Chapter+4

= =


 * Section 1**

A girl is pushing a boy in a chair with wheels. They are acting as if they are on a roller coaster. They both have a change in direction and velocity like a roller coaster. I think the drop produces the greatest because you actually feel as if you are falling and it is the greatest distance to drop.
 * What do you see?**
 * What do you think?**

The Nemesis in England acts as if it is flying people through the air. It has a very large loop and also also very many twists that cause the rider to feel as if they are falling. There is also a very large drop at one point.
 * Roller Coaster Homework**
 * []**

The Thunderbolt which is at Kennywood in Pennsylvania is a wooden roller coaster.It has a very large drop in which it drops the riders straight down into a ravine which creates such trills. There are also many turns and twists on the ride as well.


 * Physics Talk**
 * A scalar: a quantity that has magnitude (size/amount) but no direction
 * displacement: t he difference in positions; it depends only on the endpoints, not on the path. vector
 * speed: the distance traveled divided by the time elapsed
 * velocity: the displacement divided by the time elapsed
 * acceleration: change in velocity divided by the time elapsed.
 * equation for acceleration: change in velocity/time elapsed. a: change in v/ change in t

**Checking Up**  **1. Explain the difference between distance and displacement**. Distance is scalar which means that it has no direction and displacement has direction. **2. You went to school and back home in a total distance of 2 km. What is your displacement?**  0 displacement  **3. What is the difference between speed and velocity?**  Speed is the distance and time and is a scalar meaning it has no direction while, velocity is displacement and time and a vector meaning it does have direction.  **4. How can you find the acceleration of an object?** equation for acceleration: change in velocity/time elapsed. a: change in v/ change in t

**Physics To Go page: 358** **1. ** **2.** Inside the loop because you are changing speed and direction **3. a)**La Paz, Bolivia has the greatest speed. It travels the greatest distance in 24 h. **b)** v = d/t 40000 km / 24 h 1666.7 km/h **4.** a = delta v / delta t a = 16 m/s - 4 m/s / 3s a = 4 (m/s)/s **5.** a) speed b) velocity c) velocity and acceleration d) displacement and velocity e) displacement- tells direction **6.** v = d/t  v = .1m/2s  .05 m/s  **7.** v = d/t .05 m/s = .05m / s  s = 1 **8.** a = change V / change t  a = 25 m/s / 10s  a = 2/5 (m/s) **10a)** If I had to add two more things I would make a bigger radius because then the turn wont be as high, I would also make the drops shorter and makes the angles smaller.
 * c)** although it is such a high speed, it is constant so we don't feel any accelerations.
 * 10b) [[image:Photo_26.jpg width="384" height="288" caption="Photo_26.jpg"]]**

**What do you think now?** The part of the roller coaster that creates the loudest scream will be the part when you are changing direction and speed. For example the large drops and the loops. The riders will experience acceleration when going up the hill

=**Section 2**=

I see a roller coaster and there are three people that are going straight and they seem to be very bored and even sleeping. There is then other people that are going down a hill and they seem to be having a lot of fun, because its a big thrill. The roller coaster with the bigger thrill would be the one with a 90 degree angle. It is more steep so it is going to be a bigger thrill when you go don it.
 * What do you see?**
 * What do you think?**

> KE (bottom) + GPE (bottom) = KE (top) + GPE (top) > 1/2mv^2 (bottom) = mgh (top)
 * Physics Talk**
 * GPE: the energy a body possesses as a result of its position in a gravitational field
 * <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">KE: the energy an object possesses because of its speed
 * <span style="font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">KE depends on speed, GPE depends on height, and both depend on mass
 * The unit that energy is measured in is joules (J)
 * Mechanical energy- the sum of kinetic energy and potential energy
 * Mechanical energy (bottom) = mechanical energy (top)

Checking up Questions

The higher that the ball is released, the greater the speed is at the bottom. When the height increases and the mass goes up so does the GPE. When the speed increases and the mass increases the KE increases as well. As a roller-coaster car goes dow the hill the GPE decreases because it begins to lose height and the energy that it looses is converted into kinetic energy. The KE increases because the increase in velocity. As a roller-coast car rolls down a hill, the GPE decreases because it is losing height, but the lost energy is converted into KE. The KE increases because of the increase in velocity.
 * 1. What effect does changing the length of the incline have on the speed of a ball when it rolls to the bottom?**
 * 2. What does the gravitational potential energy of an object change with its height? With its mass?**
 * 3.How does the kinetic energy of an object change? with its speed? with its mass?**
 * 4. As a roller coaster car rolls down a hill, what happens to the gravitational potential energy it loses?**
 * 5. If a roller-coaster car 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 the hill?**
 * It has 30,000J KE 3/4 the way down. **

Physics To Go


 * 1. For which track is the speed of the car the greatest at the bottom?**
 * they are the same because both of the cars start at the exact same height and the distance of the track doesn't matter. The height is the factor that effects the speed.**

