Power of a man cycling up a hill.

[AJKing]

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

d_y = 850m * sin5.2

v = 15.6 m/s

Ff = 175N

Homework Equations

P = W/t

t = d/v

W_net = F_netd = KE

KE₁ + PE₁ = KE₂ + PE₂

The Attempt at a Solution

Old solution:

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

P = (1/2mv² + mgd_y)/(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:

W_net = KE₂-KE₁

KE₁ + PE₁ = KE₂ + PE₂ + E_h

W_net = - PE₂ - E_h

P = (-PE₂ - E_h)/(d/v)

P = (-85*9.8*850sin5.2 - (-175*850))/(850/15.6) = 1600 W

 

[ehild]

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

ehild

 

[AJKing]

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

ehild

Thank you, I didn't know that.