jrosenberg4

Jordan Rosenberg's Wikilog Period 6 CP Physics - Mrs. Burns - 2011 toc

Chapter 4 - Section 1
A man in a wheely chair, he's being pushed around. The direction keeps changing, which makes it similar to a roller coaster.
 * __What Do You See?__**

The loudest scream is produced during the drop from the top of the roller coaster, this part catches you off guard and scares you. The sudden acceleration and seeming drop off of the ride scares people a lot.
 * __What Do You Think?__**

Bearcat at San Souci Park __http://www.rollercoastermodels.com/bearcat.html__ The coaster has a large hill in the beginning to gain momentum and speed in order to get up any following hills
 * __Roller Coaster Designs__**

Wild Mouse at the Palisades Amusement Park __http://www.rollercoastermodels.com/PalisadesWildMouse2009.html__ The cart climbs the coaster fairly slowly on a lift, when it gets to the top it begins its descent, it has a large velocity, the turns are in place so it doesn't go to fast, because in order to make the turn it can't be going to fast.

Scalar: a quantity that has magnitude (size/amount), but NO direction Speed: distance traveled divided by time elapsed. scalar Vector: a quantity that has both magnitude and direction Displacement: the difference in positions; it depends only on the endpoints, not on the path. vector Velocity: displacement divided by the time elapsed; vector Acceleration: the change in velocity divided by the time elapsed. vector
 * __Physics Talk__**

__**Checking Up**__ 1) distance is scalar (no direction) and displacement is vector (direction). If I were to walk from my chair to the wall and back, the distance would be 3 meters, but the displacement would be 0 because the initial and final positions are the same. 2) If I went to school and back, the displacement would be 0. 3) speed is distance/time (scalar) and velocity is displacement/time (vector) 4) acceleration = change in velocity / time elapsed

1) 2) The thrills will come from the accelerations along the curve, the drops, and the horizontal circle. 3a) La Paz, Bolivia has the greatest speed. It travels the greatest distance (biggest radius) in 24 h. 3b) v = d/t 40000 km / 24 h 1666.7 km/h 3c) although it is such a high speed, it is constant so we don't feel any accelerations. 4) a = delta v / delta t a = 16 m/s - 4 m/s / 3s a = 4 (m/s)/s 5a) car traveling at 50 km/h - speed 5b) student riding bike at 5 m/s toward home - velocity 5c) roller-coaster ride whips around a left turn at 5 m/s - velocity, acceleration 5d) roller-coaster dragged up a hill 12 m tall and traveling at 3 m/s - displacement, velocity 5e) train ride takes you 150 km NW - displacement 6) v = d/t v = .1m/2s .05 m/s 7) v = d/t .05 m/s = .05m / s t = 1s 8) a = __/\__ V / __/\__ t a = 25 m/s / 10s a = 2/5 (m/s)/2 10a) If I were to add 2 more changes make the first hill less steep and I'd make the back turn much less sharp so as not to scare the little children nearly as much. 10b)
 * __Physics To Go__**

The loudest scream is produced during the loops and the largest drops because the acceleration creates a sensation. This leads to people screaming more.
 * __What Do You Think Now?__**

Chapter 4 - Section 2
Two groups on a roller coaster, one group is going slow and straight and is very bored. The other group is accelerating down a hill and having a lot of fun.
 * __What Do You See?__**

The bigger thrill will be received on the steel roller coaster with the larger steepness because there is a larger acceleration.
 * __What Do You Think?__**

__**Physics Talk**__ By changing the height and slope of a ramp one can alter the velocity of the ball. The further up a ramp the ball is, or the steeper the angle, the faster it will move down. The higher it goes the more GPE it has. When the ball comes down the incline the energy transfers from GPE to KE. The further down it goes, the more KE it has because it is moving at a faster velocity and KE = 1/2(m)(v^2). Even thought the KE and GPE will change throughout the balls path, the mechanical energy will not change because it is the sum of the two energies.

