Give an example to support you answer.

Distinguish the differences between speed and velocity:

Why is it necessary to consider both speed and direction with acceleration?

Is it ever possible for an object to be traveling in a circle and not be accelerating? Justify your answer with a physics principle or concept.

From the diagram below, draw in the tangential velocity, centripetal force, and centripetal acceleration vectors:

1.

2.

Of the two pairs velocity/acceleration, and force/acceleration, which pair can point in opposite directions and which pair always point in the same direction?

2. The moon is traveling in a near circle around the earth. The earth is pulling the moon towards its center. Wny doesn't the moon simply fall into the earth?

How would you correct someone if they were to say you leaned out while going in a circle due to the centrifugal force?

Newton's First Law was always applied to situations where the net force was zero last semester. Why do we use it to explain the "leaning out" when going in a circle, where in traveling in a circle, the net force is not zero? In other words, what insights does Newton's First Law give us about objects with mass in general?

The following questions are meant to allow you to make some conclusions based on your answers:

a. You are in a car at rest at a stop sign. When you step on the gas, your body moves in what direction (forward or backward) with respect to the car's motion?

b. You are in a car traveling at a constant speed and direction. When you step on the break, your body moves in what direction (forward or backward) with respect to the car's motion?

c. You are in a car traveling in a circle at a constant speed. Your body moves in what direction (Inward or outward) with respect to the car's motion?

Was there a force present to make your body move in part a or b?

How do you explain the motion of your body in part a and b if there was no force?

Whas there a force present to make your body move in part c? (The movement towards the outside of the circle)

How do parts a and b relate to part C? Include in your answer how all three scenarios can be explained:

3. What is the relationship between centripetal force and velocity?

What consequences does this relationship have with regards to traveling in a circle?

If you were holding on to the end of a merry-go-round with a force of 100 N, how much force will you need if the speed was doubled?

Quadrupled?

Decreased by 1/2?

If the merry-go-round's speed was such that you could not hold on anymore (Your muscles and grip could not supply the centripetal force required to stay in that circular motion), in what specific direction would you fly off of the ride?

What is the relationship between centripetal Force and the radius?

You are holding on to the end of the same merry-go-round with a force of 30 N. How much force will you need if you walk half way to the center?

1/4 of the way to the center?

Suppose the merry-go-round was three times the size and you were standing on the outer edge, how much force would be necessary?

Describe a situation where the knowledge of this inverse relationship would be useful if you needed to exhibit circular motion?

4. Suppose you were on an amusement park ride that exhibited circular motion, and the tangential velocity was 5.0 m/s, and the radius was 5.0 meters. What would be your centripetal acceleration? (5.0 m/s^2)

Find the centripetal force on your body, if your mass was 80 Kg. (400 N = 90 pounds)

Suppose as the ride continued, the tangential velocity increased by a factor of 4, but the radius increased by a factor of 2. How much force would be exerted on your body? Do this problem using the relationships between centripetal force, velocity, and radius. (8 times the force or 3200 N)

If the designer of the ride wanted to increase the tangential speed by a factor of 3, but wanted the centripetal force to stay the same, how would the radius of the ride need to change?

Now do this same problem with the numbers, which means the velocity is now 20 m/s (4 times 5.0), and the radius is 10 meters (2 times 5.0). Once you get your centripetal force, divide that number by the original force of 400 N.

For Honors Physics Only:

In the diagram below are the first two steps to the centripetal acceleration proof. Fill in the labels on the diagram, and draw the vector diagram from the vector equation in step two.

In step three below, fill in the necessary information on the line that allows you to set up a ratio. Then, fill in the missing variables in the supplied ratio.

Explain why proving the equation for centripetal acceleration also proves the equation for centripetal force:

5. Define Frequency and give an example:

Define Period and give an example:

Compare and contrast frequency and period.

suppose you are watching a friend on an amusement park ride that travels in a circle. When the ride first begins, you see your friend go by you at a certain frequency, which means there is a certain amount of time it takes for the friend to pass you and go all the way around the circle to get back to you. What happens to that time, if the ride speeds up and the frequency quadruples? (Your answer need only tell by how much the period changes)

To check your answer above, apply the following numbers: The initial frequency is 2 rotations per minute and then quadruples to 8 rotations per minute. Find the intital period and final period and divide final by initial to see if your answer agrees with the one above.

At the ride's fastest point, you observe a certain period of rotation. As it slows down, the period increases by a third. What happens to the frequency? (Again, tell by how much the frequency changes)

Again, to check your answer apply the following numbers: the fastest period was 1/12 of a minute, and then increases by a third to 1/4 of a minute. Find the inital frequency and final frequency and see if your answer agrees.

What relationship does period have with frequency?

Do all of the answers above agree with that relationship? In other words, if the relationship was direct straight line, do the answers show that if frequency increases by a factor of two, period increases by a factor of two as well? Justify your answer by showing what happened to one as the other changed from the problems above.

6. Why is the distance traveled in circular motion when finding the period equal to 2(pi)r?

An amusement park ride travels in a circle with a radius of 10.0 meters at 1/4 of a rotation per second. Find the tangential velocity. (15.7 m/s)

Find the centripetal acceleration. (24.7 m/s^2)

How many g-forces does a rider experience? (2.5 g's)

What does 2.5 g's mean?

If the rider had a mass of 60-kg, find the rider's weight. (588 N = 132 lb)

Now use the centripetal force equation to find the force exerted on the rider. (1480 N = 332 lb).

