Question

If the mass of an object triples and the power exerted to lift that object up a certain height remains the same, does the time also triple or decreased by a factor of 1/3?

Answer 1

Recall, Power is the rate at which work is done. Work done by lifting the object to a certain height is expressed as

W = mgh

where

W = work done

m = mass of object

g = acceleration due to gravity

h = height moved by object

Since power = work done/time,

Then, power exerted to lift the bject is

P = mgh/t

Let the quantities that remain the same be represented by 1. Thus, h = 1, P = 1, g = 1

Since mass is tripled, m = 3

By substituting these values into the formula,

1 = 3 x 1 x 1/t

1 = 3/t

by crossmultiplying,

t = 3

Thus, the time also triples