3. Complete the table: Mass = 200kg g=10m/s^2 �42 =649�= �50 =652�= =675�= �102 =678�= =721� �148= =722�= �158 726� �162 =728�= �170 731� �182 =736� �184= =737�=
 * **Position of car -> height (m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE+KE (J)** ||
 * top 30 m || 60,000 ||
 * **Position of car -> height (m)** || **GPE (j) = mgh** || **KE(J) = 1/2mv^2** || **GPE+KE (J)** ||
 * top 25 m || 300x10x25 = 75,000 ||
 * **Position** || **Height m** || **GPE=mgh J** || **KE=1/2mv^2 J** || **GPE+KE J** ||
 * bottom of hill || 50,000 || 50,000 ||
 * top of hill || 50,000 || 50,000 ||
 * top of loop || 30,000 || 20,000 || 50,000 ||
 * horizontal loop || 50,000 || 50,000 ||

What Do You Think Now?
 * I think that the roller coasters will have the same thrill because both tracks are the same height and both the cars are positioned at the same exact height. The cars will have to have the same speed at the bottom, because it doesn't matter the length just the height.**

= **Section 3**=

What do you see?
 * Students are measuring how high a pop up toy goes. The toy has a spring on it and the students are calculating the GPE, KE and SPE. They are also measuring with a photo gate timer and a ruler.**

What do you think?
 * Roller Coasters get up to the highest point by being pulled to the top with an engine. They can only go as high as they went up before. When the roller coaster cart has more people the rides requires more force because its heavier so it is going to take more energy to pull it up.**


 * Physics Talk**
 * **spring potential energy is the energy that is stored in a spring due to its compression or stretch.**
 * **examples: bungee cords, trampolines, and bent poles in pole vaulting all have EPE.**
 * **the larger the mass pop- up toy did not go as high as the original, lower mass pop-up toy.**
 * **The less massive and more massive pop-up toys can have the same GPE if the more massive pop up toys do not go as high.**
 * **GPE=mgh**
 * **Roller coaster has all its energy as GPE as it sits on the highest hill. Most of the energy will then become KE as the roller coaster is released.**
 * **Electrical energy is what pulls the roller coster up the hill**
 * **electrical energy comes from a power plant or a local generator that uses gasoline**
 * **After the cars are pulled to the top of the hill the total GPE and KE of the roller coaster are the same except for some loses.**
 * **SPE= 1/2 kx^2**
 * **GPE+KE+SPE= constant**


 * Checking Up Questions**
 * 1.** The spring potential energy turns into kinetic energy and GPE when it bounces off the table
 * 2.** It will have 2 J of Kinetic energy
 * 3.** At the top it will have 2 J of GPE
 * 4.** The spring constant and the distance it is stretched or compressed.


 * Physics To Go**
 * 5.** The amount it has at the beginning is the maximum that it can have in the end because it wouldn't have enough GPE and Ke to get to the top of the next hill.

099 1100. Friction is a force that creates work and it takes away from the other forces of energy. Less energy is available to make later KE and GPE.

44,100 J=
 * 7.** (300)(9.8)(15)

1/2 mv^2= = 1/2 (400) (15)^2
 * 8.****a)** KE

== 45,000 J=

=**b)** KE=GPE=

==45,000 J=

=**c)** 45,000= (400)(h)(9.8)= ==11.48 meters high=

=**9.** It is increasing because when you raise the height you the GPE increases.=

=**10.** They gain the same it doesn't matter which path because they are going the same height and time does not effect GPE.=

=**11.****a)** The GPE and KE should be around the same values=

=**b)** EPE=KE=

=EPE= 1/2 mv^2= =EPE= 1/2 (0.020)(2.7)^2= =EPE= 0.0728 J= =**c)** KE=GPE=

=1/2mv^2= mgh= =1/2 (.006)(2.7)^2= (.006)(9.8)h= =.02187= .006(9.8)h= =h= .37 m=

=**12.a)** GPE= EPE= =mgh= 1/2 kx^2= =300(9.8)(18)= 1/2 kx(4^2)= =k= 91.88 N/m=
 * b)** GPE=EPE

GPE mgh= 400(9.8)(18) 70,560 J= 70,560 1/2 kx^2= 70,560 1/2(91.88)x^2= x 39.19 m=


 * 13.** KE=EPE

KE 1/2kx^2= KE 1/2 40 (.3)^2= KE 1.8 J=


 * What do you think now?**

Roller Coasters get to the highest point by using its motor with a chain. The more mass the more weight and the more weight the more work so more GPE that is needed so it does cost more to lift the roller coaster. The electrical energy is payed for depending on work that is needed so it will cost more. The more electrical energy is needed depending on the heavier the roller coaster is.

= **Section 4**= People are on a roller coaster on the moon and they seem to be very bored and falling asleep because there is no gravity. On Jupiter they are having so much fun and screaming because the gravity is extremely high. So going on a roller coaster on Jupiter is more fun. Gravity does have a direction because on earth gravity always pulls down. Depending on which way the gravity is it forces things to go down. People in Australia can be held onto earth because gravity holds them down onto earth and doesn't allow them to fall of the earth because of this.
 * What do you see?**
 * What do you think?**


 * Physics Talk**
 * gravitational field is the gravitational influence in the space around a massive object.
 * a field is the influence that one object sets up in the space around it.
 * inverse- square relationship is the relationship between the magnitude of a gravitational force and the distance from the mass. This is how electrostatic forces depend on the distance from an electrical charge.
 * Newton's law of universal gravitation describes the gradational attraction of objects for one another.
 * 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 large, the force decreases as the square of the distances between the two bodies.
 * gravity- the force of attraction between two bodies due to their masses.


