Physics HW Question-Acceleration and Force with a truck

Question

A 2000 kg truck has put its front bumper against the rear bumper of a 2500 kg SUV to give it a push. With the engine at full power and good tires on good pavement, the maximum forward force on the truck is 18,000 N.

-What is the maximum possible acceleration the truck can give the SUV?

-At this acceleration, what is the force of the SUV's bumper on the truck's bumper?

Answer 1

4m/s/s; 10000N

Answer 2

M_t = 2000 kg is the mass of the truck

M_s = 2500 kg is the mass of the SUV

F = 18,000 N is the maximum forward force the truck can push with.

What is the maximum possible acceleration the truck can give the SUV?

Acceleration (a) is determined by writing F = (M_t + M_s)a and solving for a.

a = F/(M_t + M_s) = 18,000/4,500 = 4 m/s²

At this acceleration, what is the force of the SUV's bumper on the truck's bumper?

Since the SUV is moving with an acceleration of 4 m/s², it is being pushed by the truck with a forward force (F = ma) of (M_s)(a) = (2,500)(4) = 10,000 N.

The force of the SUV's bumper on the truck's bumper has the same magnitude but opposite direction. It is a backward force of 10,000 N.