Calculating the Power Needed to Bike Up a Hill

[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.

Homework Equations

The Attempt at a Solution

m= 85kg
g=9.8m/s^s
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?

 

[Simon Bridge]

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 :)

 

[Jimbo57]

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.

 

[Simon Bridge]

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.

 

[Nickie]

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!