Lab
Roller Coaster, Projectile Motion, and Energy
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Part I Directions
Step up your apparatus as shown in the demonstration model making sure that the tape securing the meter stick supporting the track does not interfere with the car’s motion. As you run the experiment, make sure that the "legs" of the loop-the-loop are taped securely to the table; that the upper end of the track stays as close as possible to the 33-inch mark; and that the pivoted end of the meter stick remains stationary against the table.
Initial Measurements
. Make sure to record your values in meters and kilograms, not cm and grams.
inner diameter
_{loop}
= _________ m
inner radius
_{loop}
= ___________ m
mass
_{car}
= _________ kg
Refer to the following information for the next five questions.
1. Calculate the minimum critical velocity needed for the car to just travel around the loop without losing contact with the track.
v
_{B}
= _____________ m/s
2. Using the Law of Conservation of Energy calculate the ideal height (of point A) from which the vehicle should be released so that it will successfully complete the loop-the-loop with the velocity found in
Question #1
. (Note the height at point B is the diameter of the hoop.)
h
_{A}
= _____________ meters
3. Raise the incline so the car when released from the end of the ramp is exactly at the height calculated in
Question #2
. Then release the car to test if it can actually make it around the loop-the-loop while maintaining continuous contact with the track. Be careful to make sure that the tip of the supporting meter stick remains in constant contact with the table's surface. Do NOT let it move.
Did the car complete the loop-the-loop successfully?
Yes
No
4. Which of the following describes the motion of the car while traveling around the loop-the-loop?
a. Did not make it to the top of the loop-the-loop and rolled back
b. Fell off track near the top and stopped
c. Lost contact with track but landed back on track and continued
d. Maintained contact all the way around the loop-the-loop
4b. Explain why energy was NOT conserved by the car.
5. Now increase the height of the track (at point A) by 1 cm to 2 cm (0.01 – 0.02 meters) experimenting each time to see if the car makes it completely through the loop-the-loop while maintaining continuous contract with the track. Make sure that you always release the car from the same position at the end of the track (the 33-inch mark) – heighten point A by moving the ring stand towards the pivot (increasing the track’s slope) without changing the length of the track down which the car travels. Make sure that the lowe end og the meter stick stays securely in contact with the table. Do NOT let it move.
Indicate the height of point A in meters in the far left column, then check one of the corresponding descriptions for the car going around the loop-the-loop. Once the car makes it around the loop-the-loop remaining in contact with the track, circle this value and then continue to the next step in the lab.
Record your results in the table below.
5b. Record the final height from your chart in meters.
5c. Based on the final height in
Question 5b
, what was the sine of the meter stick's angle of inclination?
5d. What was the normal force supporting the car?
normal
_{A}
= __________ N
Analysis:
6. Using the last height in
Question 5b
calculate the potential energy of the car at point A.
PE
_{A}
= ______________ J
7. Using the velocity determined in
Question #1
at point B and the height at point B (the loop’s inner diameter), calculate the total mechanical energy of the car at point B.
(PE
_{B}
+ KE
_{B}
) = ______________ J
7b. What was the normal force exerted on the car as it passed through position B?
normal
_{B}
= __________ N
Conclusions:
8. Are the total mechanical energies at point A and point B equal to each other?
Yes
No
9. Was energy lost, gained or conserved by the car?
Part II Directions
Now release the car from the last height at point A (the one that remains in continuous contact with the track). Allow the car to travel through the loop-the-loop and continue so that it moves off the table horizontally and strikes the floor. See picture to the right. Record the height (h) that the car leaves the table and the range (R) that it landed on the floor (make sure to use a plum line to get an accurate measure of the range the car traveled after leaving the table).
Data:
Height of table, H = ______________ m
Range, R = ______________ m
10. Calculate the time that the car was in the air before landing on the floor.
Time, t = _____________ seconds
11. Using the car’s range, calculate the horizontal velocity of the car when it left the table (v
_{H}
, also the velocity at point C).
Velocity at point C, v
_{H}
= _____________ m/s
12. If the speed of the car remained constant throughout the horizontal section of the track (as it approached point C), then what was the normal force exerted on the car as it passed through the bottom of the loop-the-loop?
normal
_{bottom}
= ______________ N
Analysis:
13. Calculate the kinetic energy of the car at point C.
KE
_{C}
= ________________ J
14. Are the total mechanical energies at points B and C equal to each other?
Yes
No
Conclusions:
15. Why did we not consider point C to have any potential energy when comparing its total energy to the total energies at point A and point B?
16. Determine the energy lost between point A (Question #6) and point B (Question #7).
ΔEnergy = _______________ J
17. Determine the energy lost between point B (Question #7) and point C (Question #13) .
ΔEnergy = _______________ J
18. Between which points was more energy lost?
A to B
B to C
18b. Write a hypothesis to would explain why your choice in
Question #18
happened.
19. At what position along the track did the car experience the greatest normal force?
at position A, when it was first released
at position B, at the top of the loop
at the base of the loop just as it exited the circle
at position C, just as it left the table
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The Law of Universal Gravitation
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Thin Rods: Moment of Inertia
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Uniform Circular Motion: Centripetal Forces
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Universal Gravitation and Satellites
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Vector Resultants: Average Velocity
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Vertical Circles and Non-Uniform Circular Motion
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Work
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Work and Energy
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Review: Circular Motion and Universal Gravitation
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Test #1: APC Review Sheet
Worksheet:
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Circular Orbits
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