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Answer :
The work done by the cable on a 1,438-kg elevator to lift it 50 meters at a constant velocity, accounting for friction, is 710.37 kilojoules.
To calculate the work done on a 1,438-kg elevator car by its cable to lift it 50 m at constant speed, we must account for the force of gravity acting on the elevator as well as the friction force. The total force that the cable must exert is equal to the gravitational force plus the friction force. The gravitational force (weight) is calculated using Newton's second law of motion (F = m*g, where m is the mass and g is the acceleration due to gravity, which is approximately 9.8 m/s2).
The work done by the cable (W) is then the total force exerted by the cable (Fcable) times the displacement (d), or W = Fcable * d. However, since the elevator moves at a constant speed, the work done by the friction force does not contribute to lifting the elevator but instead goes into overcoming the frictional force.
Work done by the cable = (Weight of the elevator + Friction force) * Displacement
Weight of the elevator = mass * gravity = 1,438 kg * 9.8 m/s2 = 14,092.4 N
Total force exerted by the cable = Weight of the elevator + Friction force = 14,092.4 N + 115 N = 14,207.4 N
Work done = 14,207.4 N * 50 m
Work done = 710,370 J
Converting joules to kilojoules (1 kJ = 1,000 J):
Work done = 710.37 kJ
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