110 tonne steam engine uses a force of 400 kN to pull two coal trucks (each with a mass of 45 tonnes) up a 3.00° degree incline. If the coefficient of friction involved is 0.080, determine the tension, T, in the coupling between the trucks.

Answer 1

First, determine the net force pulling the two trucks, and from that, get their acceleration.

Fnet = 400*10^3 - 90*10^3*g*sin3 -0.08*90*10^3*cos3 = 400*10^3 -46*10^3 - 7.2*10^3 = 3.47*10^5 N
a = Fnet/90*10^3 = 0.428 m/s^2

Then consider the free body diagram for a single truck, to get the tension T in the coupling.

T - Ffriction - M g sin 3 = Mtruck*a