Rolling motion of a cylinder down an incline

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Homework Help Overview

The discussion revolves around the motion of a solid cylinder rolling down an incline, specifically examining the validity of the theoretical acceleration equation a = 2/3 g sin(theta) under the assumption of smooth rolling with no resistance. The original poster aims to test this equation through experimental measurements of acceleration at various incline angles.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the discrepancies between measured and theoretical acceleration values, questioning the impact of rolling resistance on these results. There are inquiries about the methodology used to obtain the measured accelerations and whether all forms of resistance were eliminated during the experiment.

Discussion Status

The conversation is ongoing, with participants providing guidance on factors that could affect the results, such as rolling resistance and the accuracy of angle measurements. Multiple interpretations of the results are being explored, particularly regarding the relationship between incline angle and acceleration measurements.

Contextual Notes

Participants note that the original poster used a hockey puck for the experiment, which may introduce additional rolling resistance. There is also a mention of the need to ensure angles are measured correctly, as one participant questions whether angles were converted to radians appropriately.

mlostrac
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Homework Statement


Assuming smooth rolling with no resistance, it can be shown that the acceleration of a solid cylinder down an incline is equal to:

a = 2/3 g sin(theta)

The goal of my lab is to test the validity of the above equation


Homework Equations





The Attempt at a Solution


The acceleration values I found using my measured inclination angles, are smaller than what they would be if i plugged them into the above equation. What does this mean? If this is the case, does that mean that the above equation isn't valid?
 
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Did you put your angle in radiants?
 
mlostrac said:
Assuming smooth rolling with no resistance...

Were you able to eliminate all rolling resistance in your lab? With rolling resistance present would you expect acceleration to be higher or lower than theoretical? How close to theoretical were your measured accelerations?
 
tvavanasd said:
Were you able to eliminate all rolling resistance in your lab? With rolling resistance present would you expect acceleration to be higher or lower than theoretical? How close to theoretical were your measured accelerations?

I'm not sure, but I'm going to assume that I didn't eliminate all resistance; I rolled a hockey puck on it's side down a wooden board.

I'd assume that if resistance was present that it would cause the acceleration to be lower than theoretical.

One example comparing theoretical and measure for a 5.7 degree incline:
theoretical = 0.649 m/s^2
measured = 0.073 m/s^2
 
srmeier said:
Did you put your angle in radiants?

yes i did, 25.6 degrees = .46 rad
 
mlostrac said:
I'd assume that if resistance was present that it would cause the acceleration to be lower than theoretical.

One example comparing theoretical and measure for a 5.7 degree incline:
theoretical = 0.649 m/s^2
measured = 0.073 m/s^2

Your assumption is correct, but the discrepency seems quite large.
How did you arrive at your measured accel?
Were you able to sample multiple points during the test or simply average over time and displacement?
How long was the ramp?
Did you find the theoretical vs measured to be closer as the ramp slope increased?

Shouldn't be significant, but 25.6 degrees is 0.447 radians.
 

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