Question

Here is a homework question I had:

A dump truck, whose bed is made of steel, holds an old steel watering trough. The bed of the truck is slowly raised until the trough begins to slide. Steel on steel static friction is .8 and kinetic is .6. What is the acceleration of the trough as it slides down the truck bed?
Express your answer with the appropriate units.

Answer 1

First of all we need to find the sliding angle:
\alpha = atan(μ_s) = atan(0.8) = 38.66 degrees
Now we need to write Newton's second law:
ma = mg sin(\alpha) - μ_k mg cos(\alpha)
or
a = g cos(\alpha) * (tan(\alpha) - μ_k) = g cos(\alpha) * (μ_s - μ_k)
so
a = 9.8 * 0.78 * (0.2) = 1.53 m/s^2