A bead slides on a circular wire

In summary, the concept of a bead sliding on a circular wire involves circular motion and friction. The speed of the bead is affected by the angle of the wire, the mass and size of the bead, and the amount of friction. The radius of the wire also plays a role in the motion of the bead, with a larger radius resulting in a slower sliding speed and a smaller radius resulting in a faster sliding speed. The motion of the bead can be considered uniform if the speed and direction remain constant. Finally, the bead cannot slide on a circular wire without friction, as it is necessary to keep the bead from falling off due to gravity.
  • #1
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Homework Statement


A bead slides on a smooth circular wire of radius b which lies in a vertical plane. The bead starts from rest at a point that is level with the center of the hoop.
Find the time it takes for the bead to slide to the bottom of the hoop.

The attempt at a solution
at t=0
U=mgb, KE=0

at the bottom
U=0, KE=mv2/2, v=(2bg)1/2
 
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  • #2
What about the time?
 

1. What is the concept behind a bead sliding on a circular wire?

The concept is based on the principles of circular motion and friction. The bead is able to slide along the wire due to the force of gravity pulling it downwards, while the wire provides a circular path for it to follow. Friction between the bead and the wire helps to keep the bead from falling off the wire.

2. What factors affect the speed of the bead sliding on the wire?

The speed of the bead can be affected by the angle of the wire, the mass and size of the bead, and the amount of friction between the bead and the wire. The steeper the angle of the wire, the faster the bead will slide. A heavier or larger bead will also slide faster due to the force of gravity being more significant. Higher levels of friction will slow down the speed of the bead.

3. How does the radius of the wire affect the motion of the bead?

The radius of the wire plays a crucial role in determining the motion of the bead. A larger radius will result in a larger circular path for the bead to follow, causing it to slide at a slower speed. Conversely, a smaller radius will result in a smaller circular path and a faster sliding speed for the bead.

4. Is the motion of the bead on a circular wire considered uniform?

Yes, the motion of the bead on a circular wire can be considered uniform as long as the speed and direction of the bead remain constant. This means that the bead is moving at a constant speed along a circular path with no change in direction.

5. Can the bead slide on a circular wire without any friction?

No, in order for the bead to slide on a circular wire, there must be some level of friction between the two surfaces. Without friction, the bead would not be able to maintain its position on the wire and would simply fall off due to the force of gravity.

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