Dynamics: Determining amount of energy dissapated by a pulley

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Discussion Overview

The discussion revolves around a homework problem involving a pulley system with two blocks of different masses. Participants are tasked with determining the amount of energy dissipated by friction in the pulley and the tension in the cord during the motion. The scope includes concepts of energy conservation, kinetic and potential energy calculations, and force analysis.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant calculates the potential energy for both blocks and the kinetic energy for block A, but does not initially consider the entire system's energy balance.
  • Another participant suggests writing an energy balance for the entire system to account for energy losses, indicating that the initial energy should equal the final energy plus pulley loss.
  • A participant expresses confusion about how to incorporate the potential energy of block B into their calculations.
  • Another participant advises drawing free body diagrams for each mass to analyze forces, suggesting that the equations will involve two unknowns: tension and acceleration.
  • A participant acknowledges their earlier misunderstanding and expresses gratitude for the clarification on equating forces.

Areas of Agreement / Disagreement

Participants generally agree on the need to consider the entire system for energy calculations and the importance of free body diagrams for determining tensions. However, the discussion does not reach a consensus on the specific methods or calculations for finding the tensions.

Contextual Notes

Participants mention the need to determine acceleration by another means, indicating potential limitations in the provided equations and assumptions about the system.

Who May Find This Useful

Students working on problems involving energy conservation in pulley systems, as well as those interested in the dynamics of forces in mechanical systems.

jaredogden
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Homework Statement



Blocks A and B have masses 11 kg and 5 kg, respectively, and they are both at a height h = 2m above the ground when the system is released from rest. Just before hitting the ground block A is moving at a speed of 3 m/s. Determine a.) the amount of energy dissipated in friction by the pulley, b.) the tension in each portion of the cord during the motion.

(blocks A and B are hanging at the same height attached by a cable that passes through a pulley above them)

Homework Equations



KE = 1/2mv2
PE = mgz
F = ma

The Attempt at a Solution



EA = mgz
EA = (11 kg)(9.81 m/s2)(2 m)

EB = mgz
EB = (5 kg)(9.81 m/s2)(2 m)

KEA at y = 0 m
KEA = 1/2(11 kg)(3 m/s)2
KEA = 49.5 J

The answer in the book for a.) is 45.7 J
 
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You have to look at the entire system, not only the kinetic energy in block A. What you calculated is the KE for block A. Write an energy balance for the entire system such as:

Initial energy (KE+PE) = Final energy (KE+PE) + pulley loss

You'll see you will get the correct answer.
 
Oh thank you! I was trying that earlier but I was trying to figure out the height that block B would be at to add in its potential energy.

Just adding their original potentials and subtracting them from their kinetic energies assuming they were traveling at the same speed did the trick. Thanks again.

Any idea about how to go about getting the Tensions?
 
In order to find the tensions you should draw a free body diagram of each mass. You will see forces such as tensions, weights, and forces due to acceleration for each. Equate the forces. Each equation will have two unknowns, namely the tension and the acceleration. The acceleration is the same for each force balance.

So you now have two equations with three unknowns. Hint: Determine the acceleration by another means.
 
Ah perfect! Once I saw the equate the forces I felt stupid.

Thanks so much for the help I finally got it!
 

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