Pulley with cylinder and distance

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SUMMARY

The discussion centers on calculating the linear speed of a cylinder-pulley-block system after a block falls 2.5 meters, given an acceleration of 2.98 m/s². The participants suggest using the conservation of energy principle or integrating the acceleration equation twice with respect to time to derive a distance formula. By substituting the known distance into this formula, one can determine the time, which can then be used to find the velocity. This method provides a systematic approach to solving the problem based on established physics principles.

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  • Understanding of Newton's laws of motion
  • Familiarity with integration in calculus
  • Knowledge of conservation of energy principles
  • Basic concepts of kinematics
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SuperGeek
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Hey, thanks for the help. I came up with acceleration = 2.98 m\s^2

One more quick one: If the cylinder-pulley-block system starts from rest, determine the linear speed of the system after the block falls
d=2.5 meters.

Should I use conservation of energy?
 
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If you know the acceleration you can just figure it out from that.

Doug
 
I have a suggestion although I'm not entirely sure it will work.

Take the equation you used to find the acceleration and integrate it twice with respect to time. This will give you a distance formula. Substitute in the value you are given for distance to find the value for time. Substitute that time value into the first integral and you should get the proper velocity.
 

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