Question

a cable lifts a 1200 kg elevator at a constant velocity for a distance of 35 m. what is the work done by (a) the tension in the cable and (b) the elevator’s weight?

Answer 1

The work done by the tension in the cable is equal to the weight of the elevator, and can be calculated using the formula Work = Tension × Distance. The work done by the elevator's weight is also given by the formula Work = Weight × Distance.

Step-by-step explanation:

The work done by the tension in the cable to lift the elevator can be calculated using the formula:

Work = Force × Distance

Since the elevator is moving at a constant velocity, there is no acceleration, so the net force is zero. Therefore, the tension in the cable is equal to the weight of the elevator. The work done by the tension in the cable is given by:

Work = Tension × Distance

Using the formula:

Weight (W) = mass (m) × acceleration due to gravity (g)

The weight of the elevator is given by:

Weight = 1200 kg × 9.8 m/s²

Therefore, the work done by the tension in the cable is:

Work = Weight × Distance

On the other hand, the work done by the elevator's weight can be calculated using the same formula:

Work = Weight × Distance

Answer 2

The work done by the tension is 411,600 Joules, calculated by multiplying the elevator's weight by the distance it is lifted. The work done by the elevator's weight is -411,600 Joules, which is equal in magnitude but opposite in direction to the work done by the tension.

Step-by-step explanation:

The student's question involves calculating the work done by the tension in the cable and the work done by the elevator's weight when it is lifted at a constant velocity for a certain distance. Since the elevator is moving at a constant velocity, the net work done is zero because the forces are balanced (tension equals the weight of the elevator). Therefore, in this case:

• (a) The work done by the tension in the cable is simply the force of tension times the distance. The force of tension equals the gravitational force on the elevator since it's moving at a constant velocity. Hence, work done by tension, W_t = m × g × h, where m is the mass, g is the acceleration due to gravity, and h is the height the elevator is lifted. For a 1200 kg elevator lifted 35 m, W_t = 1200 kg × 9.8 m/s² × 35 m = 411,600 Joules.
• (b) The work done by the elevator's weight is negative since the weight works against the direction of motion. It is the same in magnitude but opposite in sign to the work done by the tension, hence W_w = -W_t = -411,600 Joules.

Note: We took 'g' as 9.8 m/s², which is a standard value for the acceleration due to gravity.