Maximum Upward Acceleration of a String

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To determine the maximum upward acceleration of a 10 kg mass using a string that can withstand a maximum tension of 200 N, both tension and gravitational forces must be considered. The gravitational force acting on the mass is 98 N (10 kg x 9.8 m/s²). The net force available for upward acceleration is the tension minus the weight of the mass, which is 200 N - 98 N = 102 N. Using the formula F = ma, the maximum upward acceleration can be calculated as a = F/m, resulting in an acceleration of 10.2 m/s². Properly accounting for both forces is essential for an accurate solution.
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Homework Statement


A string can withstand a maximum tension of 200 N. What is the maximum upward acceleration one can impart to a 10 kg mass using this string?


Homework Equations


T=ma
a=F/m


The Attempt at a Solution


so i tried just plugging those variables in that equation and i got 20 m/s^2 i know this is wrong but i can't seem to find the right equation to solve this problem. please help i know its simple
 
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Draw out the free body diagram. There's both gravity and the tension of the string that you need to take into account.
 
And if you know your net force in the downward direction cannot exceed 200 N, then...

And don't forget to include gravity in your force diagrams.
 

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