Mechanics of Wheel and Forces Involved

In summary, the conversation discusses the resolution of a tractive effort E into a couple and forwards force E at the point of contact with a surface. The question of whether adding a limiting friction force F acting backwards can cause the wheel to slip if exceeded by E is also raised. The conversation then transitions to discussing the inspiration for this question, which is the possibility of a skid occurring when applying braking force to a wheel. The conversation explores the forces involved and how to calculate the deceleration of the wheel, ultimately concluding that the equation of motion is -Fb = Ma.
  • #1
Eugbug
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0
If an axle is being pulled with a tractive effort E, can this be resolved into a couple and forwards force E at the point of contact with a surface? Is it correct to add a limiting friction force F acting backwards against the direction of motion and if this is exceeded by E, does the wheel slip?
 

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  • #2
Hi Eugbug! :smile:
Eugbug said:
If an axle is being pulled with a tractive effort E, can this be resolved into a couple and forwards force E at the point of contact with a surface?

Yes, that's completely correct …

the two alternative descriptions are completely equivalent. :smile:

But I don't see how that helps you with the friction force :confused:
Is it correct to add a limiting friction force F acting backwards against the direction of motion and if this is exceeded by E, does the wheel slip?
 
  • #3
The inspiration for this question came about when I was coming down a mountain at top speed on my mountain bike and was thinking about how braking works on a wheel and whether a skid can occur if enough braking force is applied and the wheels don't actually lock.
To make things simple, take a single wheel rolling along a level surface. The wheel is weightless so there is no moment of inertia to take into account, just say there is a mass M attached to the axle. If a braking force is applied at the perimeter of the wheel and this produces a sliding friction force Fb acting against the direction of rotation of the wheel, what are the forces involved and how do you work out the deceleration of the wheel? The velocity of the wheel is v.

The way I would approach things is to resolve Fb into a couple Fb and a force Fb acting against the direction of motion at the axle and then the equation of motion becomes:

-Fb = Ma where a is the deceleration of the wheel. Is this correct?
 

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1. What is the purpose of a wheel?

The primary purpose of a wheel is to reduce friction and allow for easier movement of objects. It also helps distribute weight evenly, making it easier to transport heavy loads.

2. What are the forces involved in the mechanics of a wheel?

The main forces involved in the mechanics of a wheel are the normal force, which is the force exerted by the surface on the wheel, and the frictional force, which opposes motion and helps the wheel to roll. Other forces, such as gravity and applied forces, may also play a role.

3. How does the size of a wheel affect its mechanics?

The size of a wheel can affect its mechanics in a few different ways. A larger wheel may have a larger surface area, resulting in more normal force and potentially less friction. The mass of a larger wheel may also impact its inertia and rotational motion.

4. What is the difference between static and dynamic friction in relation to a wheel?

Static friction is the force that prevents an object from moving when a force is applied to it, such as a wheel on a stationary surface. Dynamic friction, on the other hand, is the force that opposes motion between two surfaces that are in contact and moving relative to each other, such as a rolling wheel on a surface.

5. How does the shape of a wheel affect its mechanics?

The shape of a wheel can impact its mechanics in various ways. A wheel with a larger diameter may have a greater moment of inertia, making it harder to start and stop rotating. A wheel with a more streamlined shape may experience less air resistance, allowing for smoother movement. Additionally, the distribution of weight and the type of surface the wheel is rolling on can also affect its mechanics.

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