Question

The (nonconservative) force propelling a 1.50 103-kg car up a mountain road does 5.10 106 J of work on the car. The car starts from rest at sea level and has a speed of 24.0 m/s at an altitude of 2.20 102 m above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are nonconservative forces.

Answer 1

We know, Work done by all the forces is equal to change in potential energy :

$W_{friction} + W_{air} + W_{engine} = \dfrac{(mv_f^2 + mgh_f)}{2}-\dfrac{(mv_i^2+mgh_i)}{2}$

Here,

$h_i=0\ m\\\\v_i = 0\ m/s$

Putting all given values, we get :

$W_{friction} + W_{air} + 5.10\times 10^6 = m\dfrac{(v_f^2 + gh_f)}{2}-0\\\\W_{friction} + W_{air} =1.5\times 10^3 \times \dfrac{(24^2 + (9.8\times 2.2\times 10^2))}{2}-5.10\times 10^6\\\\W_{friction} + W_{air} = -3.051\times 10^6\ J$

Hence, this is the required solution.