Question

suppose a 1200-kg elevator car is lifted a distance 39 m by its cable at a constant speed, assuming the frictional force on the elevator has a constant value of 1575 n. Calculate the work done on the elevator by its cable, in joules

Answer 1

The work done on the elevator by its cable is 61325 Joules.

Step-by-step explanation:

To calculate the work done on the elevator by its cable, we need to find the net force acting on the elevator and multiply it by the distance the elevator is lifted. The net force is the difference between the force applied by the cable and the frictional force. The force applied by the cable can be found using Newton's second law:

F = ma

where F is the force applied by the cable, m is the mass of the elevator, and a is the acceleration. Since the elevator moves at a constant speed, the acceleration is zero. Therefore, the force applied by the cable is equal to the frictional force:

F = Frictional Force = 1575 N

Now, we can calculate the work done:

Work = Force x Distance

= Frictional Force x Distance

= 1575 N x 39 m = 61325 Joules

Answer 2

The work done by the elevator cable is 520065 J, calculated by multiplying the total force exerted by the cable (13335 N) to overcome both gravity and friction by the distance the elevator is lifted (39 m).

Step-by-step explanation:

To calculate the work done on a 1200-kg elevator car that is lifted 39 m by its cable at constant speed, given a constant frictional force of 1575 N, you use the formula for work done by a force: Work = Force × Distance. The cable must exert a force equal to the weight of the elevator car plus the frictional force to lift it at a constant speed. Since the elevator is moving at constant speed, the net force in the vertical direction is zero, which means the tension in the cable (lifting force) must counterbalance both gravitational force and friction.

The gravitational force (weight) acting on the elevator is calculated by multiplying the mass of the elevator by the acceleration due to gravity (g = 9.8 m/s²). So, gravitational force = mass × g = 1200 kg × 9.8 m/s² = 11760 N. The lifting force exerted by the cable, therefore, must be 11760 N + 1575 N (to overcome friction) = 13335 N. The work done by the cable is then 13335 N × 39 m = 520065 J (joules).