An object is moving vertically while being pulled from above by a rope (or cable

Question

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 ?F = ma and FG = mg Derive symbolic expressions for the acceleration in each case, then substitute and calculate

Explanation / Answer

For, upward motion

F - mg -kv2 = ma

=> a = (F - mg -kv2)/m           --------->(1)

For, downward motion

mg -F -kv2 = ma

=> a = (mg -F -kv2)/m           --------->(2)

If we substitute equal vales of m, F ,v   in both equations   1 and 2

We, find that downward acceleration is more than upwards . So, the object have a greater acceleration if it's descending .

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.