__**Checking Up Questions**__ 1) Lengthening the incline makes the ball travel faster at the bottom. 2) Because GPE = mgh, by increasing the mass or height it will also subsequently increase the amount of energy of an object. 3) Because KE = 1/2(m)(v^2), by increasing either the mass or velocity the KE is also increased. The velocity has a much larger effect on the KE than the mass does. 4) The cart transfers the GPE to KE. The mechanical energy stays the same though. 5) KE + GPE (bottom) = KE + GPE (top) (3/4)(40,000)(Kinetic Energy) + (1/4)(40,000)(GPE) = 0 + 40,000 KE = 30,000 J

__**PTG**__ 1) The roller-coaster's speed will be equal because they start at the same height. 3) 4) 5) 6) 7a) GPE=mgh GPE = .2(10)(.75) GPE = 1.5 J 7b) GPE= KE 1.5 J = GPE = KE 1.5 J = KE 7c) halfway 8) No, because even though it is a free running system and both the KE and GPE have mass in them, the are equal to each other and thus they will cancel out. Systems working by gravity are independent of mass. 9a) at point b, that is where it has just changed from the highest GPE to the highest KE. It has just accelerated the most and as it goes back up hill will gain more GPE and lose KE. 9b) It appears as though point b and g are the same. Because we are ignoring friction, the same height off the ground will equal the same GPE and thus the same KE and thus speed. They appear to be the same height. 9c) It is moving faster at D because it is lower and thus has more KE and less GPE. The more KE, the faster.
 * position of the 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 ||
 * position of the 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 (12.5 m) || 37,500 || 37,500 || 75,000 ||
 * further down (5 m) || 15,000 || 60,000 || 75,000 ||

The roller coaster with the biggest thrill will be the wooden roller coaster. The element of wood in this coaster alone makes the roller coaster scarier, thus more thrilling. Although the steel will be going faster, the wooden one will be more thrilling. On the other hand the steel one has a steeper angle, this gives it a larger acceleration, acceleration gives a very large thrill as well. It really depends on the person, if they are more "afraid" of the wooden coaster that one will definitely give them more of a thrill, if they aren't afraid of that factor and are more into the acceleration then the steel will be more thrilling because they have larger accelerations. Also, steel coasters are able to reach higher speeds than wooden roller coasters.
 * __What Do You Think Now?__**

Chapter 4 - Section 3
A group of kids using a photogate timer with a bouncy toy of sorts. There are two bouncy toys, one is in the air and the other is being compressed. There is a kid on the side measuring how high up it bounces.
 * __What Do You See?__**

Today roller coasters still get to where they are using a lift, there is a track under it with links "attached" to the bottom of the roller coaster, at the top it releases, the rest of the ride is without a track. I don't think it costs more to lift when its full of people because the links are probably capable of lifting such heavy weights that it won't make a difference.
 * __What Do You Think?__**

__**Physics Talk**__ Spring potential energy: the energy stored in a spring due to its compression or stretch Energy can be replaced with different types of energy but it will always equal the same amount GPE = mgh therefore, the larger mass has a smaller height and the smaller mass has a larger height The energy used to pull roller coasters is electric The equation for spring potential energy is SPE = .5kx^2

__**Checking Up**__ 1) What happens to the spring potential energy of a "pop-up" toy after it leaps off the table? It decreases and becomes KE 2) A "pop-up" toy has 2 J of spring potential energy before popping. How much KE will the toy have just after leaving the table? .4 J of KE 3) A "pop-up" toy has 2 J of spring potential energy before popping. How much GPE will it have at the top? 2 J of GPE 4) What two factors determine the amount of SPE that is stored in a spring? Mass and x(the amount of stretch or compression of the spring)

__**Physics To Go**__ 5) Why can the second hill of the roller coaster not be higher than the first hill? It can only have the amount it had in the beginning, if the second hill is higher it will require more GPE. 6) Why does the roller coaster not continue forever and go back and forth and up and down the hills over and over again? Because of friction, it slows the coaster down. Friction is a force that creates work, work takes away from other forms of energy. 7) A roller coaster of mass 300 kg ascends to a height of 15 m. How much electrical energy was required to raise the cars to this height? GPE = mgh = (300)(9.8)(15) = 44100 J 8) A roller coaster has a mass of 400 kg and a speed of 15 m/s. 8a) What is the KE of the roller-coaster car? KE = .5mv^2 = (.5)(400)(15^2) = 45,000 J 8b) What will be the GPE of this roller-coaster car at its highest point, where KE = 0 at that point? GPE = KE = 45,000 J 8c) How high can the roller-coaster car go with this much energy? 45000 = mgh (400)(9.8)h 45000 = 3920h h = 11.48 9) GPE increases 10) Same 11a) 0.078 11b) 0.073 11c) Yes, KE = GPE 11d) 0.13m 12a) 6600 N/m 12b) 4.62m 13) 1.8J

