Maximum Upward Acceleration of a String

[Fr3shFr0st]

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

 

[awvvu]

Draw out the free body diagram. There's both gravity and the tension of the string that you need to take into account.

 

[robertm]

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.