QUESTION 4 Consider the type of apparatus that will be used in the lab. A cube o

Question

QUESTION 4 Consider the type of apparatus that will be used in the lab. A cube of mass M-0.500kg and side length s-0.030m is free to spin on an axis through the center of one face. A massless pulley connected to this axis has a diameter of d-2r-0.010m. Another object of mass, m-0.050kg, is hung from the pulley by a string which is rung around the pulley several times. After releasing the hanging mass the Tension provided by the weight of the hung object will begin to spin up the cube. What is the torque the tension produces about the axis in SI units? 00145Nm 00491Nm .00245Nnm 00256Nm

Explanation / Answer

We know that,

torque = I alpha

alpha = mg/(mr + ml^2/6r)

alpha = 0.05 x 9.8/(0.05 x 0.005 + 0.5 x 0.03^2/6 x 0.005) = 32.13 rad/s^2

I = 1/6 x 0.5 x 0.03^2 = 7.5 x 10^-5 kg-m^2

Tau = I alpha = 7.5 x 10^-5 x 32.13 = 0.0024 N-m

Hence, Tau = 0.0024 Nm

theta = L/R = 0.3/0.005 = 60 rad

we know that

5)theta = wt + 1/2 alpha t^2

t = sqrt (2theta/alpha) = sqrt (2 x 60/32.13) = 1.93 s

w = alpha t = 32.13 x 1.93 = 62 rad/s

KE = 1/2 I w^2

KE = 0.5 x 7.5 x 10^-5 x 62^2 = 0.145 J

Hence, KE = 0.145 J

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