The Bead on a Vertical Ring: Finding Acceleration

In summary, the bead on a smooth vertical ring of radius R has a vertical acceleration at θ = cos-1 (1/3) when given a slight push.
  • #1
Paranjape
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Homework Statement



A bead rests on smooth vertical ring of radius R. Bead is given a slight push so that it slides down around the ring. At some instance the bead is at angular position θ with vertical then choose correct option from the following
A. acceleration of bead is vertical at θ = cos-1 (1/3)
B. acceleration of bead is horizontal at θ = π - cos-1 (1/3)
C. acceleration of bead is vertical at θ = π/2
D. acceleration of bead is horizontal at θ = cos-1 (1/3)



Homework Equations



Diagram in the attached file


The Attempt at a Solution


In the attached file
 

Attachments

  • Bead on ring.doc
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  • #2
, the diagram shows that the acceleration of the bead is vertical at θ = cos-1 (1/3). So, option A is the correct answer.
 

1. What is the purpose of the "bead on a vertical ring" experiment?

The purpose of this experiment is to measure the acceleration of gravity using a bead sliding on a vertical ring. This can help to verify the principles of circular motion and the relationship between centripetal acceleration and the radius of the circle.

2. How do you set up the "bead on a vertical ring" experiment?

The experiment requires a vertical ring, a bead, a ruler, and a stopwatch. The ring is attached to a sturdy support and the bead is placed on the ring at the top. The ruler is used to measure the height of the bead at different points on the ring, and the stopwatch is used to measure the time it takes for the bead to travel between these points.

3. What are the key variables in this experiment?

The key variables in this experiment are the radius of the ring, the height of the bead at different points on the ring, and the time it takes for the bead to travel between these points. These variables are used to calculate the acceleration of gravity.

4. How does the "bead on a vertical ring" experiment help us understand acceleration?

The "bead on a vertical ring" experiment helps us understand acceleration by demonstrating the relationship between centripetal acceleration and the radius of the circle. As the radius of the circle decreases, the centripetal acceleration increases, and this can be seen in the changing height of the bead on the ring.

5. What are some potential sources of error in this experiment?

Potential sources of error in this experiment include human error in measuring the height and time, air resistance affecting the motion of the bead, and friction between the bead and the ring. It is important to take multiple measurements and calculate the average to minimize these errors.

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