A Physics 211 student is studying the efficiency of braking systems for her proj

Question

A Physics 211 student is studying the efficiency of braking systems for her project. Her ultimate goal is to obtain the coefficient of kinetic friction between a solid disk and a brake pad. A schematic diagram of her experimental apparatus is shown in figure 1. She starts the disk spinning with a motor, and it reaches a particular rotational speed. Then she removes the motor and applies the brake with a constant force of 1 N. Her rotary motion sensor starts taking data just as the brake is applied. On one particular run she obtains the data shown in figure 2, which she has analyzed using a "modelingWorksheet.xls" spreadsheet and some additional curve fitting software tools to get the SDM of each coefficient. With your knowledge of fundamental mechanics and your experience with curve fitting and modeling, you should be able to infer her experimental strategy from the information displayed on the chart. The disk has a radius of 10 cm, and a mass of 1 kg. Ignore the bearing friction in this problem. Explain her experimental strategy, i.e. what assumptions is she making and what steps must she take to find the coefficient of friction? What is the initial rotational speed of the disk, including its experimental uncertainty? Is the rotational acceleration a constant? If yes, what is its magnitude, including its experimental uncertainty? Justify your answer from the information given in the problem. When the brake is applied, it generates a torque on the disk. Is the torque constant? How do you know? If yes, determine its magnitude. (If you need the result from a previous part of this question that you couldn't get (i.e., omega and/or alpha), choose a reasonable number and proceed. Explicitly state that this is what you are doing.) Determine the value of the coefficient of friction of the brake pad against the disk. Make sure that you clearly show all your steps and reasoning. (Again, if you need the result from a previous part of this question that you couldn't get (i.e., omega, alpha and/or tau), choose a reasonable number and proceed. Explicitly state that this is what you are doing.)

Explanation / Answer

a> Her experimental strategy is simple , the force of friction is given by mu*N. The normal force is the force with which the force is being exerted on brake. The force of friction and the rotational speed variation would enable her determine the braking coefficient.

b> 12.2 = w*0.2 + 0.5*alpha*0.04

24 = w*0.4 +0.5*alpha * 0.16

-> 0.5*alpha*0.04 = -0.2

-> alpha = -0.2/0.02 =-10rad/s2

w0 = 60 rad/s

c> No it isnt,

t = 0.6s

35 = 60*0.6 + 0.5*alpha*0.36

alpha =-5.5555rad/s2

d> yes a torque is generated. That is evident by the negative acceleration generated by the brake. As negative acceleration is not constant, the torque isnt constant. torque =I*alpha.

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