What Went Wrong in My Free-Body Diagram?

AI Thread Summary
The discussion revolves around a physics problem involving a 40.0 kg crate being lowered with a downward acceleration of 2.00 m/s². The user initially miscalculated the force exerted by the rope, leading to an incorrect answer. The correct approach involves recognizing that the acceleration due to gravity should be treated as negative in the free-body diagram. After realizing this mistake, the user acknowledges that the book's answer of 312 N is indeed correct. The user also expresses confusion about how to mark the thread as "SOLVED."
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Homework Statement


A 40.0 kg crate is being lowered by means of a rope. Its downward acceleration is 2.00 m/s2. What is the force exerted by the rope on the crate?

Homework Equations


Weight = mass(gravity)
Force = mass(acceleration)

The Attempt at a Solution


I solved it (look at attached picture), but my answer is wrong, because the book says the answer is: 312 N. I think that I may have drawn the free-body diagram wrong; would someone please tell me where I went wrong in my free-body diagram?

Thank you so much :) I have a test in six days & this problem will more than likely, be on it :/
 

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Well You know the the acceleration from gravity is -9.8. The actual acceleration is -2. The tension force has to account for this difference.

I can't see the free body diagram yet but the book's answer is correct.
 
Ahhh! Stupid mistake...I was forgetting to make the acceleration caused by gravity negative! :O
Thank you so much! :)

Also, I have no idea how to mark this thread "SOLVED!" I even looked in "Thread Tools" & didn't see anything ://
 
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