A solid sphere of radius = 8 cm and mass = 5 kg is sitting on a level table and

Question

A solid sphere of radius = 8 cm and mass = 5 kg is sitting on a level table and is attached with a
string over a pulley (radius = 2 cm and mass = .8 kg) to a hanging mass (m = 3 kg) which is 4
meters above the ground
d)Calculate the static frictional force, fs. What is the minimum fs required for pure rolling
motion?
e) Calculate the Total work done on the sphere, pulley, block Wsphere, Wpulley, Wblock
f) Calculate the final angular and linear speeds of the sphere, wf(angular speed) sphere, vf sphere

Explanation / Answer

f =3g where g is gravity

m is mass of sphere

f-fs =ma ...1
also fs*r =I

for pure rolling r =a

fs*r =Ia/r

here for solid sphere I =(2/5)mr^2

fs*r =(2/5)mr^2 *a/r

fs =(2/5)ma

putting thi in equation 1

we get

f-(2/5)ma =ma

a= (5/7)f =15g/7 where g is gravity

friction force =fs =(2/5)m*(15g/7) =6mg/7 = 42 N

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