What Went Wrong in My Free-Body Diagram?

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SUMMARY

The discussion centers on calculating the force exerted by a rope on a 40.0 kg crate with a downward acceleration of 2.00 m/s². The correct answer is 312 N, as confirmed by the textbook. The user initially miscalculated due to incorrectly representing the acceleration due to gravity as positive instead of negative. This error in the free-body diagram led to the incorrect solution.

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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 ://
 
Last edited:

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