An elevator weighing 6,000 N moves up a distance of 10.0 meters in 30.0 seconds.

a. How much work did the elevator’s motor do?

b. What was the power of the elevator’s motor in watts and in horsepower?

Assume that work is equal to force x distance or w=fd. The force here is 6,000n and distance is 10.0 so therefore w=(6000n)(10.0m) and use that to do p=wt (power = work x time

Answered by toml | 2024-06-10

The elevator's motor did 60,000 J (joules) of work lifting the elevator. The motor's power was 2,000 W (watts) or approximately 2.68 hp (horsepower).

To calculate the work done by the elevator's motor, we use the formula Work (W) = force (F) × distance (d). Here, the weight of the elevator acts as the force, which is 6,000 N, and the distance is 10.0 meters. So the work done by the elevator's motor is:
W = F × d = 6,000 N × 10.0 m = 60,000 J (joules).
Power (P) is the rate at which work is done, which is defined as work done (W) divided by the time (t) it takes to do that work. The formula for power is:
P = W / t = 60,000 J / 30.0 s = 2,000 W (watts).
To convert this to horsepower (hp), we use the conversion factor 1 hp = 746 W. Therefore, the power in horsepower is:
P = 2,000 W / 746 W/hp ≈ 2.68 hp.

Answered by PragatiR | 2024-06-25

The work done by the elevator's motor is 60,000 J, and the power of the elevator's motor is 2,000 W (approx. 2.68 hp). Work is calculated using the formula W = F × d and power using P = W/t. The calculations show the work done as the elevator lifts the weight and the power required to do so over a time period.
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Answered by toml | 2024-10-13