 * Checking up Questions**
 * 1. What is the direction of the gravitational field in your classroom?**
 * the direction is to the ground
 * 2 Using the idea of field lines, where is the gravitational field the strongest.**
 * it is strongest near the center of the earth
 * 3. Is you triple the distance bween two masses, what happens to the force of gravity between the two masses?**
 * the force is 1/9th of the original.
 * 4. What is the force that holds the Moon in its orbit around earth?**
 * gravity is the force
 * 5. Approximately what is the shape of the orbit of the plants around the sun?**
 * it is an elliptical shape

<span style="font-family: arial,helvetica,sans-serif;">**1.** If the force between the two asteroids doubles then the force is going to 125 N. (1/4 of 200) <span style="font-family: arial,helvetica,sans-serif;">**2a**. The gravitational force would be 1/4 of the original. <span style="font-family: arial,helvetica,sans-serif;">**2b.** The gravitational force would be 1/9 the original. <span style="font-family: arial,helvetica,sans-serif;">**2c**. The gravitational force would be 1/16. **5c**. There is more water on one side because the moon attracts it. �1175 1176�. **a)** 1/4 **b)** 1/9 **c)** 1/16 **d)** 4X
 * Physics To Go**
 * 3.** People trust gravity because it keeps our bodies on Earth and not floating up in the air. It holds us down. We are able to trust gravity because we have never had a time in which gravity was not present on earth. As long as there is mass gravitational force is always present.
 * 4.** The acceleration due to gravity is insignificant and it really doesn't make a large difference.
 * 5a. The water on the side of the earth is closer to the moon because it is on the surface than the center of the Earth **
 * 5b. There are high tides on the side that face the moon because the water gets attracted to the moon as causes a bulge. It is a mass of its own, and all masses are attracted to everything else. **
 * 6a.** A fish's life would be different if there were no gravity because it would always be forced down into the water and could just move around in the air. If there was no gravity the force of the fish would break the surface so there needs to be something else, which is gravity holding it there.
 * 6b.** Gravity holds a fish down onto the earth because the mass of the fish is less than that of the mass of the Earth.
 * 8. a)** 2X **b)** 3X **c)** 4X **d)** 1/2X
 * 9. a)** 4X **b)** 9X **c)** 16X **d)** 1/4X
 * 10. a)** 2X **b)** 9X **c)** 6X

d^2= 36000 1/36000 (10) ag= 0.0025
 * Physics Plus**
 * 1. r=1/60 re **


 * 2. v = d/t **
 * (2 x pi) x (3.84x10^8) / 244080 **
 * v = 998.505 m/s **


 * 3. a = v^2 / r **
 * a = 998.505^2 / 3.84x10^8 **
 * a= 0.0024 m/s^2 **

**4.** They are very close to each other

**5.** t^2/ R^3= (365 (24g/1d) X (3600s/1n)^2 1.50X10^11 m  =2.9 X10^-19 s^2/ m^3  =1 A.U.


 * What do you think now?**
 * I think that gravity does have a direction because it is always going downward. It is always the direction of force on a specific mass. Gravity always faces the largest mass which is the center of the earth. People in Australia are held onto the earth because even though they are upside down gravity attracts the mass of the people to the mass of the earth which holds them on. **

= = = ** Section 5 **= **What do you see?** One is a picture of someone buying some meat at a deli and it is being weighted on a scale. The scale is being pushed down. The other picture looks like a chemistry law and someone is weighing something else in the air using a spring scale to measure the meet as well. This is showing mass vs. weight as well as different ways of weighing. They are related to each other. **What do you think?** You can not use the same scale to weight an elephant and a canary. This is because their weights are so different than one tool will not accurately measuring them. You would need such a large scale for an elephant because it is so large that a canary would be too small to find its measurement. A bathroom scale works by something being pushed on top of it, and it is creating a force. The scale then measures how heavy you are on top of the scale and that is how much you weigh.

**Physics Talk**
 * **Robert Hooke- discovered this property of springs he knew it was a big discovery**
 * **many springs have the property that the stretch of the spring is directly proportional to the force that is applied to it**
 * **If you double the force, the stretch of the spring doubles**
 * **If you triple the force, the stretch of the spring triples.**
 * **Hooke's Law- the restoring force exerted by 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)**
 * **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) shows how easy or difficult it is to stretch or compress a spring**
 * **a stiff spring will have a larger value of k, an d a soft spring will have a lower value of k**
 * **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**
 * **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 gets compressed the arrow points to a specific number corresponding to the compression and force of the spring.**

