### Scenario 1: Lab Partner

In this activity, you will calculate your lab partner's power required to walk and run up a flight of stairs. You will measure the time it takes for your partner to run up a flight of stairs. As your partner runs, they do work by moving their mass against gravity. If you know the vertical distance your partner travels on the flight of stairs, you can calculate the work done in running up the stairs. The power your partner requires to do this depends on the time it takes her to run up the flight of stairs. More time means less power generated. Less time means more power generated. The work done stays the same in each trial since the force (weight) stays the same as does the distance up the stairs.

### Data

Mass of your lab partner = 53.5 kg.
The flight of stairs has 22 steps including the landing. Each step is 19 cm (vertical).

Now, click on the table below to check the time entries.

Source: Stop Watch,klaasvangend, Open Clip Art Library

 Trial Time (seconds) 1 Interactive button. Assistance may be required. ? 12 2 Interactive button. Assistance may be required. ? 7 3 ? 4

Now make a table like this in your notes. Fill in the empty cells with the appropriate values. Click the hint button if you need help.

 Name of Student Mass of Student Force Newtons m x g Vertical distance meter Work Joule(Nm) F x d Time Seconds t Power Watt(J/s) Work/time Power (Horsepower) Susan Trial 1 53.5kg Interactive popup. Assistance may be required. Hint 1 Interactive popup. Assistance may be required. Hint 2 Interactive popup. Assistance may be required. Hint 3 Hint 4 Hint 5 Susan Trial 2 53.5kg Susan Trial 3 53.5kg
Hint 1
Weight = Force
(You can start at this step by converting weight in pounds to weight in Newtons.)
W = mg; w ≈ 53.5 × 9.8 m/s2 × 525 N
Hint 2
Find vertical distance of stairs: You measure this with a meter stick.
22 steps x .19 m per step ≈ 4.2 m
Hint 3
Work = Force x displacement (displacement is the vertical height of stairs in this case)
W = F x d     W = 525 N x 4.2 m ≈ 2200 Nm or 2200 J
Hint 4
Power = Work/time     (You measure the time in seconds with a stopwatch).
P = W/Δt      P = 2200 J / 12 s ≈ 180 J/s or 180 watts
P = W/Δt      P = 2200 J / 7 s ≈ 310 J/s or 310 watts
P = W/Δt      P = 2200 J / 4 s ≈ 550 J/s or 550 watts
Hint 5
The SI unit of power is the watt, so you are finished at Step 4. Horsepower is still commonly used, so it is useful to know how to convert watts to horsepower.
1 horsepower = 746 watts

180 watts 1 × 1 horsepower 746 watts ≈ 0.24 horsepower
310 watts 1 × 1 horsepower 746 watts ≈ 0.42 horsepower
550 watts 1 × 1 horsepower 746 watts ≈ 0.74 horsepower

Interactive popup. Assistance may be required.

 Name of Student Mass of Student Force Newtons m x g Vertical distance meter Work Joule(Nm) F x d Time Seconds t Power Watt(J/s) Work/time Power (Horsepower) Susan Trial 1 53.5kg 525 N 4.2m 2200 J 12s 180 W 0.24 hp Susan Trial 2 53.5kg 525 N 4.2m 2200 J 7s 310 W 0.42 hp Susan Trial 3 53.5kg 525 N 4.2m 2200 J 4s 550 W 0.74 hp

### Scenario 2: Your Turn

Use your own personal data to calculate the power you would generate in the lab activity. Use a stopwatch to get time, and use your weight in Newtons as the force (1 lb. = 4.45 N). Remember to use the information above for the height of the stairs and the timetable.

 Name of Student Your Mass in kg Force Newtons m x g Vertical distance meter Work Joule(Nm) F x d Time Seconds t Power Watt(J/s) Work/time Power (Horsepower) Your nameTrial 1 Your nameTrial 2 Your nameTrial 3

### Scenario 3: Climbing a Ramp

Source: Witton Station – ramp, Magnus Manske, Wikimedia Commons

Using your mass (weight in Newtons ÷ 9.8) from scenario 2, calculate the power to climb a ramp to a height of 10 meters above the starting point. Suppose it takes you 20 seconds to climb the ramp.