The roller coaster is brought to the top with a motor using electricity, at the highest point the GPE is used to find out how much energy it has, this is as much as it will have, and over time it will decrease due to friction, this is why it can't go any higher than that first hill, it won't have enough energy. If it is heavier it would cost more because the GPE will be higher so more energy will be needed. If it is heavier it will also take more work. A heavier roller coaster will require more energy because GPE = mgh, the mass will be higher; the GPE at the highest point is the most amount of energy that it will have. The pop-up toy didn't bounce as high when there was a larger mass, this is what would happen to a roller coaster if they couldn't change the amount of energy at the start with the mechanical engine. The pop-up toy was supposed to have the same energy the whole time (as the mass goes up the height goes down). However, it didn't completely work out that way.
 * __What Do You Think Now?__**

Chapter 4 - Section 4
In the first picture they are on the moon and they are really bored, the other picture they are on Jupiter, there the gravity is higher, so they are having more fun because the ride is faster.
 * __What Do You See?__**

Gravity does not have a direction. It does, however, in relation to your position, its always inward toward the center of the Earth. People in Australia are being pulled into by gravity the same way people in the United States are being pulled in. Direction changes based on your location.
 * __What Do You Think?__**

__**Physics Talk **__ Newton's Law of Universal Gravitation gravitational field: the gravitational influence in the space around a massive object Earth of the source of its gravitational field because it is the first object that sets up in the space around it second object interacts with this field--moon (response/test object) Inverse-Square Relationship acceleration due to gravity becomes less as an object moves further from the surface of Earth 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 force of gravity between 2 objects decreases by the square of the distance between them Newton's law of universal gravitation: all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bodies increases Equation of Newton's law of universal gravitation Fg = (Gm1m2)/r^2 (Fg = force between the bodies, r = the distance between their centers, m1 & m2 = masses of the bodies, G = universal constant equal to 6.67 x 10^-11 The moon orbits Earth and the planets orbit the Sun in elliptical paths plants don't move in exact ellipses b/c planets tug on on another

__**Checking Up **__ 1) The direction of the gravitational field in the classroom is to the ground 2) The gravitational field is the strongest near the surface of Earth 3) If you triple the distance between two masses, the force is (1/9) the original  4) Gravity is the force that holds the Moon in its orbit around Earth  5) The shape of the orbit of the plants around the sun is approximately elliptical.

__**Physics To Go **__ 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. It's been in affect for millions of years. 4) The acceleration due to gravity is basically the same, the distance is so insignificant. 5a) The water on the side of Earth facing the moon is closer to the moon than the center of Earth. 5b) The moon has its own gravitational force, water is not attached to the Earth, its free-standing, so it gets affected by the moon's gravity. 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. 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. Water has hydrogen bonds, there is surface tension as well. 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. 7a) 1/4 7b) 1/9 7c) 1/16 7d) 4x  8a) 2x 8b) 3 x 8c) 4x <span style="font: 13px/19px Arial; margin: 0px;">8d) 1/2x <span style="font: 13px/19px Arial; margin: 0px;"> 9a) 4x <span style="font: 13px/19px Arial; margin: 0px;">9b) 9x <span style="font: 13px/19px Arial; margin: 0px;">9c) 16x <span style="font: 13px/19px Arial; margin: 0px;">9d) 1/4x <span style="font: 13px/19px Arial; margin: 0px;"> 10a) 2x <span style="font: 13px/19px Arial; margin: 0px;">10b) 9x <span style="font: 13px/19px Arial; margin: 0px;">10c) 6x

__**<span style="font-family: Arial; font-size-adjust: none; font-size: 13px; font-stretch: normal; font-style: normal; font-variant: normal; line-height: 19px; margin: 0px;">Physics Plus **__ 1) a = v^2 / r 2) v = d/t (2 x pi x [3.84x10^8) / 2440800 v = 998.505 m/s 3) a = v^2 / r a = 998.505^2 / 3.84x10^8  a= 0.0025 m/s^2

Gravity does have a direction. It's direction is towards the larger mass. On Earth, its direction is always towards the center of the Earth. Although technically Australia could be considered upside-down, gravity still pulls the people inwards.
 * __What Do You Think Now?__**

Chapter 4 - Section 5
There are people buying stuff in both pictures. One picture is in a store, they are weighing the object on a scale pushing downwards, the other seems to be in a lab, it is on a scale, where it is being pulled downwards. They are, however, related
 * __What Do You See?__**

You can weigh a canary and an elephant the same, but you'd need a scale that can hold a lot of weight, it also would have to show a lot of decimals. It would be much more practical to weigh them separately. A bathroom scale calculates the pressure that is placed upon it when you step on it, it the converts that into your weight in pounds.
 * __What Do You Think?__**

