Would lifting dumbbell in free falling lift be easier or harder?

Question

Would it be harder to lift a dumb bell in free falling lift, where the dumbbell is falling with us or would it be easier?

score 5 · Answer 1 · answered Mar 04 '20 at 08:13

In free fall both you and the dumbbell would be weightless. If you were to release it it would “float” in the air along side you. It would be as if you were in outer space far from any gravitational field. Since the dumbbell is weightless “lifting” has no meaning.

Bottom line: it would require no force to move the dumbbell at constant velocity. It would require a force to accelerate it per Newton’s second law $F=ma$.

Hope this helps

kbakshi314 · Answer 2 · 2020-03-04T13:04:46.030

1

It would be easier to cause a dumbbell to accelerate w.r.t. the person if the dumbbell was in free fall along with the person, such as in a free falling lift containing the person and the dumbbell. If $a$, $g$, $m$ and $F$ denote the acceleration of the dumbbell w.r.t. the person, the constant acceleration due to gravity, the mass of the dumbbell and the force applied by the person on the dumbbell in the direction opposite to that of gravity, respectively, then the equation of motion in the vertically upward direction will be $ma = F + m \cdot -g - m \cdot -g$ where we recognize the last term as the pseudo or non-inertial force due to the use of the non-inertial reference frame attached to the person (who is assumed to be accelerating in the direction of gravity with acceleration $g$). This implies that $ma = F$ which is in contrast to a person who is not free falling, attempting to accelerate the dumbbell by applying the force $\tilde{F}$ while stationary w.r.t. the ground with the equation of motion $ma = \tilde{F} - mg$. The answer then follows on observing that $F < \tilde{F}$. This is similar to the situation of apparent weightlessness in a steadily orbiting space station.

edited Mar 04 '20 at 13:04

answered Mar 04 '20 at 05:58

kbakshi314

2,382

I am sorry, but this description is making me confused. So in the end, does it need more or less visible effort to lift a dumb bell in free falling. – Apocaleone Mar 04 '20 at 06:16
1

It requires less apparent effort to 'lift' the dumbbell if it is free falling along with the person lifting it. – kbakshi314 Mar 04 '20 at 06:17
How much less? Like half or only point difference? – Apocaleone Mar 04 '20 at 06:23
The difference in the efforts can be measured in terms of the magnitude of the force required to cause the same relative acceleration of the dumbbell. As calculated in the answer, the difference is $\tilde{F} - F = mg$. So, the direct answer is, less by the weight of the dumbbell on the ground. – kbakshi314 Mar 04 '20 at 06:25
Does that mean only half force is exerted? Because force should be the same in lifting the weight right? I am talking about lifting the weight by gravity – Apocaleone Mar 04 '20 at 06:47
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I think you would benefit from the answer and discussion to this question. – kbakshi314 Mar 04 '20 at 07:05
I read the answer and it explains what it would feel like. I don't want that. I want to know the actual force exerted, when standing in a free falling lift and lifting the dumbbell past your waist or up your shoulders from the floor of the lift. – Apocaleone Mar 04 '20 at 07:25
@Apocaleone Do you agree that if you and the dumbbell were in free fall, that it would be floating next to you and not "falling" relative to you, as if you were both in outer space far from gravity forces? – Bob D Mar 18 '20 at 21:32
Yes, I agree that the man and dumbbell would both be floating. But my question was that whether there would be same effort in 'lifting' the dumbbell as there is in ground. The upward force applied against gravity on the dumbell...would it be same? – Apocaleone Mar 19 '20 at 01:22
@Bob D your answer did imply some force would be applied. I had assumed as much. But how much is it relative to standing on the ground? – Apocaleone Mar 19 '20 at 01:25

score 0 · Answer 3 · edited Mar 18 '20 at 16:52

Free fall is falling with the acceleration of gravity. Therefore, the person inside the elevator does not feel his weight while holding the dumbbell (unless a force is applied). However, if it exerts a force, the dumbbell acceleration decreases. So he feels as if he is up in the elevator. However, according to the external viewer, the elevator and dumbbell move downward. I threw you these detailed force analyses. I examined it in the action and inactive reference frames.

Would lifting dumbbell in free falling lift be easier or harder?

3 Answers3