Question

A bicyclist rides 1.68 km due east, while the resistive force from the air has a magnitude of 5.57 N and points due west. The rider then turns around and rides 1.68 km due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of 5.57 N and points due east. Find the work done by the resistive force during the round trip.

Answer 1

Work done by a force is given by:

W=F*s*cos

where W is the work done, F is the magnitude of force that is doing the work,s is the magnitude of displacement and is the angle between force and displacement vectors.

When the rider is going eastward:

Magnitude of displacement s= 1.68 km=1680 m

Magnitude of resistive force=5.57 N

Angle between force and displacement vectors= as displacement is towards east while resistive force is towards west.

So,W=F*s*cos =5.57*1680*cos180 = -9357.6 J

When the rider is going westward:

Magnitude of displacement s= 1.68 km=1680 m

Magnitude of resistive force=5.57 N

Angle between force and displacement vectors= as displacement is towards west while resistive force is towards east.

So,W=F*s*cos =5.57*1680*cos180 = -9357.6 J

So, total work done= -9357.6-9357.6= - 18715.2 J