A lawn roller in the form of a uniform solid cylinder is being pulled horizontal

Question

A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller, as shown in the figure. The roller has radius 0.48 meters and mass 27 kg and rolls without slipping. What magnitude of the force B is required to give the center of mass of the roller an acceleration of 9.4 m/s2?

A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller, as shown in the figure. The roller has radius 0.48 meters and mass 27 kg and rolls without slipping. What magnitude of the force B is required to give the center of mass of the roller an acceleration of 9.4 m/s2?

Explanation / Answer

The torque exrterd on the cylinder is

T = F R

Also,

T = I a / R

as

I = 1/2 M R^2

Then

T = M R a / 2

Thus,

M R a / 2 = F R

--> F = M a /2

Thus,

F = 127 N [ANSWER]

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