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.
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