A 26.6 kg box is initially kicked so that it slides up a ramp inclined at 29 degrees above the horizontal. The coefficient of kinetic friction between the box and the ramp is 0.31.

Question

Find the magnitude of the acceleration of the box, in m/s^2.

Answer 1

Write Newton's 2^nd law for the box, considering the force components along the ramp:

ma = friction + component of mg along the ramp

ma = - μmgcosθ - mgsinθ (both forces are down the ramp, opposing the motion)

Solve that equation for a, and plug in the numbers. The negative sign means the acceleration is down the ramp. The chosen positive direction is up the ramp.