Object Acceleration with Vertical Forces: Rising or Descending?

[paperboy221]

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

 

[paperboy221]

Could someone help me create a scenario? Thanks!

 

[Ray Vickson]

Could someone help me create a scenario? Thanks!

Please post your images properly; they are sideways now, and so will be ignored by almost everybody.

 

[TSny]

Welcome to PF!

Your work for the case of rising looks good. There is no need to write the friction force in terms of speed, you could just write the friction force as f, say.

You will need to repeat for the system descending. (You posted two figures for rising, but none for descending.)

I'm not sure what is meant by creating an "appropriate scenario". That could mean coming up with a specific physical scenario or it could mean different mathematical scenarios that addresses different cases depending on the relative sizes of the individual forces. I'm inclined to think it's the latter.

Anyway, after you deal with the descending case you will want to compare your acceleration formulas for ascending and descending.

As Ray pointed out, it would be appreciated if you could rotate your figures so we don't get a crick in the neck.

 

[paperboy221]

I flipped the images around!
Thanks

 

[haruspex]

(You posted two figures for rising

To be precise, the same image posted twice.

I flipped the images around!

They're still not upright.

 

[TSny]

To be precise, the same image posted twice.

Precise, indeed.

 

[Rx7man]

Since they specify ALL forces remain the same whether its rising of falling, it would lead me to believe the acceleration would be the same, as acceleration isn't dependent on direction.. the force of friction would be dependent (and opposite as always) the direction of motion, but is the only force which changes direction

 

[haruspex]

ALL forces remain the same

It says their magnitudes remain the same.

 

[Rx7man]

Sorry for the inaccuracy.. , you are right