Question

The US athlete Florence Griffith-Joyner won the 100 m sprint gold medal at Seoul Olympics in 1988, setting a new Olympic record of 10⋅54 s. Assume that she achieved her maximum speed in a very short time and then ran the race with that speed till she crossed the line. Take her mass to be 50 kg. (a) Calculate the kinetic energy of Griffith-Joyner at her full speed. (b) Assuming that the track, wind etc. offered an average resistance of one-tenth of her weight, calculate the work done by the resistance during the run. (c) What power Griffith-Joyner had to exert to maintain uniform speed?

Answer 1

Given:
Distance covered by her, s = 100 m
Time taken by her to cover 100 m, t = 10.54 s
Mass, m = 50 kg

The motion can be assumed to be uniform.
(a)
$$\begin{gathered} \mathrm{Speed},\nu =\frac{\mathrm{s}}{t}=9.487\mathrm{m}/\mathrm{s} \\ \mathrm{So},\mathrm{K}.\mathrm{E}.=\frac{1}{2}{\mathrm{m\nu }}^2=2250\mathrm{J} \end{gathered}$$
(b)
$$\begin{gathered} \mathrm{Weight}=mg=490\mathrm{J} \\ \mathrm{Average}\mathrm{resistance}\mathrm{force}\mathrm{offered}, \\ R=\frac{mg}{10}=49\mathrm{J} \\ \mathrm{So},\mathrm{work}\mathrm{done}\mathrm{against}\mathrm{the}\mathrm{resitance}\mathrm{force} \\ \mathrm{W}=-Rs=-49\times 100 \\ \Rightarrow \mathrm{W}=-4900\mathrm{J} \end{gathered}$$
(c)
To maintain uniform speed, she had to exert 4900 J of energy to overcome friction.
Power exerted by her to overcome frcition,
$$\begin{gathered} \mathrm{P}=\frac{\mathrm{W}}{t} \\ =\frac{4900}{10.54}=465\mathrm{W} \end{gathered}$$