Torque around a curb - bicyle forces problem

In summary, the smallest force to raise the wheel over the curb is when the force is perpendicular to the line from the center of the wheel to the pivot point.
  • #1
elemons
6
0

Homework Statement


A bicycle tire with radius R is attempting to go over a curb of height h. If a force F is applied to the center of the wheel, at an angle θ above the horizontal, what angle results in a force with the smallest magnitude to raise the wheel over the curb?

Homework Equations


ƩT=0
ƩF=0 (?)

The Attempt at a Solution


Having done this problem for a solely horizontal force, I tried to copy the same idea, but separated F into x and y components (giving Fcosθ and Fsinθ). The distance to Fg and Fy was √(2Rh-h^2), and the distance to Fx is R-h. After doing this, Fg is + and the other two are negative. The net torque equation I get it
0=mg*√(2Rh-h^2)-Fy*√(2Rh-h^2)-Fx*(R-h)
I don't know where to go from here (or if this is correct).
 
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  • #2
Try thinking about the problem this way.

First, Assume the tire pivots about the point where the tire makes contact with the curb. The torque due to gravity is your first term mg*√(2Rh-h^2). Now the angle of the minimum force will be where the force is perpendicular to the line from the center of the wheel to the pivot point.

Try setting FR = mg*√(2Rh-h^2) to find the force.
 
  • #3
How do I know that the angle perpendicular is the smallest? Also by FR do you mean the applied force? Sorry! I've been on this problem so long I don't even know what I'm thinking anymore
 
  • #4
FR is force X tire radius. You will get maximum torque when the force is perpendicular to the line from the tire center to the point of pivot, i.e. where the tire meets the curb. You can probably use geometry to fine the perpendicular angle.
 
  • #5
Oh! I understand. So to figure out the angle, it's probably easier to use geometrical arguments than net torque?
 
  • #6
I would think so. The angle would be a function of h and R. I think it would involve a arctan function probably. The force will be in terms of h, R, m, and g.
 
  • #7
The answer provided gives an arcsin function with just r and h, but I'm going to try it for a bit and see what I can get.
 
  • #8
I think you are correct. As I look at it, I see something like arcsin (R-h)/R -90 or something similar.
 
  • #9
Yes! That worked out. Thank you so much!
 

1. What is torque and how does it relate to bicycling?

Torque is a measure of the force that causes an object to rotate around an axis. In bicycling, torque is produced by the rider's pedaling force, which is transferred through the bike's drivetrain to the wheels.

2. What role does torque play in navigating a curve on a bicycle?

When navigating a curve on a bicycle, torque plays a crucial role in keeping the bike stable and maintaining its trajectory. The rider needs to apply the right amount of torque to the pedals in order to generate enough force to overcome the centripetal force pulling the bike towards the outside of the curve.

3. How does the weight distribution of the rider affect torque when going around a curve?

The weight distribution of the rider affects torque by changing the center of mass of the bike and the rider. A rider with a higher center of mass will have a greater tendency to lean towards the outside of the curve, requiring more torque to maintain balance. Similarly, a lower center of mass will require less torque.

4. Can tire pressure impact torque when going around a curve?

Yes, tire pressure can impact torque when going around a curve. Higher tire pressure results in a smaller contact area between the tire and the ground, reducing the amount of friction and grip. This can make it more difficult to generate enough torque to overcome the centripetal force.

5. Are there any other factors that can affect torque when navigating a curve on a bicycle?

Other factors that can affect torque when navigating a curve on a bicycle include the speed of the bike, the angle of the curve, and the surface conditions. A higher speed will require more torque to maintain balance, while a sharper curve or a slippery surface may require less torque to navigate successfully.

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