What is the Maximum Height of a Pendulum on the Right?

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SUMMARY

The maximum height of a pendulum bob after being caught by a peg can be expressed algebraically in terms of the initial height and the masses involved. When the pendulum is released from point A and passes through the vertical at point B, it converts its potential energy into kinetic energy. The height on the right can be determined using variables such as h for height, M for the mass of the pendulum bob, and m for the mass of the peg. This approach allows for a general solution without specific numerical values.

PREREQUISITES
  • Understanding of pendulum mechanics and energy conservation principles.
  • Familiarity with algebraic expressions and variable manipulation.
  • Basic knowledge of gravitational potential energy and kinetic energy.
  • Ability to apply concepts of mass in physics problems.
NEXT STEPS
  • Research the principles of energy conservation in pendulum motion.
  • Learn how to derive algebraic expressions for potential and kinetic energy.
  • Explore examples of pendulum problems involving variable mass and height.
  • Study the effects of different pivot points on pendulum motion.
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of energy conservation in pendulum systems.

dman2522
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Homework Statement


A pendulum is released at A and caught by a peg as it passes through the
vertical, B. To what height will the bob rise on the right?

Homework Equations


None given

The Attempt at a Solution


I really am unsure about how I am supposed to figure the height when no numbers were given. Thank you for any help!
 
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dman2522 said:

Homework Statement


A pendulum is released at A and caught by a peg as it passes through the
vertical, B. To what height will the bob rise on the right?


Homework Equations


None given


The Attempt at a Solution


I really am unsure about how I am supposed to figure the height when no numbers were given. Thank you for any help!

Presumably the answer will be an algebraic expression in terms of the two masses and the original height.

If numbers make you more comfortable, you could invent your own and calculate.

Then re-write your answer using h, M and m in place of you numbers, which should only prevent combinations of this numbers.
eg: first time you might have a 3 multiplied by a 5 which you would write as 15, second time through you may have M multiplied by m, which you would write as Mm.
 

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