Question

64 POINTS HAVE BEEN INVESTED IN THIS QUESTION

A motor is rated at 1500 Watts and a second motor is rated at 2200 Watts. If they each needed to lift a 100 kg box 20 meters, which one would do the most work?

A motor is rated at 1500 Watts and a second motor is rated at 2200 Watts. If they each needed to lift a 100 kg box 20 meters, which one would get the job done first? 5.

Convert each of your power values, which are in Watts, to horsepower by the conversion given earlier: 1 hp = 746 Watts

Answer 1

#1 They would both do the same amount of work.

#2 The second one would be faster.

#3 About 5 Horsepower for the dog.

About 7 Horsepower for the ox.

About 12 Horsepower for the horse.

About 6 Horsepower for the lama.

(Note the question is NOT asking for the motors' horsepower, but for the animals.)

Explanation:

Answer 2

Given:

Power of first motor (P₁) = 1500 Watts = 1500 W× (1 hp / 746 W) = 2.0 hp

Power of second motor (P₂)= 2200 Watts = 2200 W× (1 hp / 746 W) ≈ 3.0 hp

Mass of Box (m) = 100 kg

Lifted height (h) = 20 m

Formula Used: Work done = Power × time

or, W = P × t

In this case, work done by both the motors will be same because work done will be equal to the change in potential energy which is path dependent. Since, in both these cases height is same. So, only first motor will take more time as it has less power than second motor.

W₁ = P₁×t₁ and W₂ = P₂×t₂

∵ W₁ = W₂

or, P₁×t₁ = P₂×t₂

or, t α (1/P)

That is, time is inversely proportional to the power

Hence, the second motor will do work fast as compare to the first motor.