Question

A frictionless pulley with the shape of a solid cylinder has a mass of 10 kg and a radius of 10 cm. A 1 kg block is attached to a massless wire around the rim of the pulley. The system is released from rest. What height (in meters) does the block have to fall after it is released from rest for the block to obtain a velocity of 1 m/s?

Answer 1

net force on the block of mass m is Fnet = mg-T = ma

net torque is Tnet = I*alpha

alpha = a/R

Tnet = T*R and I is the moment of inertia = 0.5*M*R^2

then T*R = 0.5*M*R^2*(a/R)

T = 0.5*M*a

then Fnet = mg-T = ma

mg-0.5Ma = ma

accelaration a = mg/(m + 0.5M)

a = (1*9.81)/(1 +(0.5*10)) = 1.635 m/s^2

initial speed is u = 0 m/s

final speed is v = 1 m/s

distance travelled is S

then using v^2 - u^2 = 2*a*S

1^2 = 2*1.635*S

S = 0.305 m