# Power of a man cycling up a hill.

• AJKing
In summary, to calculate the power needed for a man of mass 85 kg to bicycle 850m up a hill inclined at 5.2 degrees at a constant speed of 15.6 m/s, we can use the equation P=F*v. By considering the change in kinetic and potential energy, as well as external work done by the force of friction, the power needed is 1600 W.
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

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

Last edited:
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.

## What is the "power" of a man cycling up a hill?

The power of a man cycling up a hill refers to the amount of energy he is exerting to overcome the resistance of gravity and move himself and his bike up the incline.

## How is the power of a man cycling up a hill measured?

The power of a man cycling up a hill is typically measured in watts, which is a unit of power that represents the rate at which energy is transferred or used.

## What factors affect the power of a man cycling up a hill?

The power of a man cycling up a hill can be affected by several factors, including his body weight, the weight of his bike, the incline of the hill, the wind speed and direction, and his level of fitness and strength.

## Is there a difference in power between cycling up a hill and cycling on a flat surface?

Yes, there is a difference in power when cycling up a hill compared to cycling on a flat surface. This is because the resistance of gravity increases on an incline, requiring the cyclist to exert more power to overcome it.

## How can a man increase his power when cycling up a hill?

A man can increase his power when cycling up a hill by training and building his strength and endurance, using proper cycling techniques such as maintaining a steady cadence, and using gear ratios that are appropriate for the incline of the hill.

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