Now take the g-forces times the rider's actual weight and compare to the answer you just computed. (1480 N = 332 lb)

How does this result agree with your answer in level 5?

For Honors Physics only:

Suppose you wanted people on an amusement park ride to experience 4.0 g's of force, and the radius of the ride is 8.0 meters. How fast must the tangential speed be to achieve this? (17.7 m/s)

What would be the frequency of rotation for this ride? (.35 Hz)

7. Explain the following inequality and how it applies to a car rounding a curve.

What is the maximum speed the car can go without sliding? (V = 17 m/s)

Suppose the frictional force between the tires and the road is a maximum of 1000 N, but the speed that you are traveling requires a centripetal force of 2000 N to stay in the circle. How could you change the radius of your circle in order for the car to not slide off of the road? Show the work to prove your anwser.

Suppose the frictional force between the tires and the road is a maximum of 1000 N, but the speed that you are traveling requires a centripetal force of 9000 N to stay in the circle. How could you change the speed in order for the car to not slide off of the road? Show the work to prove your anwser.

Often times engineers will bank the road, so that the bank is directed towards the center of the circle. In fact, race tracks will have the curves banked so much, it is difficult to stand on them. Explain why banking the road reduces the amount of friction needed to between the tires and road.

8. What must be considered when an object travels in a vertical circle that did not have to be considered when it was traveling on a horizontal plane?

As a consequence of this extra force, how does the speed of an object compare at the top of the circle to the speed at the bottom of the circle? Label your answers in the picture below.

At what point in the circle is the Potential Energy greatest and Kinetic Energy the least?

At what point in the circle is the Kinetic Energy greatest and Potential Energy the least?

How do your last two answers prove your answer to level two?

If a pilot makes a dive with his F-15 with a radius of 500.0 meters at a constant speed of 150.0 m/s, find the force that the chair exerts on him and express your answer in pounds. The pilot has a mass of 70.0 kg. (F = 3836 N = 862 lb)

How many g’s does the pilot experience? (5.6 g’s)

What does that mean?

From that same pilot problem, calculate the centripetal acceleration the pilot experiences using the centripetal acceleration equation. (45 m/s^2).

If you try to find the g-forces from the centripetal acceleration, do you get 5.6 g's? (No; 4.6 g's).

Why is that answer one less than the one you found in level seven?

9. When finding the critical speed necessary to either lift out of your seat in a roller coaster when going over a hill, or to go upside down, why do we set Ft to zero?

If you were driving in a car and went over a hill that had a radius of 15 meters with a speed of 30 mph would you come up out of your seat? Show your work to prove your answer.

How fast would you have to go so that your weight was not pressing agaisnt the seat, but you aren't experiencing air-time either? (12.1 m/s = 27 mph)

Explain why two people with different masses will experience the same air-time when going over a hill:

How do you resolve the problem of mass not being a factor, but inertia is, which depends on mass?

What is the minimum speed needed for a roller coaster to successfully complete an upside down loop so that the passengers wouldn’t really need their harnesses if the loop had a diameter of 20 meters? (v = 9.9 m/s)

What would happen if the coaster went faster than that speed?

What would happen if the coaster went slower than that speed?

10. Explain why the first hill of a roller coaster ride is taller than the rest of the ride. In your explanation, make sure to include how energy, and loss of energy plays a role.

For Honors Physics Only:

Look over the upside down loop proof, and then try to show that the minimum height necessary to make it around a loop is equal to 5/2 times the radius of the loop.

Step Two: Kinetic Energy at the top of the loop:

Step Three: Total Energy at the top of the loop:

Step Four: Conservation of Energy:

Why would one need to start from a height that is actually more than 5/2 times the radius in order to make it around the loop without falling?

Would your results for this proof be the same if the loop were on the moon? Justify your answer.

11. Explain why mass would not matter for the period of a pendulum using the same principles learned last semester regarding freelly-falling objects. In doing so, explain why a pendulum can be compared to freelly-falling objects.

The period of a pendulum depends on only two quantities: length and strength of gravity. Why would the strength of gravity affect the period?

Why would length affect the period? (Justify your answer with sound facts regarding the motion of a pendulum).

Period has a square root relationship with length. Does that mean if the length is changed by a lot, the period changes (Specifiy either increases or decreases) by a lot or a little? Use an example to justify your answer.

How is this almost counter-intuitive to what you would think?

Period has an inverse square root relationship with g. Does that mean if g is changed by a lot (larger gravity) that period changes (specify either increases or decreases) by a lot or a little? Use an example to justify your answer.

Say the period of a pendulum is a certain amount on the earth with a certain length. If you take the same pendulum on the moon (which has 1/6 the Earth's gravity), how would you have to change the length in order to maintain the same period? (Give an actual amount of change).

Suppose the length of a pendulum is 5.0 meters. Find its period. (4.5 s)

If the length of the pendulum were increased to 20.0 meters, how much would the period change? (Give the amount of change)

Suppose the period of a pendulum is 6.0 seconds. Find its length. (9.0 meters)

12. Give the displacement graph below of a pendulum, answer the following questions:

b. What is its frequency?

c. Was the pendulum pulled to the right or left before it was released? Explain how you know.

d. What length is the string for this pendulum? (1.0 meters)

e. On the diagram below, place the corresponding labels (A, B, C) from the first graph in their proper position.