There is a van that is being pushed by a car. The car is pushing the van from the van's behind. The van's mass is 4M and the car's mass is M. If the max force that the ground can provide to the car's tires is F, then what are the max forces between the car and the van? . Consider that there are no other horizontal forces acting on the van

1 answer

It depends on the motion of the two vehicles. We assume that both vehicles are on a horizontal surface.

If both are stationary, the maximum force is μs(4M)g, the frictional force of the car reisisting motion, at the point just before motion starts.
μs is the coefficient of static friction.

If they are both in uniform velocity, then the maximum force is then μk(4M)g
where μk is the coefficient of kinetic friction.

If both are accelerating at a rate of a m/s², then the maximum force is μk(4M)g+(4M)a.

All forces are in the direction of motion of the vehicles.