__**Physics Talk**__ Hooke's Law Describes the Restoring Force a Spring Exerts Stretching a rubber band, spring, or anything else of the sort requires a force There is a linear relationship between the amount of force required for each stretch of a spring Robert Hooke discovered this property of springs The stretch of a spring is directly proportional to the force applied to it If the spring is not moving, the spring exerts a force equal in magnitude to the force that stretched the spring 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 (or compression) Fs = -kx negative shows that the pull by the spring is opposite to the direction it is stretched or compressed k is an indication of how easy or difficult it is to stretch/compress a spring a stiff spring will have a large value for k; a soft spring will have a small value for k Hooke's law : F = kx bathroom scales work by compressing a spring. When you step on the scale, 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. The spring is connected to a scale that has been calibrated to give your weight. As the spring compresses, the arrow points to a different number corresponding to the compression and force of the spring.

1) If the force on the spring is increased 5 times, the stretch of the spring increases 5 times. 2) The spring constant represents how easy or difficult it is to stretch/compress a spring 3) Weight of an object in newtons compares to its mass in kg. N = Kg x m/s^2. The mass is a part of the weight. 4) On a bathroom scale, the more weight, the more compression of the spring is required.
 * Checking Up**

1a) W = mg W = (100)(9.8) W = 980 N 1b) W = mg W = 10(9.8) W = 98 N 1c) W = mg W = 60(9.8) W = 588 N 2a) 0.25 / 130 = 1 / x x = 520 N 2b) 0.25 / 1000 = 1 / x x = 4000 N 2c) 0.25 / 50 = 1 / x x = 200 N 3a)
 * PTG**

3b.

3c) Slope = 0.1491 N/(cm) = *14.91 N/m* 3d) The slope is the spring constant 3e) This spring would be loser and more stretch than the previous spring. It's slope is less steep and requires less weight to stretch it the same distance. 4) F = -kx 12 N = k (0.03m) k = 400 N/m 5) Hooke wrote "as the force, so the stretch" because the stretch/compression of a spring is directly proportional to the force pulling or pushing on the spring. The larger a spring is stretched, the larger restoring force is needed. 6) The spring with the higher constant is more difficult to stretch, so in this case 15.0 N/m would be more difficult to stretch. Greater constant 7) F = kx 3N = k(.02m) k = 150 N/m 8) Spring scales are based on Hooke's law. The stretch of the spring is directly proportional to the force pulling/pushing on the spring. When at rest, the spring exerts a restoring force equal in magnitude to the force stretching or compressing the spring. F = -kx.

You can't use the same scale to weigh a canary and an elephant. The spring can only compress so much, if it works for a canary it is most likely not going to read an elephant. It may compress all the way for an elephant; but if the spring were larger it may have stretched more. A bathroom scale works through the use of a spring. When you step on a scale the spring compresses according to your weight; the more the object (person) that steps on the scale weights the more compression the spring will need. That spring connects to a number scale that has been set to change according to the spring's compression.
 * __What Do You Think Now?__**

Chapter 4 - Section 6
The picture has a fat man that weighs nothing; the elevator is moving down, therefore balancing his weight. There's a little kid that is at maximum weight; his elevator is going up, this increasing his downward force.
 * __What Do You See?__**

No, weight does not change when riding a roller coaster; it appears to change though; this is when you're using a scale. When riding the coaster you start off at your normal weight. When you go up your weight increases and when you go down it decreases. The is because the force that you apply is being balanced out by your speed (this is all assuming you are sitting on a scale while riding the roller coaster).
 * __What Do You Think?__**

<span style="font-family: Arial,Helvetica,sans-serif;">__**<span style="font-size-adjust: none; font-size: 12px; font-stretch: normal; font-style: normal; font-variant: normal; line-height: normal; margin: 0px;">Physics Talk **__ <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> **Using Newton's First and Second Law to Explain Forces Acting During Constant Speed and Acceleration** <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> Newton's 1st (object at rest/motion stays at rest/motion) : an object at rest has no net force acting on it <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> Newton's 2nd law (a=F/m) object at rest, has zero acceleration, and has no net force acting on it <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> an object in motion at constant speed has no net force acting on it <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> sitting on a scale on a level roller-coaster at rest or constant velocity - the scale reads equal to weight <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> Accelerating Up on Roller coaster: there must be a net force pushing you up <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> -moving up on the scale, the reading will be greater in magnitude than your weight <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> -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 <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> if the elevator and the person are accelerating down, the net force on the person must be down <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> **Apparent Weight** <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> when the elevator is at rest or moving at constant velocity, your weight readings are identical <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> when an elevator accelerates up, you also accelerate up (Earth pulls down on you with a force smaller than the force the scale exerts on you upward, so the scale reads a larger force than before) <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> -you weight like you weigh more because of the contact forces <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> -force hold your stomach in place against gravity <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> when elevator accelerating down, the scale reads a smaller force than before because force of the scale up on you is less that force of your weight down <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> -feel like you weight less because the contact force w/ the bathroom scale is smaller and because the connective tissues stretch a bit less <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> Weightless feeling is due to contact force between you and bathroom scale is zero & tissues relax <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> **Air Resistance** <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> a coaster in free fall accelerates at 9.8 m/s every second. <span style="font: 12px Arial,Helvetica,sans-serif; margin: 0px;"> can't ignore air resistance on roller coaster

