MATH SOLVE

6 months ago

Q:
# 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

Accepted Solution

A:

Given: Power of first motor (P₁) = 1500 Watts = 1500 W× (1 hp / 746 W) = 2.0 hpPower of second motor (P₂)= 2200 Watts = 2200 W× (1 hp / 746 W) ≈ 3.0 hpMass of Box (m) = 100 kgLifted height (h) = 20 m Formula Used: Work done = Power × timeor, W = P × tIn 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 = W₂or, P₁×t₁ = P₂×t₂or, t α (1/P)That is, time is inversely proportional to the powerHence, the second motor will do work fast as compare to the first motor.