Language

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

Calculating the Power to Climb Stairs · Physics Playground

Exercises Work, energy and power

Example 7.11 from College Physics, 7.7 Power

Calculating the Power to Climb Stairs

What is the power output for a 60.0-kg woman who runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s? (See Figure 7.23.)

A woman is standing before a set of stairs with her weight shown by a vector w pointing vertically downward, which is equal to m times g. The normal force N acting on the woman is shown by a vector pointing vertically upward, which is equal to negative w. Her velocity at this point is v sub 0 equal to zero. She runs and reaches the top of the stairs at a height h with velocity v sub f. Now she possesses potential energy as well as kinetic energy labeled as K E plus P E sub g.

Figure 7.23 When this woman runs upstairs starting from rest, she converts the chemical energy originally from food into kinetic energy and gravitational potential energy. Her power output depends on how fast she does this.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy and concept
The work going into mechanical energy is $W = KE + PE$ . At the bottom of the stairs, we take both $KE$ and ${PE}_{g}$ as initially zero; thus, $W = {KE}_{f} + {PE}_{g} = \frac{1}{2} {mv}_{f}^{2} + mgh$ , where $h$ is the vertical height of the stairs. Because all terms are given, we can calculate $W$ and then divide it by time to get power.
Solution
Substituting the expression for $W$ into the definition of power given in the previous equation, $P = W / t$ yields
$P = \frac{W}{t} = \frac{\frac{1}{2} {mv}_{f}^{2} + mgh}{t} .$
7.70

Entering known values yields

$\begin{array}{l} P & = & \frac{0.5 (60.0 kg) {(2.00 m/s)}^{2} + (60.0 kg) ({9.80 m/s}^{2}) (3.00 m)}{3.50 s} \\ = & \frac{120 J + 1764 J}{3.50 s} \\ = & 538 W. \end{array}$
7.71
Discussion
The woman does 1764 J of work to move up the stairs compared with only 120 J to increase her kinetic energy; thus, most of her power output is required for climbing rather than accelerating.

0 of 3 steps open

How did it go?

PreviousCalculating Distance Traveled: Sliding Up an Incline Next Calculating Energy Costs

From College Physics (1st edition) by OpenStax (Rice University), section 7.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Strategy and concept

Solution

Discussion