Moving at a constant speed, an elevator lifts a 1000 N package 10 meters in 3 seconds. During this time, the impulse delivered to the package by the elevator floor is
A) 10,000 Ns up.
B) 3,000 Ns up.
C) 10,000 Nm up.
D) zero.

Question

Quizplus · Accepted Answer

The impulse delivered to an object is given by the equation:

Impulse = Force x Time

Since the package is lifted at a constant speed, that means the net force acting on the package is zero (otherwise, the package would be accelerating). Therefore, the only force acting on the package is its weight, which is 1000 N.

Since the package is lifted a distance of 10 meters, the work done by the force of gravity is:

Work = Force x Distance x cos(theta)

where theta is the angle between the force and the direction of motion. Since the force of gravity is downwards and the package is lifted upwards, theta is 180 degrees, so cos(theta) = -1.

Therefore, the work done by gravity is:

Work = (1000 N) x (10 m) x (-1) = -10,000 J

Since the only force acting on the package is its weight, and the work done by gravity is negative, the elevator must do an equal amount of positive work in order to lift the package at a constant speed. Therefore, the impulse delivered by the elevator is:

Impulse = Force x Time = (1000 N) x (3 s) = 3000 Ns up

Therefore, the correct answer is B.

Moving at a Constant Speed, an Elevator Lifts a 1000