Calculate the work done on a 1500 kg

EMALY HENDERSON

EMALY HENDERSON

Answered question

2022-09-24

Calculate the work done on a 1500 kg elevator car by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N.

 

Answer & Explanation

fudzisako

fudzisako

Skilled2023-06-01Added 105 answers

The work done on an object is given by the formula:
W=F·d·cos(θ)
where F is the force applied, d is the distance moved, and θ is the angle between the force and the direction of motion.
In this case, the elevator car is being lifted at a constant speed, which means the net force acting on it is zero. Therefore, the force applied by the cable is equal in magnitude and opposite in direction to the force of friction.
Hence, the force applied by the cable is fapplied=ffriction=100 N.
Since the elevator car is lifted vertically, the angle between the force applied by the cable and the direction of motion is 0°. Therefore, cos(0)=1.
Substituting the given values into the formula for work, we have:
W=fapplied·d·cos(θ)
W=(100N)·(40.0m)·cos(0)
Simplifying this expression, we find:
W=4000 J
The negative sign indicates that work is done against the direction of motion.
Therefore, the work done on the elevator car by its cable to lift it 40.0 m at constant speed, assuming an average friction force of 100 N, is -4000 J.

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