Question

Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by Lance Armstrong (m = 75.0 kg) is 6.50 W per kilogram of his body mass. (a) How much work does he do during a 187-km race in which his average speed is 11.2 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule = 2.389 x 10^-4 nutritional Calories.

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 760-kg helicopter rises from rest to a speed of 10.0 m/s in a time of 5.0 s. During this time it climbs to a height of 8.9 m. What is the average power generated by the lifting force?

Answer 1

given Data:

The average power generated by Lance Armstrong is, 6.50 W / kg

The mass of Lance Armstrong is, m=75.0 kg

Part (a):

The expression for the work done in terms of power is,

W= power×time..................(1)

For 75.0kg body

the power is, 6.50×75 = 487.5 W

P = 487.5 W

The expression for the time taken by Lance Armstrong is,

t = d/v

distance is d= 187 km = 187000 m

v = velocity =  11.2 m/s

plugging values in formula

t = (187000)/11.2 = 16,696.43 seconds

work done = power * time = (487.5 W)( 16,696.43 s) = 8139508 J

work done is = 8139508 J

B)

1 joule = 2.389 x 10^-4 nutritional Calories.

so work done in calories is given by

w = (8139508)(2.389 x 10^-4) = 1944.53 nutritional Calories.

work done =1944.53 nutritional Calories.

....................................................................................................................................

now for

helicopter

the total energy is

E = mg(h_f-h_o) + (1/2 m( v_f² - v_o² )

here given data

m =  760-kg

h_f= 8.9 m and h_o= 0 m

v_f = 10.0 m/s and v_o = 0 m/s

plugging values in the formula

E = ((760)(9.8)( 8.9-0) )+( (1/2)(760)((10)² -(0)))

E = 104287 J

AVERAGE POWER IS Energy per time AND

TIME IS t = 5.0 s

SO

P = (104287 )/(5) = 20857.4 W

ans is

average power is P = 20857.4 W

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