In the figure, a constant horizontal force ModifyingAbove Upper F With right-arr

Question

In the figure, a constant horizontal force ModifyingAbove Upper F With right-arrow Subscript a p p of magnitude 62.7 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 23.1 kg, its radius is 0.441 m, and the cylinder rolls smoothly on the horizontal surface. (a) What is the magnitude of the acceleration of the center of mass of the cylinder? (b) What is the magnitude of the angular acceleration of the cylinder about the center of mass? (c) In unit-vector notation, what is the frictional force acting on the cylinder?

Explanation / Answer

Here ,

a) let the acceleration of the cyclinder is a

Using second law of motion

a = F/(I/r^2 + m)

a = 62.7/(0.50 * 23.1 + 23.1)

a = 1.81 m/s^2

b)

magnitude of angular acceleration = a/radius

magnitude of angular acceleration = 1.81/0.441

magnitude of angular acceleration = 4.104 rad/s^2

c)

frictional force = - (Fapp - m * a)

frictional force = - (62.7 - 23.1 * 1.81)

frictional force = -20.9 N

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