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

1) Vf = Vi(0) + at 1a) (9.8)(2) = 19.6 m/s 1b) (9.8)(5) = 49 m/s 1c) (9.8)(10) = 98 m/s 2a) (1.6)(2) = 3.2 m/s 2b) (1.6)(5) = 8 m/s 2c) (1.6)(10) = 16 m/s 4) 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 Net Force
 * __Physics To Go__**
 * **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 ||

5) A student who weighs 140 lb and is 137 lb on a scale on an elevator has just and increased down acceleration, or they had a decreased upward acceleration. Net Force = m a  Nscale - W = ma  137 - 140 (negative number so the acceleration is down v and a are both down, which means increase down v is up & a is down, which means decrease up 6) The person will observe that her weight increases. An increased upward acceleration increases the weight on the scale because the force that the scale is exerting is greater than the force of the person downward. Seams heavier.  v is up & a is up ; therefore the bigger force points up, which is the scale 7a) Once the elevator starts to descend, the scale's reading will decrease. 7b) Fnet = ma (accelerating down so the weight will be the bigger force) W - Fscale = ma (50)(9.8) - Fscale = (50)(1.5) Fscale = 415 N 8a) The scale will read zero Fnet = ma Fnet = 0 Scale reading = 490 N 8b) Fnet = ma (acceleration is up, so the bigger force is Fscale) Fscale - weight = ma Fscale - (50)(9.8) = (50)(2) Fscale = 590 N 8c) The scale will read zero as it travels up at constant speed because the acceleration is zero. Fnet = m(0) = 0. Therefore, the scale reading is 490 N 9a) At rest, the force up (scale) and force down (gravitation) are both equal, so the Fnet is zero. When the Fnet = zero, the scale reads your accurate weight. 9b) An elevator in free fall has no force from a scale pushing up, so there is only the force of you pushing down. Therefore, the scale reads as 0. g = a 9c) The scale reads a greater number than that at rest because it is accelerating upward. When acceleration is up, that means the bigger force is the Fscale. When Fscale is bigger than weight, the number is positive, and the scale reads a higher number. 10) They would find the loops exciting because they feel heavier throughout the loop. They'd enjoy the change between increasing upward/downward acceleration and decreasing upward/downward acceleration. The increase acceleration upward would make them feel heavy and the increase downward would change their feeling to light. The decrease upward would then keep them feeling light, but the decrease downward would have them feeling heavier.

Your weight does not change when riding a roller coaster; your apparent weight does, however; that means you feel like your weight is changing, but its not. This is because of acceleration in a specific direction, the acceleration changes the force. If sitting on a bathroom scale the scale would give you different readings because the force applied on the scale is different based on acceleration. Going up a coaster the scale would read a heavier number because you are being forced downwards, when going down your body is being held in place, but wants to go up, so it will read a lighter number.
 * __What Do You Think Now?__**

Chapter 4 - Section 7
There are people on a roller coaster. They go up a large hill, then they go down and go around a vertical loop. They then go around a horizontal turn; they had way too much speed, and as a result they are barely able to stay on the track. The car wants to keep going straight (off the track).
 * __What Do You See?__**

Because the forces of acceleration are greater than gravity, the cart will be going fast enough that it will not be "pulled" by the forces of gravity off of the tracks.
 * __What Do You Think?__**

