Final answer:
The work done on a 1250-kg elevator car by its cable to lift it 43 m, overcoming a frictional force of 1525 N at constant speed, is calculated by summing the gravitational force and the frictional force exerted by the cable and multiplying by the distance moved. The result is 592525 joules.
Step-by-step explanation:
The question involves calculating the work done on an elevator car by its cable while lifting the car at a constant speed and overcoming a frictional force. To find the work done by the cable on the 1250-kg elevator lifted by a distance of 43 m, we'll use the formula for work, which is product of the force exerted by the cable and the distance moved in the direction of the force:
Work done by the cable = (force exerted by the cable - frictional force) × distance.
In this case, the only forces doing work are the cable and friction. The gravitational force does no work since it is perpendicular to the direction of movement (elevator moves horizontally). Since the elevator moves at a constant speed, the force exerted by the cable must balance out both the gravitational pull and the frictional force.
The force due to gravity acting on the elevator is the product of the mass of the elevator and the acceleration due to gravity (9.8 m/s²). Thus, the force due to gravity is 1250 kg × 9.8 m/s² = 12250 N. The total force that the cable must exert is:
Force exerted by the cable = force due to gravity + frictional force
Force exerted by the cable = 12250 N + 1525 N = 13775 N.
The work done by the cable can be calculated as:
Work done by the cable = 13775 N × 43 m = 592525 J.
Hence, the work done on the elevator by its cable is 592525 joules.