Final answer:
The work done on the 1500-kg elevator by the gravitational force during its 40.0 m ascent is -588,600 J, which is negative because the force of gravity acts in the opposite direction of the motion.
Step-by-step explanation:
Work Done by Gravitational Force on an Elevator
To calculate the work done on a 1500-kg elevator car by the gravitational force during its 40.0 m ascent, we use the equation for gravitational potential energy,
which is also the work done by gravity when lifting an object: W = mgh, where W is the work done by gravity, m is the mass of the elevator, g is the acceleration due to gravity (approximately 9.81 m/s2), and h is the height lifted.
Substituting the given values, we have W = (1500 kg)(9.81 m/s2)(40.0 m). This results in W = 588,600 J. However, since the elevator is being lifted against the force of gravity, the work done by the gravitational force is negative, so Wgravity = -588,600 J.
The negative sign indicates that gravity does work against the direction of motion. Because the elevator is moving at a constant speed, the cable does work to overcome both the force of gravity and any friction present.