Final answer:
The work done by the elevator cable was 592000 J, the work done by the gravitational force was -588000 J (which translates to zero net work due to constant speed), and so the total work done on the elevator car was 4000 J.
Step-by-step explanation:
To calculate the work done on a 1500-kg elevator car by its cable to lift it 40.0 m at constant speed with an average frictional force of 100 N, we apply the work formula which is work (W) = force (F) × displacement (d). Since the lift moves at a constant speed, the force exerted by the cable is equal to the gravitational force plus the frictional force.
Gravitational force (weight) = mass (m) × gravitational acceleration (g), which is (1500 kg) × (9.8 m/s²) = 14700 N.
The total force the cable needs to exert is 14700 N (to counteract gravity) + 100 N (to counteract friction) = 14800 N.
Then, work done by the cable: W = F × d = (14800 N) × (40.0 m) = 592000 J (joules).
(b) The work done on the elevator car by gravitational force over the 40.0 m is given by the opposite of the gravitational force times the displacement, since work by gravity is negative when it’s in the direction opposite to displacement. Thus, W = - (weight) × d = - (14700 N) × (40.0 m) = -588000 J. However, since the speed is constant, the net work done by gravity is zero as kinetic energy does not change.
(c) The total work done on the elevator car is the sum of the work done by the cable and the work done by gravity, which is 592000 J - 588000 J = 4000 J.