A spool of wire of mass M and radius R is unwound under a constant S force F (Fi

Question

A spool of wire of mass M and radius R is unwound under a constant S force F (Fig.P10.76). Assuming the spool is a uniform, solid cylinder that doesn A spool of wire of mass M and radius R is unwound under a constant S force F (Fig.P10.76). Assuming the spool is a uniform, solid cylinder that doesn A spool of wire of mass M and radius R is unwound under a constant S force F (Fig.P10.76). Assuming the spool is a uniform, solid cylinder that doesn A spool of wire of mass M and radius R is unwound under a constant S force F (Fig.P10.76). Assuming the spool is a uniform, solid cylinder that doesn???t slip, show that (a) the acceleration of the center of mass is 4F/3M and (b) the force of friction is to the right and equal in magnitude to F/3. (c) If the cylinder starts from rest and rolls without slipping, what is the speed of its center of mass after it has rolled through a distance d?

Explanation / Answer

I =- Icm + M*R^2 (1/2)*M*R^2 + M*R^2 = (3/2)*M*R^2

Torque due to F = I*alfa

F*2R = (3/2)*M*R^2*a/R

F*2 = (3/2)*M*a

F = 4F/3M

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b) F + f = M*a

f = M*a -F = F/3

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c) v^2 = 2*a*d = 2*(4F/3M)*d

v = sqrt(8Fd/3M)

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