**Checking Up Questions** **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?** The stretch of the spring increases 5 times as well. **2. What is meant by the "spring constant" of a spring?** ** The spring constant (k) shows how easy or difficult it is to stretch or compress a spring ** **3. How does weight of an object in newtons compare to its mass in kilograms?** **<span style="font-family: arial,helvetica,sans-serif; font-weight: normal;"> N = Kg x m/s^2. The mass is a part of the weight. ** **4. When you stand on a bathroom scale, how does the force of compression of the spring compare to your weight?** ** A bathroom scale works 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 gets compressed the arrow points to a specific number corresponding to the compression and force of the spring. **


 * Physics To Go**
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">1. a) w=mg **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 100 x 9.8 **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 980 N **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> b) w=mg **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 10 x 9.8 **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> =98 N **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> c) w=mg **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 60 x 9.8 **
 * <span style="font-family: Arial; font-weight: normal; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 588 N **

<span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">2. a) .25/130 = 1/x <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> x=520 N <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> b) .25/1000 = 1/x <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> x= 4000 N <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> c) .25/50: 1/x <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> x=200 N

3. a) c) **The slope of the graph is 1.47 cm** d) **The meaning of the slope is the spring constant** e)
 * The new spring would have a smaller spring constant so it would easier for the spring to stretch, making the slope of the line less steep.**

<span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> <span style="font-family: Arial; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">4. Fs= -kx <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 12= k (.03) <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 400 N= k

<span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> 5. Hooke meant that the distance the spring is either compressed or stretched it is going to be related to the amount of force that is put onto the spring. The relationship is proportional.

<span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">6. T<span style="font-family: arial,helvetica,sans-serif;">he spring with the spring constant of 15 (N/m) is going to be harder to stretch because the greater the spring constant is then the harder it is to be able to stretch the spring.

<span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;"> **<span style="font-family: arial,helvetica,sans-serif; font-weight: normal;">7. F = kx ** <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">**<span style="font-family: arial,helvetica,sans-serif; font-weight: normal;"> 3 = k.02 ** <span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">**<span style="font-family: arial,helvetica,sans-serif; font-weight: normal;"> k = 150 N/m **

<span style="font-family: arial,helvetica,sans-serif; font: normal normal normal 13px/normal Arial; line-height: 19px; margin: 0px;">8. When there is no acceleration the force on the spring is equal to the amount of weight that is then added onto the spring. The larger the force the larger the stretch of the spring will be. They are directly proportional. Each spring has a different spring constant so the higher the spring constant is the harder it is going to stretch the spring.

You cannot use the same scale to weigh a canary an an elephant because their weights are so different. When you go onto a scale the spring has to exert the same force so you know how much it is weighing. Because of such the drastic difference of weight the same scale will not work with this. The compression and dials on the scale are calibrated with the spring. The spring cannot compress for an elephant as well as for a canary. The springs on the scales would have to be very different sizes. A 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 gets compressed the arrow points to a specific number corresponding to the compression and force of the spring.
 * What do you think now?**

= Section 6 =

**What do you see?** There are two men that are riding elevators and they are both on scales. One man is much larger and it says that his weight is 0 and it is dropping because the tension. The other smaller man is moving up and it says that he weighs 200 pounds. There is more force pushing him up than he is pulling back down. **What do you think?** Your weight technically always stays the same when you are on a roller coaster, but it may appear different on the scale because of the forces of where you are located on the roller coaster. If you are sitting on a bathroom scale the weight would appear different because of the forces that are present depending on where you are on a roller coaster.

**Physics Talk**
 * Newtons First Law-and object at rest stays at rest or in motion stays in motion until an unbalanced force acts upon it. (they want to continue what they are already doing)
 * Newtons Second Law- unbalanced force creates acceleration
 * the bigger force is in the same direction as acceleration and the same is for the other way around as well.
 * to do this draw a free body diagram and a motion map (increasing v and a in the asme direction. decreases speed v and a are in opposite directions)
 * from here you can tell which force is greater
 * F=ma
 * If there are forces on the x and y axis then you need to split them and treat them separately. You cannot combine them
 * An object moving down at constant speed is identical to the object moving up at constant speed.
 * On a scale in a level roller coaster car at rest or moving with a constant velocity, the scale reading would be equal to your wright.
 * The force of earth pulling on your weight would be equal in magnitude to the force of the compressed spring within the bathroom scale.
 * The magnitude of the force of the Earth pulling on your weight would be less than the magnitude of the force of the compressed spring within the bathroom scale.
 * When the elevator is at rest or moving up or down at constant velocity your weight readings are identical. This is because at rst or moving at a constant velocity requires no net force at all.
 * when an object accelerates there has to be a net force acting on the object
 * The the elevator accelerates you are also accelerating up.
 * This is because earth pulls down on you with a force that is smaller than the force that the scale exerts on you upward.
 * You feel that you weight more because of the contact forces between your body and other objects
 * When you stand on the floor you feel the floor pushing up on you. Never endings in those tissues allow you to feel that stretching.
 * A roller coaster in free fell will acceleration at 9.8 m/s^2 for every second. The acceleration due to gravity is identical for all objects falling on Earth, if there are no other forces acting on the object.
 * air resistance (raindrops, snowflakes, leaves)

INCREASING SPEED: VELOCITY AND ACCELERATION POINT IN THE SAME DIRECTION DECREASING SPEED: VELOCITY AND ACCELERATION 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. **Checking up Questions**

