# Freewheeling bicycle and friction

Background question:
A bicycle and rider have a combined mass of 75 kg. They freewheel down a slope whose maximum height is 6 meters above sea level. The slope is 20 meters long. At the end of the slope, the bicycle and rider are travelling with a velocity of 10 m/s. Calculate the work done against friction whilst descending the slope.

mass = 75 kg
max. height = 6 meters
slope = 20 meters
Vf = 10 m/s

PE at start = KE at end + work done to overcome friction.

mgh = 1/2mv2 + friction force x distance moved against friction.

= 75 x 9.81 x 6 = 1/2 x 75 x 102 + f x 20
= 4414.5 = 3750 + 20f
= 4414.5 - 3750 = 20f
= 664.5 = 20f
Force = 664.5/20
Force = 33.225N

Question needing assistance with:
Using the calculated values from the question above, calculate how far the bicycle will travel before coming to a stop if the surface of the road is the same as the slope. State why this distance would not be achieved in a real world experiment.

## Answers and Replies

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Forgot to show my attempt...

Force = change of momentum/time

33.23N = (75 x 10) - (75 x 0)/time

33.23N = 750/time

time = 750/33.23 = 22.6s

It will take 22.6s to come to a complete stop.

Find distance = S = 1/2 (v-u) x t
S = 1/2 6 x 22.6
S = 113 meters

It will take 113 meters to come to a complete stop.

This would never happen due to air resistance.

gneill
Mentor
Hi Worthatry,

Welcome to Physics Forums.

The question sort of hints that the surface is involved in the friction (although you correctly point out later that air resistance would likely be a factor, too). For your distance calculation you've assumed that the friction force remains the same for both segments of the journey, on the slope and on the level. Would this be true? How does one normally compute the force due to friction when the surface is a slope? How about when it's level?

scottdave
Homework Helper
Hi Worthatry,

Welcome to Physics Forums.

The question sort of hints that the surface is involved in the friction (although you correctly point out later that air resistance would likely be a factor, too). For your distance calculation you've assumed that the friction force remains the same for both segments of the journey, on the slope and on the level. Would this be true? How does one normally compute the force due to friction when the surface is a slope? How about when it's level?
This should be a different problem than a sliding down a slope (which is kinetic friction with the road). The bicycle tire is always in static contact with the road and is rolling. From experience, air resistance is the major source of friction, for situations like this. Air resistance is proportional to v^2, so it is not a constant, like was assumed to solve the problem.

gneill
Mentor
This should be a different problem than a sliding down a slope (which is kinetic friction with the road). The bicycle tire is always in static contact with the road and is rolling. From experience, air resistance is the major source of friction, for situations like this. Air resistance is proportional to v^2, so it is not a constant, like was assumed to solve the problem.
I agree that in reality this scenario would not be properly modeled by sliding friction. Unfortunately the problem leaves the nature of the frictional losses quite vague except for the brief mention of the road surface. The OP did well to mention air resistance, but should probably flesh out the implications to properly answer the question for full marks.

It might be interesting to consider how applying a constant force (or force averaged over distance) model for friction affects the calculation accuracyif we consider different types of friction sources.

scottdave
haruspex
Homework Helper
Gold Member
the work done against friction
Most of the work would be done against air resistance and rolling resistance (principally, flexing the tyre walls). The only work done against friction would be against axle friction.
assumed that the friction force remains the same for both segments of the journey, on the slope and on the level.
Given that it would be rolling resistance and axle friction, might need to be careful here.
Yes, the rolling resistance will be greater when the normal force is more (i.e. on the flat), but how linear is it?
Axle friction probably is linear with the normal force from the road.

Edit: according to section 2.2.3 of http://publications.lib.chalmers.se/records/fulltext/200040/200040.pdf, rolling resistance is linear with normal load.

Last edited:
Hi guys.

Thank you for your input. I am trying to work through all your replies, and applies these into an answer; which I am having difficulity doing. The level of this question is aimed at A Level Physics (18 yo). I have not worked with Physics for over 10 years, so it all seems blurred into one.

Again, I appreciate your input and welcome any simplified suggestions on how to complete this question.