Answer to Question #77460 in Mechanics | Relativity for Monique Carey

Question

Provide quantitative examples of how two winches of different power ratings could lift an object at different speeds over the same change in displacement.

Answer 1

For example, let`s take following values :

· power rating of first winch is 1kW=1000W

· power rating of second winch is 2kW=2000W

· mass of object is 100kg

· g is 10m/s^2

Power is work per time P=A/t

Formula of work for load lifting is A=m*g*h.

Speed is displacement per time V=h/t

On the basis of these formulas we obtain:

t=A/P=m*g*h/P

V=h/t=h/(m*g*h/P)=P/(m*g)

First winch V= P/(m*g)=1000/(100*10)=1m/s

Second winch V= P/(m*g)=2000/(100*10)=2m/s

As you see two winches of different power ratings lift an object at different speeds over the same change in displacement (speed has direct dependency on power)