Question 14 Marks
The US athlete Florence Griffith $-$ Joyner won the $100\ m$ sprint gold medal at Seol Olympic $1988$ setting a new Olympic record of $10.54s$. 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 $50\ kg.$
- Calculate the kinetic energy of Griffith $-$ Joyner at her full speed.
- Assuming that the track, the wind etc. offered an average resistance of one tenth of her weight, calculate the work done by the resistance during the run.
- What power GriffithJoyner had to exert to maintain uniform speed?
Answer
View full question & answer→$S = 100m, t = 10.54 \ \sec, m = 50\ kg$ The motion can be assumed to be uniform because the time taken for acceleration is minimum.
Speed $\text{v}=\frac{\text{s}}{\text{t}}=9.487\text{m}/\text{s}$
So, K.E. $=\frac{1}{2}\text{mv}^2=2250\text{J}$ Weight $= mg = 490J$ given $\text{R}=\frac{\text{mg}}{10}=49\text{J}$ so, work done against resistance $W_F= -RS = -49 \times 100 = -4900J$
To maintain her uniform speed, she has to exert $4900J$ of energy to over come friction $,\text{P}=\frac{\text{W}}{\text{t}}$
$=\frac{4900}{10.54}=465\text{W}$
Speed $\text{v}=\frac{\text{s}}{\text{t}}=9.487\text{m}/\text{s}$
So, K.E. $=\frac{1}{2}\text{mv}^2=2250\text{J}$ Weight $= mg = 490J$ given $\text{R}=\frac{\text{mg}}{10}=49\text{J}$ so, work done against resistance $W_F= -RS = -49 \times 100 = -4900J$
To maintain her uniform speed, she has to exert $4900J$ of energy to over come friction $,\text{P}=\frac{\text{W}}{\text{t}}$
$=\frac{4900}{10.54}=465\text{W}$