A constant horizontal force of magnitude 14 N is applied to a wheel of mass 10 k

Question

A constant horizontal force of magnitude 14 N is applied to a wheel of mass 10 kg and radius 0.30 m. The wheel rolls smoothly and the acceleration of its center of mass is 0.6 m/s^2. (a) What is the magnitude of the force of friction. (b) Find the moment of inertia of the wheel through its center of mass? (Not using a formula, you can solve for this value.) A solid cylindrical pulley with a mass of 1.30 kg and a radius of 0.230 m is free to rotate about its axis. An object of mass 0.240 kg is attached to the pulley with a light string. Assume the string does not stretch or slip. (Express your answer to three significant figures. Use: I_disk = 1/2 M R^2) (a) Calculate the linear acceleration of the mass. (b) Is this less than g? (c) What if you increased the mass of the pulley? Would the acceleration be greater or less that your answer for part (a)? (d) Calculate the angular acceleration of the pulley. (e) Calculate the tension in the string.

Explanation / Answer

(1)

(A) Fnet = m a

Fapp - f1 = m a

14 - f = 10 x 0.6

f = 8 N .......Ans

(B) Applying torque equation,

net torque = I alpha

alpha = a / r = 0.6 / 0.30 = 2 rad/s^2

f1 r = I alpha

8 x 0.3 = I x 2

I = 1.2 kg m^2

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