Question

Question 29.6 on p. 982 of the textbook university physics 13th edition states that a magnet would reach terminal velocity even if there is no air resistance. How would air resistance change the situation? Is it significant?

Answer 1

if it is TERMINAL velocity it means the velocity is not changing anymore (terminal, done, finito)

so velocity remains constant, acceleration is ... ZERO.

When an object is falling with significant air drag, initially air drag isn't significant.

Eventually, air drag is nearly equal to the gravitational force acting on the object.

At a condition called terminal velocity, gravitational force will be EXACTLY equal (and opposite) to the air drag acting on the object. Hence the net force will be zero.

At terminal velocity, due to zero net force, NEITHER the object's velocity will change nor will the object's acceleration change.

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UNLESS you consider what actually happens, other than the hypothetical state of terminal velocity.

A falling object with air drag, believe it or not, will never be exactly at the terminal velocity. It will only approach terminal velocity asymptotically.

Acceleration will be continuously getting closer and closer to zero, but never actually get there.



Also, another factor:

Our atmosphere is not of uniform density. As we examine closer and closer to ground level, the density is higher.

Therefore, terminal velocity is even more of a hypothetical state. The conditions of air CAUSING the air drag actually do cause acceleration to change, as the atmosphere keeps re-defining what the terminal velocity is