Solving the Atwood Machine - Descending Mass

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In the Atwood machine scenario with masses m1 = 2.20 kg and m2 = 7.30 kg, the tension in the string is calculated to be 33.1 N. The problem involves determining how far mass m1 descends after being released with an initial downward velocity of 2.70 m/s. To solve this, one must find the acceleration of the masses and apply kinematics for uniformly accelerated motion. The key is to identify the point where the speed of m1 becomes zero. The original poster successfully resolved the issue with the provided hints.
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In the Atwood machine regular 2 mass machine,m1= 2.20kg and m2=7.30kg . The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not stretch. The lighter object is released with a sharp push that sets it into motion at an initial velocity of 2.70m/s downward. I found the Tension to be 33.1N, but i don't understand how to apply to find how far will m1 descend below its initial value? Could anyone help me out?
 
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Find the acceleration of the masses, which for m1 will be upward. Use the kinematics of uniformly accelerated motion to find out how far m1 descends before coming back up. Hint: Find the point where its speed is zero.
 
i figured it out thanks for the suggestion. Closed!
 

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