How Do You Balance Forces in a Bicycle Free Body Diagram?

[ultra york]

Homework Statement

Bicycle with a rider applying weight to on pedal. Draw as free bodies in equilibrium. There are different situations.

Homework Equations

N/A

The Attempt at a Solution

So I am working on part a).
1. I believe it is only referring to just the pedal, chain, and the two smaller circles of the (sprocket??).
2. Assuming that is correct to balance the 800N there would need to be an opposing force, is this the torque that is created on the smaller rear circle or is it just as simple as an opposing force in the left side of the pedal?

 

[Doug Huffman]

"Pedal, crank and pedal sprocket assembly" aren't standard bicycle terminology. For clarity it should be pedal, crank and chainring. The pedal is where the 800N is applied at the end of the 160mm crank arm opposite its attachment to the 100mm radius chainring. The 800N force is resisted by the resultant tension force in the top/power run of chain.

The smaller circle at the left end of the top chain is the "cog(wheel/set)" where the top chain tension force times the cog radius creates the torque moment on the rear wheel.

The bottom return run of chain is slack.

 

[OmCheeto]

Homework Statement

Bicycle with a rider applying weight to on pedal. Draw as free bodies in equilibrium. There are different situations.

Homework Equations

N/A

The Attempt at a Solution

So I am working on part a).
1. I believe it is only referring to just the pedal, chain, and the two smaller circles of the (sprocket??).
2. Assuming that is correct to balance the 800N there would need to be an opposing force, is this the torque that is created on the smaller rear circle or is it just as simple as an opposing force in the left side of the pedal?

Hello, and welcome to the Forum, ultra york!

Since the system is in equilibrium, all forces and torques must be equal to zero.
So to begin with, you should list, under "Relevant equations", the equation for torque.

It looks to me as though the 800 N force on the pedal is going to create a clockwise torque around the axis of the "pedal sprocket assembly", so you will have to figure out a force at the perimeter of the sprocket that produces a counter-clockwise torque of equal magnitude.

 

[OmCheeto]

Since bicycles are a bit weird, I've taken the liberty of drawing the FBD for you.
You can effectively ignore all aspects of the chain, except for the "point of interest".

So to more fully answer your questions, forget about the smaller rear circle/sprocket/cog for now.
Until you get to part b, it's irrelevant.

 

[HalfLostAndSearching]

I would like to clarify that there are a few different situations that could be considered when drawing a free body diagram of a bicycle with a rider applying weight to one pedal.

Firstly, it is important to define the system of interest. In this case, the system would include the bicycle, rider, and the ground the bicycle is resting on.

Now, in order to draw a free body diagram, we need to identify all the external forces acting on the system. These would include the weight of the bicycle and rider, the normal force from the ground, and the force applied by the rider on the pedal.

In the situation where the rider is applying weight to only one pedal, we would see a torque being created around the axis of the pedal. This would be due to the force applied by the rider on the pedal, which would be countered by an equal and opposite force from the ground. This torque would also be countered by the torque created by the weight of the bicycle and rider on the opposite pedal.

In order for the system to be in equilibrium, the sum of all the forces in the horizontal and vertical directions must be zero, and the sum of the torques must also be zero. This would result in a balanced free body diagram, with the forces and torques cancelling each other out.

However, it is important to note that there are other situations that could be considered, such as when the rider is standing on the pedals or when the bicycle is in motion. In these cases, there would be additional forces and torques to consider, and the free body diagram would look different.

In conclusion, drawing a free body diagram of a bicycle with a rider applying weight to one pedal requires careful consideration of the system and all external forces and torques acting on it. It is important to be clear about the specific situation being considered in order to accurately represent the forces and torques involved.