Power of a man cycling up a hill.

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SUMMARY

A man with a mass of 85 kg must exert a power of 1600 W to bicycle 850 meters up a hill inclined at 5.2 degrees at a constant speed of 15.6 m/s, accounting for a frictional force of 175 N. The initial calculation yielded 1400 W, but the correct approach incorporates the net work done against gravitational potential energy and friction. The formula used for power is P = F * v, confirming the accuracy of the second solution presented in the discussion.

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Homework Statement



What power must a man of mass 85 kg have to bicycle 850m up a hill, inclined at 5.2 degrees to the horizontal, at a constant speed of 15.6 m/s? The force of friction on the man and the bicycle is 175N parallel to the incline.

m = 85 kg

d = 850m

dy = 850m * sin5.2

v = 15.6 m/s

Ff = 175N

Homework Equations



P = W/t

t = d/v

Wnet = Fnetd = KE

KE1 + PE1 = KE2 + PE2

The Attempt at a Solution



Old solution:
W = KE2 + PE2 = 1/2mv2 + mg(850sin5.2)

P = (1/2mv2 + mgdy)/(d/v)

P = (1/2*85*15.62 + 85*9.8*850sin5.2)/(850/15.6) = 1400 WAm I correct? I feel strange having not used Ff. But I assumed it would have already been included in the constant velocity.
New Solution:

Wnet = KE2-KE1

KE1 + PE1 = KE2 + PE2 + Eh

Wnet = - PE2 - Eh

P = (-PE2 - Eh)/(d/v)

P = (-85*9.8*850sin5.2 - (-175*850))/(850/15.6) = 1600 W
 
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As power=F*v (force times velocity) your second solution is correct.

ehild
 
ehild said:
As power=F*v (force times velocity) your second solution is correct.

ehild

Thank you, I didn't know that.
 

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