Pendulum - Kinetic Energy at Lowest Point?

In summary, the question asks for the kinetic energy of a pendulum's bob at its lowest point. Using conservation of energy, we can determine that the maximum potential energy is equal to the maximum kinetic energy. By calculating the maximum potential energy at the point of release, we can determine the kinetic energy at the lowest point. The correct answer is option E, which is 0.26 J.
  • #1
crazyog
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[SOLVED] Pendulum - Kinetic Energy at Lowest Point?

1. The Problem Statement:

A pendulum of length L= 1.0 m with an attached bob of mass m= 0.2 kg is released from a point where the cord makes an angle of 30 degrees with the vertical. The kinetic energy of the bob at its lowest point is...?
a. 2.0 J,
b. 1.7 J,
3. 1.1 J,
4. 1.0 J,
5. 0.26 J

Homework Equations


I believe Relevant equations include:
(1/2)mv^2 -- kinetic energy
(mgy) -- potential energy

The Attempt at a Solution


I know that at the lowest point in the pendulum, it is the highest speed. There is no potential energy. But, how do I get the value for velocity?
 
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  • #2
Well from conservation of energy, the maximum potential energy is equal to the maximum kinetic energy. Can you calculate the maximum potential energy?
 
  • #3
Ok so Maximum potential energy would be where it is released...
Thus,
U= gmy
(9.8)(0.2)(y)
and (y) is the height it is released so when I solve for that
and I get (1-cos(30)
U=gmy
(0.2)(9.8)(1-cos(30))
=0.26

and I just realized that my professor said the answer was E.
Thank you!
 

1) What is a pendulum?

A pendulum is a weight suspended from a pivot point that is able to swing back and forth due to the force of gravity. It is used to demonstrate the principles of simple harmonic motion and is often used in timekeeping devices.

2) How does a pendulum gain kinetic energy at its lowest point?

When a pendulum reaches its lowest point, it has the maximum potential energy and zero kinetic energy. As it swings back up, the potential energy is converted into kinetic energy, reaching its maximum at the highest point of the swing. This cycle continues as the pendulum swings back and forth.

3) What factors affect the kinetic energy of a pendulum at its lowest point?

The kinetic energy of a pendulum at its lowest point is affected by the length of the pendulum, the mass of the weight, and the angle at which it is released. A longer pendulum will have a higher maximum kinetic energy, while a heavier weight will have a greater impact on the pendulum's potential and kinetic energy. The angle at which the pendulum is released also affects the maximum kinetic energy, with a larger angle resulting in a higher kinetic energy.

4) Can the kinetic energy of a pendulum at its lowest point be calculated?

Yes, the kinetic energy of a pendulum at its lowest point can be calculated using the equation KE = 1/2 * m * v^2, where m is the mass of the pendulum and v is the velocity at the lowest point. This equation assumes that there is no friction or air resistance present.

5) How is the kinetic energy of a pendulum used in real-world applications?

Pendulums are used in various real-world applications, such as in clocks and metronomes to keep time. They are also used in seismometers to measure the movement of the earth during earthquakes. Pendulums are also used in physics experiments to demonstrate the principles of simple harmonic motion and to calculate gravitational acceleration.

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