Help in understanding a question about a pebble and a wheel and friction....

In summary, when a wheel of radius R rolls along the ground with velocity V and a pebble is released on top of the wheel at rest, the pebble will start to slide when the wheel is rotated through an angle given by ##\theta = \arccos (1/\sqrt{2}(V^2/Rg)) - \pi/4##, assuming that ##V < \sqrt{Rg}## and the coefficient of friction is ##\mu = 1##. The pebble will remain in contact with the surface as it slides. A free-body diagram can be drawn to illustrate this situation.
  • #1
Buffu
849
146

Homework Statement



A wheel of radius R rolls along the ground with velocity V. A pebble is carefully released on top of the wheel so that it is instaneously at the rest on the wheel. Show that in the case ##V < \sqrt{Rg}## and the coefficient of friction is ##\mu = 1## the pebble starts to slide when it is rotated through an angle given by ##\theta = \arccos (1/\sqrt{2}(V^2/Rg)) - \pi/4##

Homework Equations

The Attempt at a Solution



I would attempt at the solution if only I understand what its by "sliding" in the question ? Does it mean that the pebble will fly off the wheel ? or its accelaration is zero ?
 
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  • #2
Buffu said:

Homework Statement



A wheel of radius R rolls along the ground with velocity V. A pebble is carefully released on top of the wheel so that it is instaneously at the rest on the wheel. Show that in the case ##V < \sqrt{Rg}## and the coefficient of friction is ##\mu = 1## the pebble starts to slide when it is rotated through an angle given by ##\theta = \arccos (1/\sqrt{2}(V^2/Rg)) - \pi/4##

Homework Equations

The Attempt at a Solution



I would attempt at the solution if only I understand what its by "sliding" in the question ? Does it mean that the pebble will fly off the wheel ? or its accelaration is zero ?
Can you post a picture of the problem? It's kind of hard to help when I can't visualize the situation. Thanks.
 
  • #3
berkeman said:
Can you post a picture of the problem? It's kind of hard to help when I can't visualize the situation. Thanks.
There was no picture in the book.
 
  • #4
Buffu said:
There was no picture in the book.
upload_2017-5-21_6-40-27.png

Initially, the pebble stays in rest on the wheel moving together with the rim. When the wheel turns by angle theta, then the pebble starts to slide on the surface downward. Draw the free-body diagram.
 
  • #5
ehild said:
View attachment 203898
Initially, the pebble stays in rest on the wheel moving together with the rim. When the wheel turns by angle theta, then the pebble starts to slide on the surface downward. Draw the free-body diagram.

When it slide is it still on contact with the surface ?
 
  • #6
Buffu said:
When it slide is it still on contact with the surface ?
Yes.
 

Related to Help in understanding a question about a pebble and a wheel and friction....

1. What is friction and how does it relate to a pebble and a wheel?

Friction is the resistance force that occurs between two surfaces that are in contact with each other. In the case of a pebble and a wheel, friction occurs when the pebble is placed on the wheel and the two surfaces come into contact with each other. This friction can cause the pebble to roll or slide along the wheel, depending on the force applied.

2. How does the size and shape of the pebble affect the amount of friction?

The size and shape of the pebble can greatly affect the amount of friction that occurs when it is placed on the wheel. A larger and smoother pebble will have less surface area in contact with the wheel, resulting in less friction. However, a smaller and rougher pebble will have more surface area in contact with the wheel, resulting in more friction.

3. Does the material of the pebble and the wheel make a difference in friction?

Yes, the material of the pebble and the wheel can affect the amount of friction that occurs. For example, if the pebble is made of a smooth material like glass and the wheel is made of a rougher material like sandpaper, there will be more friction between the two surfaces compared to if both were made of the same material.

4. How does the force applied to the wheel affect the friction between the pebble and the wheel?

The force applied to the wheel can greatly affect the friction between the pebble and the wheel. If a greater force is applied, the two surfaces will be pressed together with more force, resulting in more friction. On the other hand, a smaller force will result in less friction between the two surfaces.

5. Can friction between a pebble and a wheel be reduced or eliminated?

Yes, friction between a pebble and a wheel can be reduced or eliminated by introducing a lubricant between the two surfaces. This lubricant, such as oil or grease, reduces the amount of surface contact between the pebble and the wheel, resulting in less friction. However, complete elimination of friction is not possible due to the roughness of all surfaces.

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