For this winter fun project, I decided to calculate the average tension in the rope of a sled when the person is being pulled on ice. As seen in the video above, my friend Shaila volunteered to be pulled in the sled. This was done at our friend Victoria's house, as her dad made an ice rink in their backyard.
Process
To calculate the tension, my friend Abby recorded a video of me pulling Shaila on the sled. This video was then imported into Logger Pro, and the initial and maximum velocities were found (the final velocity would be 0, so it was not used). Since I could not find any useful measuring device to use as a reference, I used an 8.5" x 11" piece of paper. As a result, all of the data was captured in inches, and the data had to be converted to meters. The below calculations were then computed in order to find an estimation of the average tension.
Calculations
Using kinematics the average acceleration can be calculated.
Vf = Vi + at
0.297 = 0 + a(2.37)
a = 0.125 m/s2
Next, a free body diagram and sum of forces equations can be used to find the tension. The friction will be considered negligible.
ΣFx: Tcosθ = ma
Tcos(51.6) = (49.2)(0.125)
T = [(49.2)(0.125)]/[cos(51.6)]
T = 9.90 N
Result
The average tension I found for this situation was 9.90 N. This is most likely an underestimation, however, since friction was not accounted for. With the friction on the ice, the tension would have to be higher in order to compensate for friction acting in the opposite direction of travel.
Can you think of an easy way to find the coefficient of the sled on ice given the materials you had on hand?
ReplyDeleteIf I had pushed her, I could've used Logger Pro to find her deceleration from her max velocity. Then I could've used sum of forces to find the force of friction, and then solve for the coefficient using the normal force.
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