__**Physics Talk**__ __centripetal force and acceleration__ normal force: the force acting perpendicular to the surface -coaster curve where car tilts vertically and the wheels face outside, normal force is the force towards the center -track acts directly on the wheels of the car centripetal force: any force directed toward the center that causes an object to follow a circular path at constant speed -roller coaster around a curve on its side has the force of the track as its centripetal force -centripetal force is larger when speed is increased, mass is increased, and radius is shorter Fc = mv^2 / r centripetal acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed In vertical loop, the Fc is gravitational force, a normal force of track on the coaster car or a combo -when it is a combo, the two vectors are added -at bottom of circle, the normal force points toward center & gravitational points downward (sum is towards center, so the normal force is larger) -at top of circle, the gravitational force and normal force both act downward towards center and the sum is the Fc. Mass and speed of the car determines how much of the normal force is needed to keep the car moving in a circle -There is more Fc at the bottom than the top because there is more speed at the bottom -the weights at bottom and top are the same Normal + weight = net centripetal force __apparent weight and the roller-coaster ride__ -feel lighter at the top of the loop because acceleration is downward -feel heavier at the bottom of the loop because acceleration is upward -on a level track at constant speed, the sum of forces is 0 -at the bottom, there is a force up keeping you moving in a circle -at the top there is a force down to continue to the circle clothoid loop: big radius at bottom and small radius at the top, so the coaster is moving in a small circle at the top -these ensures that it can turn at the top but not have an accel. at the bottom that is greater than 4 g's. __Safety on the Roller coaster__ experiencing an accel more than 9 x gravity causes unconsciousness accelerations other than 9.8 or 10 (acceleration due to gravity) is referred to as 1 g. 2 gs = 20 m/s/s, 8 gs = 80 m/s/s

__**<span style="font-size-adjust: none; font-size: 12px; font-stretch: normal; font-style: normal; font-variant: normal; line-height: normal; margin: 0px; min-height: 14px;">Checking Up **__ 1) Centripetal force is required the make an object travel in a circle. 2) If you are traveling in a circle at constant speed, you are accelerating, which is called centripetal acceleration 3) At top of a loop, the gravitational force and normal force provide the Fc. 4) Normal force is responsible for your apparent weight on a roller coaster. 5) Centripetal force is larger when speed is increased (direct), mass is increased (direct), and radius is shorter (inverse).

1a) As the mass increases on the right side of the equation Fnet get larger as well. 1b) If the velocity increases on the right side of the equation then Fnet increases as well. 2) If the speed of the roller coaster is doubled then the track should be 4 times as strong because there is a squared relationship. 3) If the radius of the curve increases on the right side of the equation the Fnet decreases. 4) The larger the radius for the curve, the __smaller__ the force required to keep the car moving along the curve. If the curve is tight (r is very small) then a __larger__ force is required. 5) When you release the car it goes off on a "straight line" or tangent; there is no longer a force holding it on a specific path, it just goes off on that path.
 * __Physics Plus__**

1a) the path of the car would be in a circle 1b) if the string were to break while the car was moving in a circle, the car would follow a straight line tangent to the circle 2a) Friction has replaced the string of the toy car. 6a) The speed of the roller coaster did not change, it stayed 20 m/s. 6b) The velocity of the roller changed because it changed direction. 6c) The change in velocity was 28.2 m/s at 45 degrees NW  V2 - V1 = change in V  20m/s ^, 20 m/s < 20^2 + 20^2 = c ^ 2 c = 28.2 m/s tan theta = 20/20 theta = 45 7) Ac = v^2 / r Ac = (20)^2 / 200  Ac = 2 m/s^2  10) Fast Moving Roller Coaster Slow-moving roller coaster <span style="font-family: arial,helvetica,sans-serif;">13a) Bottom of hill #1- heavier <span style="font-family: arial,helvetica,sans-serif;"> 13b) Top of vertical loop- uncertain <span style="font-family: arial,helvetica,sans-serif;"> 13c) Bottom of vertical loop- heavier <span style="font-family: arial,helvetica,sans-serif;"> 13d) Bottom of hill #2- heavier <span style="font-family: arial,helvetica,sans-serif;"> 13e) Lift hill (going up at constant speed)- "normal"
 * __Physics To Go__**
 * || Required Fc || Force of gravity (weight) || Normal force (the force of the track on the car) ||
 * at the bottom of the loop || 4000 N || 500 N || 3500 N ||
 * at the bottom of the loop || 6000 N || 500 N || 6500 N ||
 * || Required Fc || Force of gravity (weight) || Normal force (the force of the track on the car) ||
 * at the top of the loop || 800 N || 500 N || 300 N ||
 * At the bottom of the loop || 2800 N || 500 N || 3300 N ||

<span style="font-family: arial,helvetica,sans-serif;">14a) Bottom of hill #1- up <span style="font-family: arial,helvetica,sans-serif;"> 14b) Top of vertical loop- down <span style="font-family: arial,helvetica,sans-serif;"> 14c) Bottom of vertical loop- up <span style="font-family: arial,helvetica,sans-serif;"> 14d) Bottom of hill #2- up <span style="font-family: arial,helvetica,sans-serif;"> 14e) Lift hill (going up at constant speed)- zero <span style="font-family: arial,helvetica,sans-serif;"> 14f) Horizontal loop- to center <span style="font-family: arial,helvetica,sans-serif;"> 14g) Back curve- to center

