Determine the smallest possible speed of the bob at A

In summary, the bob of a pendulum swings in a full circle around the pivot point when its speed never reaches zero.
  • #1
Alexanddros81
177
4

Homework Statement


14.34 The 0.5-kg bob of the pendulum travels a complete circle about the pivot
point O. Determine the smallest possible speed of the bob in position A if it is
suspended from (a) a rigid rod of negligible mass; and (b) a string

Fig P14_33_34.jpg

Homework Equations

The Attempt at a Solution


Pytels_Dynamics117.jpg

[/B]
I can see that the above solution is not correct.
Do I take the potential energy at A to be 0 and potential energy at ##B=mgy## where y = 4 ?

Can you check this?

Any hints for part (b)?
 

Attachments

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  • Pytels_Dynamics117.jpg
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Last edited:
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  • #2
It looks like you swapped the kinetic energies of A and B. You have TA + VA on left side of one line, then it goes to 0 - 2mg on the left side of the next line. TA is -2mg, but VA should be ½mv2, and VB should be 0.

Taking point A to be y=0 is a valid strategy, as well.
 
  • #3
Ah yes you're right about the swapped kinetic energies. I wasn't consentrated.
Here is the corrected solution:

Pytels_Dynamics119.jpg


Is this correct?
Any hints for part (b)?
 

Attachments

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  • #4
Alexanddros81 said:
Any hints for part (b)?
What's the critical point in the trajectory in case of a string ?
 
  • #5
Alexanddros81 said:
Any hints for part (b)?
What is the essential difference between a rod and a string, both being massless?
 
  • #6
Hi! I have found this:
https://physics.stackexchange.com/q...on-in-string-and-light-rod-in-vertical-circle

A movement of a string pendulum above 90deg will cause the string to fold up.
However, this does not happen if the pendulum bob is moving fast enough and its speed v never reaches zero when it goes up
above 90deg Then the pendulum swings in a full circle and keeps going in the same direction into the next circle.

How do interpret this to equation form?
 
  • #7
For the rod uB=0 was the limiting case because the rod could take the weight of the bob.
For the string the bob has to pull on it in order to keep it stretched. The limiting case is when the tension in the string reaches zero. What determines the tension in the string at various positions ?
 

1. What is meant by "bob" in this context?

The term "bob" refers to a weight or mass that is suspended by a string or wire and can move freely in a circular motion.

2. What does "speed of the bob at A" mean?

The "speed of the bob at A" refers to the velocity or rate of movement of the bob at its highest point, point A, in its circular motion.

3. How is the smallest possible speed of the bob at A determined?

The smallest possible speed of the bob at A can be determined by using the equation v = √(gr), where v is the speed, g is the acceleration due to gravity, and r is the radius of the circular motion.

4. What factors affect the smallest possible speed of the bob at A?

The smallest possible speed of the bob at A can be affected by the acceleration due to gravity, the length of the string or wire suspending the bob, and the angle at which the string or wire is suspended.

5. Why is it important to determine the smallest possible speed of the bob at A?

Knowing the smallest possible speed of the bob at A is important in understanding the limits of the bob's circular motion and how it may be affected by different variables. It can also help in designing experiments or devices that involve circular motion.

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