1. What is the sum of all the forces acting on an object when it is moving up a constant speed? **The sum of all of the forces is zero.** 2. A person sitting on a bathroom scale on a roller coaster is accelerating upward. How does the reading on the bathroom scale compare to the person's weight? **The reading on the scale is greater than your weights magnitude.** 3. When you accelerate upward, why do you feel as if you weigh more? **the contact forces as well as your stomach tissues that are holding your stomach in face feel yourself accelerating.** 4. Suppose you are standing on a bathroom scale in an elevator when the cable breaks. What does the bathroom scale read when you are falling with the elevator? **If the cable were to break you would only have the force from your weight pulling you all the way down. The force on the scale would be zero and it would feel as if you weighed nothing.** 5. What is the force that slows a failing raindrop?
 * air resistance**


 * Physics To Go**

vf= (9.8)(2) vf=19.6 m/s vf= (9.8)(5) vf= 49 m/s vf= (9.8)(10) vf= 98 m/s
 * 1a)** vf=vi+at
 * 1b)** vf=vi+at
 * 1c)** vf=vi+at

1.6)(2) = 3.2 m/s (1.6)(5) = 8 m/s  **2c)** Vf = Vi(0) + at  (1.6)(10) = 16 m/s
 * 2a)** Vf = Vi(0) + at
 * 2b)** Vf = Vi(0) + at


 * 4)**
 * **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.** F=ma nscale-wiehgt=ma Because his weight is getting smaller then that means that the acceleration has to be decreasing. The acceleration has to either be decreasing or both the velocity and acceleration are moving downwards. The acceleration must be negative because the reading on the scale is less so its going to be negative.

**6)** Acceleration points up and so is velocity. The bigger force is pointing up because the net force is also going up. the normal force is bigger because this is the net force which is greatest. Net force= direction of acceleration.


 * 7a)** the bathroom scales reading will read less than what your actual weight is
 * 7b) f=ma**
 * n-w=ma**
 * m=ma+mg**
 * = (50)(-1.5)+ (50)(9.8)**
 * =415 N**

**8a)** w=mg w= (50)(9.8) =490 N n-w=ma(0) n=w=490 n=50 (2) +490 n=590 N w= (50)(9.8)  =490 N  n-w=ma(0)  n=w=490
 * 8b)** n-mg=ma
 * 8c)** w=mg

**9)** In the first picture the two forces are equal because there is no unbalanced force acting upon the elevator. In the second picture the elevator is going down at the same speed of the things around it so there is normal force. This elevator is dropping in free fall. In the third picture it is accelerating up so the ground is exerting a force on the object to try and get moving. There has to be an unbalanced force in the direction that you are trying to accelerate in.

**10)** Around 6 g is the average amount of acceleration. We created our roller coaster for teenagers so I think a little less than 6 g would be a good amount of acceleration.

**What do you think now?** Your weight does not change when you are riding a roller coaster yet it may appear that it does because of the readings on the scale. Depending if you are increasing and decreasing and which direction the forces make it appear as if your weight is changing. Because of your body and the way your stomach is made up your apparent weight changes. The scale would give different readings if you were sitting on one on a roller coaster because of the way you are acceleration and which way the forces are pointing. When you are increasing up you would feel heavier that normal.

= **Section 7** =

**What do you see?** There is a roller coaster and after a big loop it looks that the cart is starting to tilt off of the track and the people are going to fall off of the ride around the big curve. It is a part of the horizontal curve, you feel like you are going to fall off because the roller coaster wants to continue moving straight in the direction is was going before.

**What do you think?** You don't fall of a roller coaster when it goes upside down because of the forces that are exerted on you hold you in place


 * Physics Talk**
 * centripetal force is the force that points to the center of the circle. It refers to any force that points to the center of the circle. It is either normal, tension, friction or weight. Any one of those or combination can be one of those.
 * Centripetal acceleration- the acceleration that forces an object to move in a circle. It always points to the center of the circle. If it is equal to 0 you are not moving in a circle you are moving in a straight line. there may only be acceleration because you can change direction.
 * tangental speed- constant, usually
 * Fc= mv^2/R
 * if the radius increases the centripetal force goes down
 * if you increase the mass the centripetal force increases
 * if you increase velocity the centripetal force increases a lot.
 * To find apparent weight in a circle, you need to find acceleration and the net force and then you can figure out what the bigger force is.
 * the difference between a circular loop and a clothoid loop is that in a clothoid loop there are more than 1 radius involved. It is not the same throughout the entire loop. In a circular loop it is a uniform radius throughout the entire circle.
 * <span style="font: normal normal normal 13px/normal Arial; margin: 0px;">Normal force: the force acting perpendicular to the surface.
 * <span style="font: normal normal normal 13px/normal Arial; margin: 0px;">Centripetal force: any force directed toward the center that causes an object to follow a circular path at constant speed. Force that points to the center of the circle- refers to any force that points to the center of the circle- Normal, tension, friction, or weight. Any can be a centripetal force.
 * <span style="font: normal normal normal 13px/normal Arial; margin: 0px;">Centripetal acceleration: the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed. It always points to the center of the circle. Fc=mv^2/r