You don't fall out of a roller coaster when you go upside down because inertia is throwing you into the seat, this keeps you in. The normal force is pointing towards the center so you need to stay in, you have to be accelerating downwards or you'd go off on a straight path. In order to fall at the top of a loop the force of acceleration is greater than that of gravity.
 * __What Do You Think Now?__**

Chapter 4 - Section 8
__**What Do You See?**__ There is a roller coaster with a large hill; there are people doing work to pull a cart up. The people are sweating because they are doing work to carry the cart up the hill. Once at the top of the hill, the cart goes down the incline very fast.

__**What Do You Think?**__ It takes more energy to pull the roller coaster up a steep incline than a gentle incline because it has to go higher. It is less difficult to walk up a gentle incline because the steepness is not as hard on our muscles and we need less force to get up the hill.

__**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 -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 gone into GPE 2) The roller coaster gets its GPE at the top of the first hill from work done by the spring (electricity or heat) that gains that amount of energy 3) Truckers 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) The unit for power is watts. 1 W = 1 J/s

__**Physics To Go**__ 1a) The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline. 1b) As the cart went from the top to the bottom, all of the work is done by gravity. 1c) All of the work is don't by the spring as the spring compressed 1d) SPE = 1/2kx^2 1e) The total energy just before it hits the spring is GPE. 1f) You begin to slow down just when you first touch the spring. 2a) W = F x d work is zero because the force and distance are perpendicular, or not in the same direction.  2b) W = F x d  W = 60 x .5 W = 30 N 2c) W = F x d  W = 75 x 40  W = 3000 N  2d) 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 5a) W = F x d W = 10,000 x 20  W = 200,000 N  5b) 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 --> GPE) down hill (GPE-->KE) up loop at the top (KE & GPE) back curve (KE) up second hill (GPE & KE) horizontal loop (KE) braking (work)

A steep incline takes more energy because although work stays the same, you require more power. Walking up a steep incline is more difficult than walking up a gentle incline because in order to do so requires a larger amount of power.
 * __What Do You Think Now?__**

Chapter 4 - Section 9
The children thinking about a crazy roller coaster. One is thinking about energy, she has an entire sheet full of equations and numbers, the other is thinking of force, his paper is empty. She has it full because she can calculate GPE, using that she can find other things. His is empty because he needs something to work off of to get the force.
 * __What Do You See?__**

The most thrilling part of the roller coaster would either be the steepest downhill section or vertical (clothoid) loop. It will still be fun because there are different loops and directions, you aren't expecting anything that will happen next.
 * __What Do You Think?__**

__** Physics Talk **__ Vectors include direction and magnitude and scalar quantities only take in to account magnitude. A type of vector quantity is velocity and a scalar example is energy. Scalars are easily added and subtracted. Vectors need to take into consideration direction. If the direction is at right angles the Pythagorean theorem must be used to find the resultant. Mechanical energy is always the same throughout the system and can be used do determine GPE and KE. The KE = the mechanical energy minus the GPE. Use energy when there is heights and velocity changing. Acceleration is the joint between energy and forces. Forces cause work and acceleration. Work is measured in energy.

__** Checking Up **__ 1.) Pythagorean theorem 2.) Energy is scalar and force is vector. 3.) Energy considerations tell us GPE, KE, and the total energy. We can use them to find height and velocity. 4.) No, the path doesn't change the energy. 5.) Work is needed to change the energy.

1) 2.) Even though their accelerations will be different, the speeds will be the same. The longer track accelerates more slowly but it has more time to accelerate and the shorter one does it quicker but for not as long. As long as the heights were the same in the beginning and the same at the end the KE will be the same and thus the velocity will as well. 3.) a) distance- scalar b) displacement- vector c) speed- scalar d) velocity- vector e) acceleration- vector f) force- vector g) KE - scalar h) PR - scalar i) work- vector 4.) a) scalar b) vector c) scalar d) vector 5.) When you are given a height or a changing velocity it would be best to look at it in terms of energy. An example would be a roller coaster starts at 15 meters high and weighs 10 kg find the speed at the bottom. Here you would find the GPE in terms of energy and then find the KE at the bottom and then speed. Use in terms of force when given circle problems. If a question wants to know what the net force is, then you would need to draw a free body diagram and then find the weight and normal and do vector addition or subtraction. 6a. - 6b.) c) It is easier to analyze roller coaster 2 because there the normal force and weight are always going to be in the same ratio. In roller coaster 1, at all the different points, the normal force and weight vary and change which is bigger. 7a.)
 * __ Physics To Go __**

b) The total energies are the same at those points. The total energy in the system is always the same in the system. It is just altered between GPE and KE. c) The KE is the same because they all started at the same height. d) Because the height of the cart is the only thing that determines the GPE and thus KE of the cart

__**What Do You Think Now?**__ The turns of the snake with the smallest radius will be the most thrilling. There is more of an acceleration where the radius is the smallest. Thus there are more g-forces acting on the cart and it is the most thrilling. It is still thrilling because the constant change in direction gives an acceleration.

