Question

2. You race a child that is exactly half your mass up identical ladders. If you took 5 s, and the child took 7 s, who did more work? Who had greater power?

Answer 1

Answer:

You did more work, and you also had greater power.

Explanation:

Work is defined as a force doing a motion.

Particularly, when we lift an object of mass M by a distance H, the work is written as:

W = M*g*H

where g is the gravitational acceleration, then M*g = weight.

In this case, you and the child both are at the same distance to the ground after both of you finish the race, but your mass is twice the mass of the child.

Then if the child's mass is M, then the child's work is:

Wc = M*g*H

your work will be:

W = (2*M)*g*H

meaning that your work is twice the work.

Power is defined as the amount of work you do in a given amount of time.

So, if you needed 5 seconds to do the work W = (2*M)*g*H, then the (average) power will be equal to the quotient between the total amount of work you did and the time it took to do it.

Then your work is:

P = W/5s = (2*M)*g*H/5s

And the power for the child will be:

Pc = Wc/7s = M*g*H/7s

Your power has a larger numerator and a smaller denominator then is easy to see that you had greater power.