Centripetal Force Yes you are accelerating or you will not be moving in a circle. Weight and Normal Normal On the mass it is direct relationship and on the radius it is an inverse relationship. The speed relationship is direct square relationship.
 * Checking up Questions**
 * 1. What is required to make an object travel in a circle?**
 * 2. If you are traveling in a circle at constant speed, are you accelerting**
 * 3. At the top of a roller coaster loop, what two forces provide centripetal force?**
 * 4. What force is responsible for your apparent weight on a roller coaster?**
 * 5. How does the centripetal force acting on an object depend upon the objects mass? On the radius of the curve? On the objects speed?**


 * Physics To Go**


 * 1.**
 * a)** circle
 * b)** tangent to the circle


 * 2.**
 * a)** friction
 * b)** straight or tangent to the circle

v2=20 m/s N vi= 20 m/s W 20^2+20^2= 28.7 m/s tan 0 (20/20)= 1 theta=45 degrees
 * 6.**
 * a)** speed is how big it is, it does not change
 * b)** the velocity changed
 * c)** changeV= v2-v1

20^2/200 = 2
 * 7.** v^2/R (time doesn't matter) [moving in a circle]


 * 10.**
 * fast moving roller coaster**
 * || required centirpetal force || force of gravity || normal forcce ||
 * at the top of the loop || 4000 N || 500 N || 3500 N ||
 * at the bottom of the loop || 6000 N || 500 N || 6500 N ||


 * || requrired centripetal force || force of gravity (weight) || normal force ||
 * 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;">**13.** <span style="font-family: arial,helvetica,sans-serif;"> a) Bottom of hill 1- **heavier** <span style="font-family: arial,helvetica,sans-serif;"> b) Top of vertical loop- **can't tell** <span style="font-family: arial,helvetica,sans-serif;"> c) Bottom of vertical loop- **heavier** <span style="font-family: arial,helvetica,sans-serif;"> d) Bottom of hill 2- **heavier** <span style="font-family: arial,helvetica,sans-serif;"> e) Lift hill- **should feel normal**

<span style="font-family: arial,helvetica,sans-serif;"> **14**. <span style="font-family: arial,helvetica,sans-serif;"> a) Bottom of hill 1- **up** <span style="font-family: arial,helvetica,sans-serif;"> b) Top of vertical loop- **down** <span style="font-family: arial,helvetica,sans-serif;"> c) Bottom of vertical loop- **up** <span style="font-family: arial,helvetica,sans-serif;"> d) Bottom of hill 2- **down to the center** <span style="font-family: arial,helvetica,sans-serif;"> e) Lift hill - **there is none because you are not in a circle** <span style="font-family: arial,helvetica,sans-serif;"> f) Horizontal loop- **sideway to the center** <span style="font-family: arial,helvetica,sans-serif;"> g) Back curve- **sideway to the center**

You don't fall our of a roller coaster because when you are upside down you feel pressed into your seat because of inertia. Also when you are moving in a circle the net force must point towards the center of the circle because of centripetal force. You cant fall because you have to have a force pointing to the center of the roller coaster. Also acceleration points towards the center so you have to continue around the loop and go off on a straight line or a tangent.
 * What do you think now?**

= = =**Section 8**=

There is a roller coaster and there are people that are pulling the roller coaster up the hill as well as people behind it. Once you get to the top there are people that are moving down the hill very fast and their is a hat in the air which shows how fast it moves going down the hill. It takes more energy to pull the roller coaster up a steep incline. It is more difficult to walk up a steep incline because you need more work and its harder to walk when its steep compared to gentile.
 * What do you see?**
 * What do you think?**

> **Normally breaks stop the coaster cars. The breaks use friction to convert the KE of the car's motion into thermal energy.** > **power = work done/ time elapsed** > **-electrical energy calculated by measuring voltage, current, and time** > **-steam also could raise it** > P = work done / time elapsed
 * Physics Talk**
 * **work: the product of displacement and the force is the direction of displacement, the energy transferred to an object.**
 * **The product of force times displacement was the same regardless the angle.**
 * **Work increases the energy of the roller coaster.**
 * **W= Fxd**
 * ** Force is larger on a steeper incline ; but the distance along the incline was smaller **
 * <span style="font: normal normal normal 12px/normal Helvetica; margin: 0px;">**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.**
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">**-cart is raised with electrical energy supplied by a motor**
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font: normal normal normal 12px/normal Helvetica; line-height: 19px; margin: 0px;">power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred

The energy goes into GPE It gets its GPE from he work done by the spring that gains that amount of energy They use a ramp because it makes the force less to get the things into the truck, the force becomes less because it is not as steep of a height so there is less work to be done. The KE is converted into thermal energy The unit for power is watts, 1W=1 J/s
 * Checking up questions**
 * 1. When a spring scale is used to do work pulling a cart to the top of an incline where has the energy gone when the cart is at rest at the top?**
 * 2. Where does the roller coaster get its GPE when it is at the top of the first hill?**
 * 3. Why do truckers use a ramp when loading a trick if the work required is the same with or without a ramp?**
 * 4. When the brakes stop a roller coser, what happens to the coasters kinetic energy?**
 * 5. What is the unit for power?**


