Kinetic energy of cylinder is consumed in doing work against friction in rolling motion.
A body of mass
m moving with velocity
v, Possess kinetic energy given by
K=21mv2…(1) This kinetic energy is utilized in doing work against the frictional forces.
W=μmgs…(2) Where
μ is coefficient of kinetic friction,
m is mass,
g is gravity and
s is displacement.
Equating Egs. (1) and
(2), we get
21mv2=μmgs Where
21mv2=21×10×(10)2=500kg−m/s Given,
v=10m/s,μ=0.5,m=10kgg=10m/s2⇒s=μmg21×m×(10)2=0.5×1050=10m