Question

Championship swimmers take about 22 s and about 30 arm strokes to move through the water in a 50 m freestyle race.The swimmer's metabolic power is 800 W . A) If the efficiency for swimming is 25 %, how much energy is expended moving through the water in a 50 m race? B) If half the energy is used in arm motion and half in leg motion, what is the energy expenditure per arm stroke? C)Model the swimmer's hand as a paddle. During one arm stroke, the paddle moves halfway around a 90 cm-radius circle. If all the swimmer's forward propulsion during an arm stroke comes from the hand pushing on the water and none from the arm (somewhat of an oversimplification), what is the average force of the hand on the water?

Answer 1

Answer:

4400 Joules

73.33 Joules

25.9325 Joules

Explanation:

P = Power = 800 W

t = Time = 22 s

F = Force

r = Radius of arm = 90 cm

Energy

$E=P\times t\\\Rightarrow E=800\times 22\\\Rightarrow E=17600\ J$

As the efficiency is 25%

$E=0.25\times 17600\\\Rightarrow E=4400\ J$

Energy used in the race is 4400 Joules

Half of the energy is used in the arm

$E=\frac{4400}{2}=2200\ J$

So, per stroke of paddle

$E=\frac{2200}{30}=73.33\ J$

The energy expenditure per arm stroke is 73.33 Joules

Displacement will be the half of the perimeter of the circle

$s=\frac{1}{2}\times 2\pi r\\\Rightarrow s=\frac{1}{2}\times 2\pi 0.9\\\Rightarrow s=2.82743$

Work done

$W=F\times s\\\Rightarrow F=\frac{W}{s}\\\Rightarrow F=\frac{73.33}{2.82743}\\\Rightarrow W=25.9352\ J$

The average force of the hand on the water is 25.9325 Joules