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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Work and Energy

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Work and Energy

The athlete Emily Davis won the 100 m sprint gold medal at London...

The athlete Emily Davis won the 100 m100 \text{ m} sprint gold medal at London Olympic 2012 setting a new Olympic record of 10.54 s10.54 \text{ s}. Assume that she achieved her maximum speed in a very short time and subsequently ran the race with that speed till she crossed the line. Take her mass to be 50 kg50 \text{ kg}. Assuming that the track, the wind etc. offered an average resistance of one tenth of her weight, determine the power Emily Davis had to exert to maintain uniform speed.

Options

  1. A465 W465 \text{ W}
  2. B232 W232 \text{ W}
  3. C930 W930 \text{ W}
  4. D490 W490 \text{ W}

Correct answer

A. 465 W465 \text{ W}

Step-by-step solution

Given distance s=100 ms = 100 \text{ m} and time t=10.54 st = 10.54 \text{ s}.

Since the maximum speed is achieved in a very short time, the uniform speed of the athlete is:

v=st=10010.54 m/sv = \dfrac{s}{t} = \dfrac{100}{10.54} \text{ m/s}

The average resistance force offered by the track and wind is one-tenth of her weight. Taking g=9.8 m/s2g = 9.8 \text{ m/s}^2:

F=110mg=110×50×9.8=49 NF = \dfrac{1}{10}mg = \dfrac{1}{10} \times 50 \times 9.8 = 49 \text{ N}

To maintain a uniform speed, the athlete must exert a force equal to the resistance force. The power exerted by the athlete is:

P=F×v=49×10010.54P = F \times v = 49 \times \dfrac{100}{10.54}

P=490010.54≈464.9 WP = \dfrac{4900}{10.54} \approx 464.9 \text{ W}

Rounding to the nearest integer gives 465 W465 \text{ W}.
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