# Can kinetic energy and potential energy both increase?

## Homework Statement

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. (a) What type(s) of energy is (are) changing? Is each type increasing or decreasing? Why?

## Homework Equations

Power=Work/Time
Work=Change in KE

## The Attempt at a Solution

a) I would think that potential and kinetic energy are both changing; both increase because the helicopter gains altitude (increasing PE) and increases velocity (increasing KE). Is this correct? I know that in a situation where energy is conserved, one must decrease as the other one increases. I'm not sure whether this qualifies as an energy-conservative situation, though.

b) The work-energy theorem. The work done by gravity + work done by helicopter = change in KE. Is this correct?

Many thanks!

## Answers and Replies

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Your answer to a) is correct. Energy is conserved when there are no external forces do work on the system. In this case, the system is the helicopter, and the external force is the air is pushing it up. (Gravity doesn't count as an external force because you're already taking it into account with the potential energy.) That's why both types of energy can increase.

You're also correct about the work-energy theorem.

Thank you, Vela! I really appreciate it.