Help with a question form 1984 physics B AP exam

[Petrikovski]

Two 10-kilogram boxes are connected by a massless string that passes over a massless frictionless pulley. The bxes remain at rest, with one on the right hanging vertically and the one n the left 2.0 meters from the bottom of an inclined plane that makes an angle of 60 degrees with the horizontal. The coefficients of kinetic and static friction between the box on the incline and the plane are .15 and .30 respectively. You may use g = 10 m/s^2, sin60 = .87 and cos60 = .5

The string is then cut and the left-hand box slides down the inclined plane

d) Determine the amount of mechanical energy that is converted into thermal energy during the slide to the bottom?

e) Determine the kinetic energy of the left-hand box when it reaches the bottom of the plane. I assume for this i use KE = 1/2mv^2 but how do i get V?

 

[Astronuc]

Well the box is sliding down the incline under influence of gravity, however there is a resistive force of friction. One calculates the net force.

From force, one obtains the acceleration.

From acceleration one can apply the appropriate relationship between velocity, distance and acceleration. The initial velocity is zero.

The thermal energy is related force of friction applied over distance.