# Calculating the Power Needed to Bike Up a Hill

• Jimbo57
In summary, the man must have a power of 3900W to bicycle 850m up a hill, inclined at 5.2° to the horizontal, at a constant speed of 15.6m/s.
Jimbo57

## Homework Statement

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

## The Attempt at a Solution

m= 85kg
g=9.8m/ss
v=15.6m/s
θ= 5.2°

F = 175N + mgsinθ
= 175N + 75.497N Here I'm determining the forces required to overcome gravity and friction.
= 250.497N

P = F*v
= 250.497N * 15.6m/s Here I took the calculated force and the velocity and determined the power.
= 3900W

How does it look?

Last edited:
The way to work out if you have done well is to write out the reasoning that lead you to this calculation. It also makes it easier for an examiner to mark your work, which contributes to your ability to get a higher grade :)

Simon Bridge said:
The way to work out if you have done well is to write out the reasoning that lead you to this calculation. It also makes it easier for an examiner to mark your work, which contributes to your ability to get a higher grade :)

Thanks for the tip Simon. I added a couple lines describing the steps I took. It wasn't much.

Well OK - did that help you gain confidence with your work?

How would you explain to a less experienced student why you chose that particular approach to solving the problem - or did you just guess and hope it turned out right?

I know this sounds like an obtuse way to tell you you've done OK but you are at the next step where you need to be able to work out for yourself if you did right or not: the point of learning physics is to be able to solve problems that nobody knows the answer to so there is nobody to ask. The earlier you start learning how to tell if you've got it right the better you'll be at it - and the skill is general, you'll use it whatever you end up doing.

Your solution looks correct! Just a small clarification, the force of friction should be multiplied by cosθ instead of sinθ since it is parallel to the incline. So the final equation for power would be P = (175N + 85kg*9.8m/s^2*cos5.2°)*15.6m/s = 3900W. Great job!

## 1. How is power calculated when biking up a hill?

Power is calculated by multiplying the force applied to the pedals by the speed at which the pedals are turning. This equation is also known as the power equation, P = F x v.

## 2. What factors affect the power needed to bike up a hill?

The main factors that affect the power needed to bike up a hill include the grade of the hill, the weight of the rider and bike, the wind resistance, and the speed at which the rider is going.

## 3. How can I determine the grade of a hill?

The grade of a hill can be determined by dividing the rise (vertical change in elevation) by the run (horizontal distance). This number is typically expressed as a percentage, with higher percentages indicating steeper hills.

## 4. How does wind resistance affect the power needed to bike up a hill?

Wind resistance can significantly affect the power needed to bike up a hill. The force of the wind pushing against the rider increases as the speed increases, requiring more power to overcome it. Additionally, wind direction can make it easier or more difficult to bike up a hill depending on whether it is a headwind or tailwind.

## 5. Is there a way to calculate the power needed to bike up a hill in real-time?

Yes, there are various cycling computers and apps that can calculate and display the power needed to bike up a hill in real-time. These devices use sensors to measure factors such as speed, cadence, and elevation, and use algorithms to calculate the power output.

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