Question

A 2000 kg car moves down a level highway under the actions of two forces. A 1000 N forward force exerted on the drive wheels by the road and a 950 N resistive force. Find the net work done on the car after it has moved a distance of 20 m, assuming that it starts from rest.

• A. $1.8\times {10}^{5}J$
• B. $5.4\times {10}^{3}J$
• C. $1.0\times {10}^{3}J$
• D. $0.1\times {10}^{5}J$

Answer 1

The correct option is C

$1.0\times {10}^{3}J$

The forward force exerted on the car by the road is in the direction of the displacement $({\theta }_1=0^{\circ })$ while the resistive force is directed opposite to the displacement $({\theta }_2={180}^{\circ })$

Other forces acting on the car (that is, the normal force exerted by the road and the gravitational force)

Are perpendicular to the displacement and hence does not work.

Therefore, the net work done on the car is

$W_{net}=\left(Fcos{\theta }_1\right)s+\left(fcos{\theta }_2\right)s$

$W_{net}=\left[1000Ncos{0}^{\circ }\right]s+\left[950Ncos{180}^{\circ }\right]s$

$W_{net}=(1000N-950N)20m$

$W_{net}=1.0\times {10}^{3}J$