Alawn roller in the form of a solid uniform cylinder is being pulled horizontally by a horizontal force b applied to an axle through the center of the roller. the roller radius 0.59 m and mass 48 kg. what magnitude b of the force is required to produce and acceleration a=4.2 m/s^2 of the center of mass of the roller if the lawn rolls without slipping?

Explanation:

mass, m = 48 kg

radius, r = 0.59 m

acceleration of center of mass, a = 4.2 m/s2

The free body diagram of cylinder is as follows:

Since the cylinder is rolling without slipping, therefore,a=αr,

which gives, angular acceleration, α = a/r = (4.2/0.59)rad/s2 = 7.12 rad/s2

Moment of inertia of cylinder about center of mass C, IC= (1/2)mr2

So, by parallel axis theorem, moment of inertia about point A,IA = (1/2)mr2 + mr2 =(3/2)mr2 = (3/2)*48*0.592 kg.m2 =25.06 kg.m2

Now, taking the moment of forces about point A, T =IAα

which gives, B*r = IAα, and we get, B =(25.06*7.12)/0.59 N = 302.42 N

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more

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