Is holding a falling object the same effort as lifting it?

Question

It seems like lifting objects requires more effort compared to dropping them, although the law of conservation of energy still applies. As discussed Physics Stack Exchange answer, energy transfers from my muscles to the object and then back to my muscles.

(I suppose equal conditions for both case (such as speed, time, etc.)

Now, considering the concept of resisting negative energy from my body's perspective, it feels like my muscles need to exert force to oppose this effect. The mathematics suggests that my body must generate the same amount of energy (if I use the correct formula...) to counter the potential energy released by the fall. It's correct?

Why do I have the impression that it takes more effort to lift than to retain the fall, even though the energy is the same?

Answer 1

Why do I have the impression that it takes more effort to lift than to retain the fall...?

Because it does take more energy to lift it.

A table can hold a heavy object above the floor without expending any energy at all, but a table cannot lift an object. Lifting an object increases the gravitational potential energy of the Earth/object system, and that energy has to come from somewhere.

Your muscles don't work like a table. You have to expend energy even to simply hold the object up. But you'd have to expend even more energy to first lift the object off of the floor.

Answer 2

One of the most frustrating parts about teaching physics is that it's so hard to make examples involving the human body. The human body so chock full of complex higher order effects that often our intuition about the human body leads us astray from the physics principles.

From a pure physics perspective, you need to put the same energy into lifting an object as you do into arresting its motion, and holding it in place transfers no energy at all. We can write the simple physics equation $W=fd$, work is physics times distance, smile, and say we're done.

But with the human body, "effort" is not always a good metric for "energy." It turns out that our muscles are far more complicated than that. Our muscles operate on fascinating chemical reactions. These chemical reactions do not work the same for "concentric" motion, where the force is in the direction of motion, as they do for "eccentric" motion, where the force is in the opposite direction. So while catching a falling object and lifting an object require the same energy in the nice easy physics world, in the real world with real muscles, the story can be more complicated.

Even more complex, it turns out that "isotonic" force, where one applies force with no motion, is something that our muscles do even better than either eccentric or concentric motion (in fact, it's on the order of 3x stronger than concentric contractions). In many cases, our brains are astonishingly good at this, and will naturally lead us to use the weak arm muscles isotonically, and instead manage motion using concentric/eccentric motion of the abdominal muscles, which are far stronger. As a result, your instinct about what is "easier" turns out to be frustratingly far from the "energy" we teach in physics.

If you want a better intuitive connection to "energy," consider simple machines rather than the complex human body. If you consider a play-ground see-saw catching an object versus lifting it, it's easier to see that it involves the same energy transfer. The human body is just... complicated.