The circular disk of 200-mm radius has a mass of 25 kg with centroidal radius of

Question

The circular disk of 200-mm radius has a mass of 25 kg with centroidal radius of gyration k = 175 mm (I = mk2). It has a concentric circular groove of 75 mm radius. A steady force T is applied, not jerked but very slowly, at an angle theta to the cord wrapped around the groove as shown. The coefficients of friction arc mu5 = 0.1 and mu k = 0.08. Assume rolling motion and determine the followings, in terms of T and theta: normal reaction force (P) the actual friction force (f) angular acceleration (alpha) Plot alpha/T for theta = 0 to 90 degree and determine when it changes the direction from the graph or analytically. Set T = 50 N and determine the actual friction force f and fmax = mus P as functions of the angle 0. Graph them for theta = 0 to 90 degree in a single plot. What can you tell from the plot?

Explanation / Answer

Fx=0     -F +30 = 25 aG ....F is Fricitonal Force

Fy=0     N - 25(9.81)=0....N is a Normal reaction acting between ground and roller in upward direction

MG=IG*alpha      F(0.2) - 30(0.075) = 25(0.175)2 (alpha) ...Equation 1

Assuming its rolling: aG =0.2 (alpha)

F= 30-25(0.2)(alpha) -- ---Subsititute in Equation 1

we get, alpha = 2.124 radians/sec2

aG = 0.4245m/s^2

F=30-25(0.4248) = -19.38 N

This is how we appraoch the problem.. I hope it helps

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