Physics- Work

Question

A car goes at a constant 16 m/s up a hill. the frictional force is 500N. The height of the hill is .3 km and it the car travels a distance of 4.8 km. What is the work done in order to get to the top of the hill.

Answer 1

OK, with the mass of 1000 kg:

 

There is no acceleration, so the work is done by a force that balances the opposing forces of gravity and friction.  I assume the hill is like an inclined plane with a base of 4800 m and a height of 300 m.  The travel distance parallel to the plane is

 

d = √(4800² + 300²) m ≅ 4809 m.

 

The inclination of the plane is 

 

θ = tan^-1(0.3/4.8) ≅ 3.58°

 

Without acceleration, the work done against gravity (mg sinθ) and friction (f = 500 N) along the inclined plane is

 

W = (mg sinθ + f)d

 

W = [(1000 kg)(9.8 m/s²)sin3.58° + 500N](4809 m) ≅ 5.35 x 10⁶ J = 5.35 MJ