A classical mechanics problem by adarsh sharma

Classical Mechanics Level 3

A mass of 10 g, moving with a velocity of 1 m/s, strikes the bob of a massless pendulum and sticks to it. The mass of the bob is also 10 gm. What is maximum height the bob will reach (in m)?

Assumptions and Details

  • g = 10 g = 10 m/s 2 ^2
  • Apart from the bob, the pendulum is massless.


The answer is 0.0125.

Adarsh Sharma by adarsh sharma , 19, India

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1 solution

Lawrence Mayne
Jan 1, 2016

Energy must be conserved in the process and therefore

The initial KE 1 2 \frac{1}{2} m v 2 v^{2} must equal the GPE gained: Mg∆h

1 2 \frac{1}{2} m v 2 v^{2} =Mg∆h. (M is double m)

∆h= v 2 4 g \frac{v^{2}}{4g} = 1 2 4 × 10 \frac{1^{2}}{4 \times10} = 0.025

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when the bob and mass collide ,there are some energy loss....the correct answer must be 0.0125

Christian Leonardi - 5 years, 5 months ago

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I think .0125 m is the correct answer also. The answer of .025 m would be correct if the collision was perfectly elastic (no sticking together). In this problem, where the 10 gram masses stick together, conservation of momentum tells us the 20 grams moves off with velocity .5 m/s - energy is NOT conserved in this case. Either the question should be changed to "smash together but do not stick" or the answer should change to match the stated situation.

Bob Kadylo - 5 years, 5 months ago

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