Question

The (non-conservative) force propelling a 1.70 x 103-kg car up a mountain road does 8.20 x 106 J of work on the car. The car starts from rest at sea level and has a speed of 27.0 m/s at an altitude of 1.70 x 102 m above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are non-conservative forces.

Answer 1

Using energy conservation:

Work-done by non-conservative forces = Change in kinetic energy + Change in potential energy

W_net = dKE + dPE

W_net = W_fr + W_air + W_rest

dKE = KEf - KEi = (1/2)*m*Vf^2 - (1/2)*m*Vi^2

dPE = PEf - PEi = m*g*hf - m*g*hi

So,

W_net = (1/2)*m*Vf^2 - (1/2)*m*Vi^2 + m*g*hf - m*g*hi

W_net = (1/2)*1.70*10^3*27.0^2 - (1/2)*1.70*10^3*0^2 + 1.70*10^3*9.8*1.70*10^2 - 1.70*10^3*9.8*0

W_net = 3451850

W_net = W_fr + W_air + W_rest = 3451850 J

W_rest = Work-done on the car by non-conservative forces = 8.20*10^6 J

So,

W_fr + W_air = 3451850 - 8.20*10^6

W_fr + W_air = -4748150 J

W_fr + W_air = -4.75*10^6 J

Let me know if you've any query.