 * Physics to Go**


 * 1a) all GPE at the top and zero at the bottom**
 * 1b) all of the work is done by gravity**
 * 1c) all of the work is done by the spring, they are all the same**
 * 1d) EPE= 1/2 kx^2**
 * 1e) KE and a little bit of GPE**
 * 1f) The point when you start to slow down is when you first touch the spring, it becomes decreasing speed.**


 * 2a)** W= F x d The work done is 0 because they are moving in two different directions

(60)(.5) = 30 N
 * 2b)** W= F x d

= (75)(40) = 3000 N
 * 2c)**W= F x d

(500)(.7) =350 N
 * 2d)** W= F x d


 * 3)** Another way of saying this would be to use less of it or don't waste the energy if it is not really needed.


 * 4)** There would be more mass so therefore it would be more force, so there would be more force which means more work would be done.

= 10,000 (20) 200,000 N
 * 5a)** W= F x d


 * 5b) power= work/ time**
 * = 10,000/150**
 * 66** **J/S**


 * 6)** When you start there is work and then at the top of the first hill it is GPE, at the bottom of the first hill there is KE and then on the top of the loop there is GPE and KE. At the bottom of the loop there is KE and then on the horizontal loop it is KE as well. On the back curve there is Ke and then at the top of the next hill it is GPE and KE. At the end when its breaking it is work.

It takes more power to get up a steep incline on a roller coaster because there is more work needing to be done to make it up a very steep hill compared to a small hill. Because of this reason it makes it harder to walk up a steeper incline because it takes more power and this means that more work is needed. It also takes more energy to go up a steep incline because the height is higher and W= GPE. GPE is dependent on height.
 * What do you think now?**

=**Section 9**=

There is a boy and a girl and they are both thinking about roller coasters and the girl is thinking about it using energy and the boy is thinking aboutit using forces.
 * What do you see?**

The part of the snake that will be the most thrilling would be the sharp turn, the loops and when there are hills. If the speed stays the same it will stil be fun because there are loops and turns.
 * What do you think?**


 * Physics Talk**
 * Scalar- always has magnitude and size but no direction, has to do with speed, energy and distance,
 * Scalars are easy to add, subtract, multiply and divide.
 * Displacement is described by a vector. (have magnitude and direction)
 * a vector: a quantity that has both magnitude (size/amount) and direction, related to force, work is a vector
 * Energy is a scalar
 * to find total energies you just add up all the different types of energies
 * Force is a vector- on a straight line incline the gravitational force and the normal force remain in fixed directions. On curved inclines the normal force changes direction and changes in magnitude
 * the speeds of the carts are identical on two of the same points, when the heights above the ground the GPE is the same
 * Use energy: with height and velocity


 * Checking up Questions**

1**. What process is needed to add vector quantities?** Pythagorean theorem Energy is a scalar and force is a vector 4**. Does the energy of the roller coaster depend upon the path the roller coaster takes?** No work
 * 2. Is energy a vector or a scalar? Is force a vector or a scalar?**
 * 3. For roller coasters what three things do energy considerations tell you about the coaster at different points?**
 * You will know the total energy and it will always have the same speed at that exact height. **
 * 5. What is required to provide a change in the energy of a roller coster?**


 * Physics to Go**

a^2+b^2=c^2 5^2+5^2+c^2 50=c^2 c=50 m/s SW

1b) tax x= 5/5 x=45 degrees

2.If they both start at the same height then that means they will have the same change in speed, even if the inclines are different. They will reach the bottom at the same time but actual time will be different.

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- **scalar**

4.
 * a)** **Scalar**
 * b)** **Vector**
 * c)** **Scalar**
 * d)** **Vector**

5. If it was an energy ride it would have mostly GPE and KE. This is because of the hills and when you are going up and down them. When it approaches the first hill it uses all KE and work to be able to reach up to the top of the hill. At the top of the hill it then becomes GPE. As it moves back down the hill it is KE again. If it was a force ride there would be a lot of loops because you must have force to be able to make it around all the different loops. There needs to be more weight holding the cart down.

6a)

6b)

c) It is easier to look at the second roller coaster because the normal force as well as the weight are pointing in the exact same direction. In the first roller coaster the normal force and the weight force are different so it is harder to compare the two of them.

7.

7b) The GPE at all of the points are equal because they are the same height so there is the same amount of energy. 7c) the KE is equal because the GPE is the same, they are moving at the same speed. 7d) You are able to ignore all of the other points because they are at the same height. The mass and gravity are always constant and these are the things that control the GPE. The total GPE is mainly effected be the height that the cart is located at. GPE and KE must be equal if it is at the same point of the roller coaster.

