 62.5 m/s^2  b) yes it is a safe acceleration 4a) 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. 5a) 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  6a) 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. 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 24,000 and the ride can exert 25,000.  8a) 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) Yes because if you need more normal force you will need a stronger material.

Physics Plus 5/3/11 What Do You Think Now? 5/4/11 If I knew that a roller coaster was unsafe, I would not ride it. The roller coasters most dangerous part is around the loop. If the acceleration is over 4g's, there's a possibility you could die from it. Also, if the velocity isn't big enough the cart would not be able to make it around the loop. Therefore, to increase the riders of roller coasters you make sure the roller coaster is not larger than 4gs and it has a fast enough velocity.