Force/magnitude/acceleration scenario

[paperboy221]

Homework Statement

1. Homework Statement
An object is moving vertically while being pulled from above by a rope (or cable, wire, or string). The object is also subject to a significant air resistance force that can't be ignored. All forces acting on it are strictly vertical (pointing up or down only).

Question: If the magnitudes of all forces remain the same, does the object have a greater acceleration if it's rising or if it's descending?

To answer this question, create an appropriate scenario, then draw two FBDs for the object, one for the case in which it's rising, and one for the case in which it's descending. Use N2L and your FBDs to derive expressions that will allow you to calculate the magnitude of the object's acceleration in each case.

Review the summary sheet on FBDs before starting your solution

The only starting equations permitted for this assignment are ΣF = ma and FG =mg

Derive symbolic expressions for the acceleration in each case, then substitute and calculate

 

[haruspex]

This appears to be a duplicate of https://www.physicsforums.com/threads/magnitude-force-acceleration.856945/, which has been marked solved. I assume you did this because the original images were not right.
Forces are vectors. Their magnitudes may be the same but it does not follow that the forces are the same.
You correctly obtained two different expressions for the two accelerations. Try subtracting one from the other.

 

[paperboy221]

This appears to be a duplicate of https://www.physicsforums.com/threads/magnitude-force-acceleration.856945/, which has been marked solved. I assume you did this because the original images were not right.
Forces are vectors. Their magnitudes may be the same but it does not follow that the forces are the same.
You correctly obtained two different expressions for the two accelerations. Try subtracting one from the other.

I'm having troubling understanding how to put numbers into the equation.

 

[haruspex]

I'm having troubling understanding how to put numbers into the equation.

You don't need to.
You have two algebraic expressions, one for the acceleration if moving up, one for the acceleration if moving down. You want to find out which acceleration has the greater magnitude.
There are two cases to consider: the accelerations may be in the same direction or in opposite directions.
Pick one of those cases, and write an expression for the difference in the magnitudes.