Chapter 4 - Section 10
The picture is of a large roller coaster, everyone is falling off of it. There are quite a few flaws with the coaster. There are missing pieces of track, to much acceleration, a lot of problems.
 * __What Do You See?__**

Yes, knowing the danger of a roller coaster would change the thrill. If I were on it I'd be pretty scared most of the time that I'd get hurt. If I found out that 1/2 of all roller coaster rides ended in death my opinion would definitely change, I definitely wouldn't even ride the roller coaster.
 * __What Do You Think?__**

Acceleration- safe values --> up to 4 g's Ac = V^2/R How to fix if values greater than 4 g's - Radius increase - Lower velocity -- Reduce height of start -- Increase height of position Weight = 1 g In free fall you feel 1 g Acceleration is greatest at the bottom of the loop Normal is the greatest at the bottom of the loop
 * __Physics Talk__**

__**Checking Up**__ 1.) 4 g's is the max acceleration 2.) Increasing the radius of the turns or lowering its speed will decrease the turns acceleration 3.) The bottom of a loop has the greatest acceleration because that is where you are moving the fastest with the smallest radius 4.) The bottom of a vertical loop has the most normal force because that is were you're pushed down on the cart the most.

1.) Acceleration is under 4 G's, the acceleration at the top of the loop must be bigger than 1 g, and the materials need to be able to withstand the normal force needed at the bottom of the vertical loop. 2a.) mgh + 1/2mv^2 = mgh (9.8)h + 1/2(20)^2 = (9.8)h h = 20m 2b.) ac= v^2/r ac= (20)^2/12  ac= 33 m/s^2  2c.) yes, it is 3.4 g's  2d.) ac=v^2/r  39.6=v^2/12  v= 22 m/s  2e.) ac=v^2/r 39.6= v^2/7 v= 17 m/s 3a.) ac=v^2/r ac=25^2/10  ac=63 m/s^2  3b.) no, it is closed to 6 g's  4a.) mgh=1/2mv^2  (9.8)(50)=.5(v)^2  v= 31 m/s  4b.) ac= v^2/r ac= 31^2/10 ac=96 m/s^2 4c.) KE=GPE1 - GPE2 KE= 50(9.8) - 20(9.8)  KE=294  KE=1/2v^2  294=1/2 v^2  v = 24 m/s  4d.) ac=v^2/r =24^2/10 ac=58 m/s^2 4e.) It isn't safe, the bottom of the loop has an acceleration of 5.9 g's and the acceleration required to keep the car moving is close to 10 g's. 5a.) ac=v^2/r 9.8=v^2/8 8.9 m/s= v 5b.) GPE= KE + GPE  mgh = 1/2mv^2 + mgh  (9.8)(h)=1/2(8.9)^2 +(9.8)(16)  h=20.1 m  6a.) ac= v^2/r =12^2/18 ac= 8 m/s^2 6b.) Fc=mv^2/r =900*12^2/(18)  Fc= 7200 N  6c.) The friction of the track on wheels 7a.) ac= v^2/r = 20^2/ 15  ac= 26.7 m/s^2  7b.) Fc= mv^2/r =900(20^2)/15 Fc= 24000N 7c.) Yes, the roller coaster can withstand 25000 N and there is only 24000N 8a.) No, it doesn't depend on mass because it isn't in the V^2/r formula. 8b.) No, mass will cancel out so the speed will no change 8c.) If the weight gets bigger the normal force must also increase. The track strength is also dependent on weight.
 * __Physics To Go__**


 * __Physics Plus__**

Knowing about the danger of a roller coaster would definitely scare me. If i knew about the amount of weight it could hold I'd be concerned about the material that they are using. If it is poorly designed then weight is the most easily mistaken calculation or problem, this changes normal force, therefore changing the material they would have to use. No roller coaster should have a reputation involving any injuries, that would definitely lead to a lot of doubt in its safety.
 * __What Do You Think Now?__**