Question

Two blocks are attached to opposite ends of a string that passes over a massless, frictionless pulley (see the figure). Block ? of mass 10.0 kg lies on a 60.0° incline with a coefficient of friction of 0.500, and block ? of mass 1.00 kg is attached to a vertical spring of force constant 200 N/m. The blocks are initially at rest with the spring at equilibrium. Find the maximum height that the block ? rises.

Answer 1

for block A

work done by gravity

WAg = mA*g*sintheta*h

for block B

work done by gravity

WBg = -mB*g*h

work done by spring force

Ws = -(1/2)*k*h^2

work done by friction

Wf = -uk*mA*g*costheta*h

initial and finally the blocks are at rest

Ki = Kf = 0

from work energy relation total work = change in KE

mA*g*sintheta*h - mB*g*h - (1/2)*k*h^2 - uk*mA*g*costheta*h = 0

(10*9.81*sin60*h) - (1*9.81*h)-(1/2)*200*h^2 - (0.5*10*9.81*cos60*h) = 0

h = 0.506 m <<------------answer