What Do You Think Now? = = =**Section 10**=
 * I think that when the ride switches direction from left to right the ride will cause the most thrill. There is a change in direction taking place and this means that the velocity is also changing. The change in direction is what is really causing the thrill.**

There are a lot of roller coasters. There is a gap in the tracks people are falling off the roller coaster and flying in the air. Some people have parachutes. There are two guys that are going way to fast and there mouths are open, showing this. The knowledge that people can get hurt or die on a roller coaster does change the thrill of the ride. It makes you more nervous and scared to go onto it and can even create a larger thrill not knowing what is going to happen in the end. If I found out that one half of the roller coaster rides ended in death my answer would for sure change. I would not go on the roller coaster knowing that there was this big a shot that I could die.
 * What do you see?**
 * What do you think?**


 * Physics Talk**
 * **acceleration safe values**
 * **the max safe value goes up to 4 g's**
 * **how to fix ones that are greater:**
 * **is to increase the radius**
 * **lower the velocity by reducing the height of the initial velocity**
 * **lower velocity by increasing height of the position of the loop.**
 * **A free fall provides an acceleration of 1 g**
 * **When the roller coaster rips around a corner, the acceleration can be more than 1 g.**
 * **a= v^2/r**
 * **By varying the speed or the radius of the circle in the roller-coaster design, you can limit the acceleration to less than 4 g.**
 * Force
 * **The largest centripetal acceleration also requires the largest centripetal force.**
 * **The max force will inform you as the roller coaster designer of the strength of the materials required to built it.**
 * **The force acting on the coaster is a combination of its weight and the normal force from the track.**
 * **N= mv^2/R -mg (can figure this our for the marble)**
 * **The speed at the top of the loop is enough to compete the loop.**
 * **A cart that has too little speed will not make it to the top of the roller coaster and will not be able to move in the circle.**
 * **It will fall to the ground**
 * **If gravity were the only force acting on the top of the roller coaster, than the car must require a centripetal acceleration equal to that free fall.**

4 g's is to increase the radius lower the velocity by reducing the height of the initial velocity lower velocity by increasing height of the position of the loop. The bottom because the velocity is the greatest. If the radius is equal at the top and the bottom. The bottom
 * Checking Up Questions**
 * 1. What is the max safe acceleration for a roller coaster?**
 * 2. List two ways to keep the acceleration of coaster cart low enough to be safe.**
 * 3. At what part of the loop is the acceleration the greatest on a roller coaster cart?**
 * 4. At what part of the loop is the normal force the greatest?**


 * Physics To Go**
 * 1.** I would check the accelerations at each point of the ride to make sure that they are under 4 g's because this is the max that it can be while still being safe. this will make sure that people won't fall out of the ride. I would also make sure that the ride is going to have enough speed to make it through the loop. If it wasn't the people could fall out of the ride, if it didn't have enough speed to make it all the way over.

**2a.)** mgh+1/mv^2 20 m a = 20^2/ 12 a= 400/12 a= 33.33 m/s^2 39.2= v^2/12 470.4= v^2 v= 21.69 m/s 274.4=v^2 v= 16.57 m/s a= 25^2/ 10 a= 62.5 m/s^2 mgh= mv^2 9.8(50)= v^2 490=v^2 v= 31 m/s a= 22.14 ^2/ 10 a= 96 m/s^2 v= sqrt(49.02)( 10) v= 22.14 m/s **4d.)** 58 m/s 9.8(16)=v^2 v= 8.9 m/s mgh=1/2mv^2 9.8h= 1/2(12.52)^2 h= 20 m a= 12^2/18 a= 8 m/s^2 F= 900(12)^2 / 18 F= 7,200 N a= 20^2/15 a= 26.67 m/s^2 F= 900(20)^2/15 F= 24,000 N
 * 2b.)** a= v^2/ r
 * 2c.)** No it is over 4 gs
 * 2d.)** 4g= 39.2 m/s
 * 2e.)** 39.2=v^2/ 7
 * 3a.)** a= v^2/r
 * 3b**.) Yes, the acceleration is safe
 * 4a.)** GPE= mgh
 * 4b.)** a= v^2/r
 * 4c.)** v= sqrt(a)(r)
 * 4e.)** This roller coaster is safe because the acceleration isn't over 4 g's
 * 5a.)** mgh= mv^2
 * 5b.)** GPE= KE
 * 6a.)** a= v^2/r
 * 6b.**) F=mv^2/r
 * 6c.)** The normal force on the track and the weight will provide the centripetal force.
 * 7a.)** a= v^2/r
 * 7b.)**F= mv^2/r
 * 7c.)** The ride is safe because the cart exerts 24,000 and the ride can exert only 25,000.
 * 8a.)** It will not change because it doesn't require mass, soit would not make a difference.
 * 8b.)** It will be going the same speed because the mass down the hill cancels and on the way up it also cancels.
 * 8c.)** If the weight was larger the normal force is also going to be bigger, they have to consider this because it will not be safe if you need a stronger material to hold it up.


 * PHYSICS PLUS**





If i knew that a roller coaster could cause injury or death I would for sure not go onto it and it would definitely cause a greater thrill. I wouldn't want to risk my life for a ride. If i knew half of the riders died I would be even more sure not to go on the roller coaster. If a ride is poorly designed then their can be many things possibly wrong with it. One is that the acceleration can be more than 4 g's and this means that it is unsafe for humans. there could not be enough strength to be able to hold up the roller coaster and make sure that it is secure. Also there needs to be enough speed to make sure that the cart can safely make it through the loop.
 * What do you think now?**