Practice Problem about the Energy of a Pendulum

In summary, a pendulum is a weight suspended from a pivot used to measure time. It works by converting potential energy into kinetic energy and its energy is affected by factors such as mass, length, and release angle. The energy of a pendulum can be calculated using the equation E=1/2mgh, and it is directly proportional to its amplitude.
  • #1
stephy
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Homework Statement
A small sphere of mass m is fastened to a weightless string of length 0.5m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 60 degrees with the vertical.
a) What is the velocity of the sphere when it passes through the vertical position?
b) What is the instantaneous acceleration when the pendulum is at its maximum deflection?
Relevant Equations
a) v=sqrt(L*g*sine(thet)*tan(thet)
b) ac= v^2/r
Answer:
a) 7.35 m/s
b) 216.09 m/s^2

*Is this correct?
 
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  • #2
It would be easier to offer you help if you offer a bit more detail for your reasoning.

In both of the cases a) and b), what is your argumentation behind the expressions?
 
  • #3
stephy said:
*Is this correct?
I suggest you read the forum rules, one of which is that you are required to show work (not just answers).
 
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  • #4
No working out offered by me (yet), but I would look at energy considerations for the first part.
 

FAQ: Practice Problem about the Energy of a Pendulum

What is the formula for calculating the energy of a pendulum?

The formula for calculating the energy of a pendulum is E = mgh, where E is the energy in joules, m is the mass of the pendulum in kilograms, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the pendulum in meters.

How does the length of a pendulum affect its energy?

The length of a pendulum has a direct effect on its energy. The longer the pendulum, the greater the distance it will travel and the more potential energy it will have. This means that a longer pendulum will have more energy than a shorter one.

Can the energy of a pendulum be changed?

Yes, the energy of a pendulum can be changed. The energy of a pendulum is constantly changing as it swings back and forth between potential and kinetic energy. The energy can also be changed by altering the mass, height, or length of the pendulum.

How does the angle of release affect the energy of a pendulum?

The angle of release does not have a significant effect on the energy of a pendulum. As long as the pendulum is released from the same height, the angle at which it is released will not affect its energy. However, releasing the pendulum from a higher height will result in more energy due to the increased potential energy.

What factors can affect the energy of a pendulum?

The energy of a pendulum can be affected by several factors including its mass, height, length, and the force of gravity. Other factors such as air resistance and friction can also affect the energy of a pendulum.

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