Lab
Loop-the-Loop
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Equipment
toy car
hot wheels track
2 stands
2 pole clamps
meter stick and/or ruler
masking tape
Preliminary data: Calibrating the track for frictional losses between the track and the car
Set up the track so that both ends are the same distance above the ground. Make sure that the track is taped securely to the floor and remember that the better the track is braced, the less energy will be lost to its movement during the experiment. Release the car from rest at the start position, A. Measure its height above the ground. Note its finish position, B, on the other side and measure its height above the ground. Finally measure the linear distance along the ramp from A to B. Repeat this process three times to calibrate your ramp's energy loss per linear meter.
height A
Start (m)
height B
Finish (m)
linear distance
AB (m)
PE
_{A}
(J)
PE
_{B}
(J)
PE loss
(J)
Δenergy/meter (J/m)
1
2
3
What was the mass of your car (kg)?
What was your track's
average
energy loss per meter (J/m)?
Theory
For a more complete explanation, reference the resource lesson on vertical circular motion.
In the absence of friction, when the car is at the top of the track the following two forces are acting on it: a normal contact force and its weight.
Since the car is moving through a circle, the net force on the car is the centripetal force which is acting towards the center of the "loop-the-loop."
N + mg = m(v² / r)
N = m(v² / r) - mg
As the car travels slower and slower, the normal force decreases until it equals zero signifying that gravity alone is sufficient to produce the required centripetal acceleration. At that time, the car's critical velocity will equal
rg.
Experiment
Now, lower one end of the track and insert a "loop-the-loop" section so that the car will initially travel through a linear distance AB before it reaches the bottom of the "loop-the-loop" portion. The purpose of the experiment is to determine the minimum height of the start position A from which the car must be released in order for it to make it completely around the loop without "leaving the track at the top."
description
value
diameter of "loop-the-loop" (m)
radius of "loop-the-loop" (m)
car's critical velocity (m/sec)
total mechanical energy the car needs to just get through the top of the "loop-the-loop" (J)
car's ideal release height in the "absence of friction" (m)
total running "track length" for car during the experiment (m)
total energy loss to friction (J)
calculated release height including frictional losses (m)
Did your car just make it through the top of the "loop-the-loop" on Trial #1?
yes
no
If no, calculate a
second release height
that is adjusted from the results of Trial #1.
What is your new value?
Did your car just make it through the top of the "loop-the-loop" on Trial #2?
yes
no
If no, calculate a
third release height
that is adjusted for the results of Trial #2.
What is your new value?
Did your car just make it through the top of the "loop-the-loop" on Trial #3?
yes
no
Conclusions:
Give one PROCEDURAL source of error that occured during your experiment.
State a method to correct this error in future years using the SAME EQUIPMENT.
Be sure to show and explain all of your calculations and adjustments on your papers.
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Mechanical Energy
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Properties of Friction
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Work
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Review: Circular Motion and Universal Gravitation
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