# How much power is generated when climbing a set of stairs?

Put on your running shoes and sharpen your pencil! Investigate the mathematical connection between work and power in this hands-on activity.

## What You Need

- Stairs
- Tape measure
- Scale
- Stopwatch or watch that measures seconds

## What To Do

- Measure the vertical height of the set of stairs (or a portion that’s easily measured), in metres (m). The vertical height refers to the height from the bottom to the top (straight down), not the slope.
- Determine your body mass, in kilograms (kg) by getting on the scale.
- Time the number of seconds (s) it takes you to run up the stairs.
- The amount of
**power**used is equal to the amount of**work**done over a given amount of**time**(P = W/t). To determine the amount of work done, you calculate the amount of force that is exerted over a given distance (W = f • d). The force in this case is calculated by multiplying the downward acceleration due to gravity (9.81 m/s2) by your mass (in kg) - Breaking it down, you get:

Power = Work/time

Power = (acceleration due to gravity) x mass x distance/time

Power = 9.81 m/s2 x kg x m /s or 9.81 Watts

(NOTE: The unit for power is the Watt, which is kg•m2/s3) **Example:**Calculate the power generated by a 54 kg person who takes 5 seconds to run up a 3 metre high set of stairs.- Power = [g (9.81 m/s2) • mass (kg) • vertical height (m)] / time(s) = watts

= (9.81 m/s2 • 54kg • 3m) / 5s

= 318 W

## Discovery

#### What’s happening?

Most people associate power with muscles and muscle strength - the larger the muscles, the greater the power. This is only partially true. Smaller muscles that are properly toned can generate larger amounts of power than larger muscles that are not properly toned. This is why athletes that appear small may still be capable of great feats of strength and stamina. Power is the rate at which work is done. The greater the power, the more work that is being done. In sports, the more power that the athlete can generate, the faster, farther, higher, etc., the athlete can go. Ultimately, the amount of power the athlete can generate goes back to how, and how much, the athlete trains and prepares for that particular sport.

#### What’s happening?

Most people associate power with muscles and muscle strength - the larger the muscles, the greater the power. This is only partially true. Smaller muscles that are properly toned can generate larger amounts of power than larger muscles that are not properly toned. This is why athletes that appear small may still be capable of great feats of strength and stamina. Power is the rate at which work is done. The greater the power, the more work that is being done. In sports, the more power that the athlete can generate, the faster, farther, higher, etc., the athlete can go. Ultimately, the amount of power the athlete can generate goes back to how, and how much, the athlete trains and prepares for that particular sport.

#### Why does it matter?

Power is measured in Watts. The best known every day reference to watts is with the light bulb. The greater the number of Watts a light bulb can generate, the brighter the bulb. The greater the number of Watts an athlete can generate, the stronger they will be in sports. The greater your level of fitness, the faster you should be able to run up the stairs or hill, thus the greater the amount of Watts of power that you can generate.

#### Why does it matter?

Power is measured in Watts. The best known every day reference to watts is with the light bulb. The greater the number of Watts a light bulb can generate, the brighter the bulb. The greater the number of Watts an athlete can generate, the stronger they will be in sports. The greater your level of fitness, the faster you should be able to run up the stairs or hill, thus the greater the amount of Watts of power that you can generate.

#### Investigate further

- How could you improve the amount of power you generate going up stairs?
- How would you determine the power required to climb up a tobogganing hill?
- What other factors may influence the power you need? (i.e., walking through snow, in wind, on uneven ground, etc.)

For more information on this topic check out these Let's Talk Science resources:

- Introduction to Energy (Backgrounders) - Learn about energy in its different forms, in particular kinetic, potential and mechanical energy.
- How it Works: Hydroelectric Power (STEM in Context) - Learn how moving water can be used to generate electricity. This is called hydroelectric power generation.

#### Investigate further

- How could you improve the amount of power you generate going up stairs?
- How would you determine the power required to climb up a tobogganing hill?
- What other factors may influence the power you need? (i.e., walking through snow, in wind, on uneven ground, etc.)

For more information on this topic check out these Let's Talk Science resources:

- Introduction to Energy (Backgrounders) - Learn about energy in its different forms, in particular kinetic, potential and mechanical energy.
- How it Works: Hydroelectric Power (STEM in Context) - Learn how moving water can be used to generate electricity. This is called hydroelectric power generation.