How to find the velocity of a pendulum

In summary, the problem involves finding the velocity of a pendulum at a distance of 0.250 m from its rest position. Using conservation of energy and trigonometry, the velocity can be calculated by equating potential energy to kinetic energy and finding the height at the given horizontal displacement.
  • #1
grr_physics
16
0
How to find the velocity of a pendulum...need help!

Homework Statement


A 3.60 m long pendulum with a 1.25 kg bob is pulled sideways until it is displaced 1.80 m horizontally from its rest position. If the bob is released, calculate the speed of the bob when it is 0.250 m about it's rest position.


Homework Equations



I found the potential energy when it passes through rest position= 5.91 J
and the velocity when it passes through rest position is 3.08 m/s. I don't know how to find it at 0.250 m & need help please!
 
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  • #2
Need help to find the velocity of a pendulum at a distance please!

1. Homework Statement
A 3.60 m long pendulum with a 1.25 kg bob is pulled sideways until it is displaced 1.80 m horizontally from its rest position. If the bob is released, calculate the speed of the bob when it is 0.250 m about it's rest position.


2. Homework Equations

I found the potential energy when it passes through rest position= 5.91 J
and the velocity when it passes through rest position is 3.08 m/s. I don't know how to find it at 0.250 m & need help please!
 
  • #3


I think you mean you found the kinetic energy when it passes throught the rest position this being equal to the loss of potential energy.Use the same method,find the vertical distance moved when the horizontal displacement goes from 1.8m to 0.25m and use PE lost=KE gained.
 
  • #4
Welcome to PF!

Hi grr_physics! Welcome to PF! :wink:
grr_physics said:
I found the potential energy when it passes through rest position= 5.91 J and the velocity when it passes through rest position is 3.08 m/s.

You don't need to do that …

just use conservation of energy (and a bit of elementary trig). :smile:
 
  • #5


so do i do this:

Ep = Ek
mgh = 1/2mv^2
gh = 1/2v^2
(9.81)(0.250)=1/2v^2

and keep going til i get the answer? where do i do trig?
 
  • #6


so do i do this:

Ep = Ek
mgh = 1/2mv^2
gh = 1/2v^2
(9.81)(0.250)=1/2v^2

and keep going til i get the answer?
 
  • #7
That's right.

And you'll need the trig to find the height when the horizontal displacement is 1.80 m :wink:
 
  • #8


thanks! :)
 
  • #9


grr_physics said:
1. Homework Statement
A 3.60 m long pendulum with a 1.25 kg bob is pulled sideways until it is displaced 1.80 m horizontally from its rest position. If the bob is released, calculate the speed of the bob when it is 0.250 m about it's rest position.


2. Homework Equations

I found the potential energy when it passes through rest position= 5.91 J
and the velocity when it passes through rest position is 3.08 m/s. I don't know how to find it at 0.250 m & need help please!

Two threads merged into one. Please do not multiple post your questions, grr.
 
  • #10


sorry, promise i won't anymore!
 

1. What is the formula for calculating the velocity of a pendulum?

The formula for calculating the velocity of a pendulum is v = √(g * L * (1-cosθ)), where v is the velocity, g is the gravitational acceleration, L is the length of the pendulum, and θ is the angle of the swing.

2. How do you measure the length of a pendulum?

The length of a pendulum can be measured by measuring the distance from the point of suspension to the center of mass of the pendulum's bob. This length should be measured in meters for accurate calculations.

3. Can the velocity of a pendulum change?

Yes, the velocity of a pendulum can change depending on factors such as the length of the pendulum, the angle of the swing, and the gravitational acceleration. However, in a vacuum, the velocity will remain constant due to the principle of conservation of energy.

4. How does the mass of the pendulum's bob affect its velocity?

The mass of the pendulum's bob does not affect its velocity. The velocity is only affected by factors such as the length of the pendulum and the angle of the swing.

5. How does air resistance affect the velocity of a pendulum?

Air resistance can decrease the velocity of a pendulum as it swings back and forth. This is because air resistance acts as a force that opposes the motion of the pendulum, causing it to lose energy. In a vacuum, where air resistance is absent, the pendulum's velocity will remain constant.

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