Question

Work and Energy

A 68 kg students runs up a flight of stairs 3.5 meters high in 11.4 seconds. The student takes 8.5 seconds to run up the same flight of stairs during a second trial. Determine the following:

a. The work done in each trial. You should identify these values as W1 and W2.


b. The power exerted by the student in each trial. You should identify these values as P1 and P2.

Answer 1

a)
`W_1 = 2332 J`,
`W_2= 2332 J`

The work done by the student in each trial is equal to the gravitational potential energy gained by the student:

`W=mg\Delta h`

where

m = 68 kg is the mass of the student

g = 9.8 m/s^2 is the acceleration of gravity

`\Delta h` is the gain in height of the student

For the first student,
`\Delta h = 3.5 m`, so the work done is

`W_1 = (68)(9.8)(3.5)=2332 J`

The second student runs up to the same height (3.5 m), so the work done by the second student is the same:

`W_2 = (68)(9.8)(3.5)=2332 J`

2)
`P_1 = 204.6 W`,
`P_2 = 274.4 W`

The power exerted by each student is given by

`P=(W)/(t)`

where

W is the work done

t is the time taken

For the first student,
`W_1 = 2332 J` and
`t=11.4 s`, so the power exerted is

`P_1 = (W_1)/(t_1)=(2332 J)/(11.4 s)=204.6 W`

For the second student,
`W_2 = 2332 J` and
`t=8.5 s`, so the power exerted is

`P_2 = (W_2)/(t_2)=(2332 J)/(8.5 s)=274.4 W`