Solving the Pendulum Problem: Mass, Speed, Frequency and Trajectory

  • Thread starter ice97531
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In summary: So the final velocity will bev = (2P r)atan(theta)+gIn summary, the ball has a mass of 9.8 kg, a speed of 16.7 m/s, and swings at a frequency of 2.4 Hz.
  • #1
ice97531
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Ok here is what I know:
A ball is attached to a string with length of L. It swings in a horizontal circle, with a constant speed. The string makes an angle (theta) with the vertical, and T is the magnitude of the tension in the string.

Determine the Mass of the Ball.
Determine th Speed of the Ball.
Determine the Frequency of revolutions of the Ball.
Suppose the strings breaks as the ball swings in its circular path. Describe the trajectory of the ball after the strings breaks but before it hits the ground.

Good luck.
 
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  • #2
By the way...
I'm not just posting here cuase i don't want to do it
I've been working on it forever
This is the only part I can't figure out
 
  • #3
The ball moves in a circle with uniform speed. So its acceleration is given by
[tex]a=\frac{v^2}{r}[/tex] where r is the radius of the circle.
You can find r rather easily.
There is only one force that can provide this acceleration and that is the tension T. Gravity acts down, and so it won't produce a centripetal acceleration. However, only the horizontal component of T will provide an acceleration. The vertical component acts up and merely counteracts the gravity. So,
[tex]F_{net}=Tsin\theta=ma[/tex]
I mentioned that the vertical component of the tension counteracts gravity. This is true by Newton's second law.
[tex]mg=Tcos\theta[/tex]
You can now find the mass and speed of the ball. The frequency is rather easy. You must know that
[tex]T=\frac{2\pi r}{v}=\frac{1}{f}[/tex]
 
  • #4
I'm still a little confused
Tell me if my thinking is right

For the mass I got:
F=Tsin(theta)=ma
therefore:
(Tsin(theta)) / 9.8 = m

Is this right?

or do I use the cos instead of sin to find the mass?
 
  • #5
it should be cos
 
  • #6
For the last part the motion will be projectile with initial velocity which is in horizontal direction and tangentially to the circle
 

1. What is the pendulum problem?

The pendulum problem refers to the challenge of determining the motion of a pendulum, which is a weight suspended from a fixed point that can swing back and forth.

2. How do mass, speed, frequency, and trajectory affect the motion of a pendulum?

The mass of a pendulum affects its period, or the time it takes to complete one swing. The speed of the pendulum is determined by the length of the pendulum and the force of gravity. The frequency is the number of swings per unit of time. The trajectory is the path that the pendulum follows as it swings back and forth.

3. What is the equation for calculating the period of a pendulum?

The equation for calculating the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

4. How can I determine the mass of a pendulum?

The mass of a pendulum can be determined by weighing it on a scale. Alternatively, if the pendulum is made up of multiple objects, the individual masses can be added together to get the total mass.

5. How can I change the frequency of a pendulum?

The frequency of a pendulum can be changed by altering the length of the pendulum or the force of gravity acting on it. Shortening the length of the pendulum or increasing the force of gravity will result in a higher frequency, while lengthening the pendulum or decreasing the force of gravity will result in a lower frequency.

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