Question

Work and Energy

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

$P=\frac{W}{t}$

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

$P_1 = \frac{W_1}{t_1}=\frac{2332 J}{11.4 s}=204.6 W$

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

$P_2 = \frac{W_2}{t_2}=\frac{2332 J}{8.5 s}=274.4 W$