Pendulum - Kinetic Energy at Lowest Point?

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SUMMARY

The kinetic energy of a pendulum bob at its lowest point can be calculated using the conservation of energy principle. For a pendulum of length L = 1.0 m and mass m = 0.2 kg released from an angle of 30 degrees, the maximum potential energy is converted to kinetic energy at the lowest point. The correct calculation yields a kinetic energy of 0.26 J, confirming that the answer is option E. This conclusion is derived from the formula U = mgy, where y is determined using the equation (1 - cos(30)).

PREREQUISITES
  • Understanding of basic physics concepts such as kinetic and potential energy.
  • Familiarity with the conservation of energy principle.
  • Knowledge of trigonometric functions, specifically cosine.
  • Ability to perform calculations involving gravitational acceleration (g = 9.8 m/s²).
NEXT STEPS
  • Study the derivation of the conservation of energy in mechanical systems.
  • Learn how to apply trigonometric functions in physics problems.
  • Explore different types of pendulum motion and their energy transformations.
  • Investigate the effects of varying mass and length on pendulum dynamics.
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of energy conservation in pendulum motion.

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?
 
Last edited:
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Well from conservation of energy, the maximum potential energy is equal to the maximum kinetic energy. Can you calculate the maximum potential energy?
 
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!
 

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