# How Can We Jump When the Ground Does No Work?

#### nsaspook

Joined Aug 27, 2009
9,987
https://www.physicsforums.com/insights/how-can-we-jump-when-the-ground-does-no-work/
It is relatively common on Physics Forums to see arguments that are effectively similar to the following: When we jump off the ground, the ground does not move. Because of this, the force from the ground on us does zero total work. Since the force does no work, we cannot gain any kinetic energy. We therefore cannot jump off the ground. Now, the conclusion here is obviously false. The world high jump record is 2.45 meters, definitely larger than zero. So where did the energy come from? This Insight seeks to clarify this in a fairly accessible way.

#### Alec_t

Joined Sep 17, 2013
12,890
When we jump off the ground, the ground does not move.
The law of conservation of momentum says otherwise.

#### BobTPH

Joined Jun 5, 2013
5,227
If course it falls back to you, just like you fall back to it. The next time I fall and get hurt, I am going to claim the earth came up and smacked me.

Bob

#### Alec_t

Joined Sep 17, 2013
12,890
I hadn't thought about it before, but it occurs to me that in response to a person jumping, planet Earth moves the tiniest amount, hence our entire solar system, our galaxy and indeed the whole universe must be affected through the gravitational field. Wow!

xox

#### BobTPH

Joined Jun 5, 2013
5,227
I would be that simple only if the earth was a rigid body. In reality, it is compressible, so when we jump, we are actually creating an acoustic wave.

Bob

#### nsaspook

Joined Aug 27, 2009
9,987
The law of conservation of momentum says otherwise.
Yea, just like in the Matrix.

#### Alec_t

Joined Sep 17, 2013
12,890
so when we jump, we are actually creating an acoustic wave.
..... which in theory will cause instantaneous movements of the planet's centre of gravity; hence propagation of the effect beyond Earth..

#### nsaspook

Joined Aug 27, 2009
9,987
..... which in theory will cause instantaneous movements of the planet's centre of gravity; hence propagation of the effect beyond Earth..
Gravity moves at light speed so it's not instantaneous. https://en.wikipedia.org/wiki/Speed_of_gravity
The total tiny gravity wave propagation effect depends on the level of mutual gravitational attraction between you, the earth and everything on the earth during the entire jump sequence.

#### MrChips

Joined Oct 2, 2009
26,480
How can we jump when the ground does no work?

I find that a very bizarre question.
Certainly, earth has to move.
Try standing on a floating paddle board and trying to jump.

#### Alec_t

Joined Sep 17, 2013
12,890
Gravity moves at light speed so it's not instantaneous.
Yes. I meant instant-by-instant. I realise any wave takes a finite time to propagate.

#### nsaspook

Joined Aug 27, 2009
9,987
Yes. I meant instant-by-instant. I realise any wave takes a finite time to propagate.
Exactly. If you analyze instant-by-instant the path integral (sum up all contributing paths.) of the jumper and earth you would see the total gravitational effect to be pretty near zero at the speeds and mass for a normal human jumper.

#### cmartinez

Joined Jan 17, 2007
7,744
Let's see... a guy jumps, and pushes the Earth downwards, in the opposite direction. When gravity pulls pulls him back down, the net amount of displacement will be zero.

Except that the Earth is not a perfectly rigid body, and neither a completely solid one. So even if an acoustic wave is formed (it is) when the guy jumped, it would very quickly dissipate ... as heat. And when the guy landed another wave would be produced that would also partially disipate as heat.

So in that scenario although the net amount of energy is zero, the net amount of motion would not be zero ... what gives?

#### BobTPH

Joined Jun 5, 2013
5,227
The movement of the jumpers body would have just as much effect in the universe as that of the earth since the distance moved will be proportional to the masses.

Bob

#### crutschow

Joined Mar 14, 2008
30,100
I fail to see whether the ground moves or not would be related to the energy involved in the jump.
That's determined by the gravitational force between you and the earth.
It's basically the same as the energy if there were a spring pulling you back.

#### cmartinez

Joined Jan 17, 2007
7,744
To clarify my point. Whenever any of us jumps up and falls back down entropy is involved. Something is irreversible lost in the universe.

#### nsaspook

Joined Aug 27, 2009
9,987
To clarify my point. Whenever any of us jumps up and falls back down entropy is involved. Something is irreversible lost in the universe.
but much is gained by the jumping process.

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