# What is the rower actually doing? Pushing the water or pushing the lake?

A well-known example to demonstrate Newton's third law is rowing a boat on water. It can be simply explained as follows: The rower is pushing the water backwards with the oar and the water exerts a reaction force on the oar. That force is received by the entire system of boat (beacuse the rower holding the oar is inside the boat) causing the boat to move forward. But does that phrase "pushing the water backwards" mean the rower is pushing back the lake? (by 'lake' I mean the entire system including the dam as well)

Considering the confusion poped-up in the comments, I thought it will be easier to visualize the lake as a huge basin, and I think you can now understand my question. Does the oar push that basin back?

• What's the difference? The water is the lake.
– d_b
Aug 4 '21 at 18:01
• Related question by OP(me): Can the fish topple the bowl
– ACB
Aug 4 '21 at 18:22
• I think the water molecules move in a curve very simmilar to the magnetic dipole lines field curve and the boat just move where the lines go away from the boat while the space left by the boat is filled by water molecules that move towards the boat. Just immagine a magnet dipole field lines curve... Aug 5 '21 at 16:59
• The physics of rowing are really remarkably complex in detail. I recommend Anu Dudhia's very readable and brief "Physics of Rowing" pages to the interested reader -- eodg.atm.ox.ac.uk/user/dudhia/rowing/physics -- he's an atmospheric physicist in Oxford and rather legendary in the "rowing scene". Aug 5 '21 at 20:23

During the rowing action, all that is necessary is that an increase in the boat's forward momentum is created by an increase in rearward momentum for something else.

We can easily think of this as a parcel of water. As the oar moves, it's creating a force couple that pushes (accelerates) the rower forward and pushes the water backward.

For the purpose of moving the boat, this is sufficient. But after this action the water interacts with its environment (the lake) and creates forces. The result is that the parcel of water slows down and the rest of the water accelerates backward a teeny bit.

Then that water does the same to its environment. Eventually the forces and momentum of the oar spread out to the lake and the earth. (And then they run in reverse as viscous forces bring the boat to a halt).

So the eventual result is that the rower ends up pushing on the lake/dam/earth, but that isn't required to move the boat. Only the acceleration of the water parcel by the oar is necessary. The rest happens after the oar is gone and doesn't (directly) affect the boat.

• So if we think the lake as a huge basin, does the oar pushing that basin back?
– ACB
Aug 4 '21 at 18:38
• You could say that. Same as when walking you could say you push your shoe back, you push the street back and you push the earth back. All of them transmit forces to the next. Aug 4 '21 at 18:43
• Put your hand in a basin of water, move it, observe the water. But yeah, the basin will move a little too. Aug 5 '21 at 5:48
• @ACB "should the basin move?", that depends on lots of things like friction between the basin and what supports it. It is possible that it might move, and it is possible that it might stay fixed (with respect to the earth). Aug 5 '21 at 6:30
• Note that the center-of-mass of the water in the basin plus the boat says the same no matter where the boat goes (since the boat's mass is the same as that of the water it displaces), so there's no need for it to exert a net horizontal force on the basin. Aug 5 '21 at 16:18

Yes, the force generated by the oarsperson is applied to the Earth as a whole eventually. The force of the oars is applied initially to a local volume of water in the lake, causing it to move backwards relative to the boat. The momentum of the water propelled backwards in the immediate vicinity of the oars is dissipated into the lake as a whole and subsequently by the Earth as an isolated system.

• This is an important reality of newton's second law. While we like to think of the earth as "fixed," when you really apply the laws properly, its rotation can speed up and slow down in response to forces you apply to the ground. Aug 5 '21 at 7:55
• Indeed, although the effects are vanishingly small in the main. Aug 5 '21 at 8:52
• Give me a big enough monster truck and a circumferential highway, and I will lengthen the days ... Aug 5 '21 at 10:17
• True- assuming you drive in the right direction! Aug 5 '21 at 12:06
• @CortAmmon If your row boat was the only thing on earth that was moving, yes, that theoretically true (although almost surely immeasurable) but there are also billions of other things moving around in all different directions. The idea that an ant walking on the ground is 'moving the earth' has no real implications. Aug 5 '21 at 17:59

The boatman's oars push the water backwards.

Practically, this is almost equally balanced by the boat pushing water forward (from the bows, and sideways in both directions, and pulling it forwards from the stern, creating waves) due to its form drag and the skin resistance of its wetted area.

If the boatman stops rowing, the boat stops moving forwards in a few seconds; less than a minute. So if you consider the boat and a local region of water around it as a system, very little energy escapes from that system, mostly in the form of a wake, which will eventually push equally on both sides of an idealised lake (or a 1-D lake, i.e canal); net force 0.

Assuming the lake is large compared with that local region (ignoring degenerate cases like a bathtub) there is very little interaction with the lake as a whole.

So except for the first stroke away from a dock, where he pushes aft (acceleration), and for grounding the bows on the far shore (deceleration), (and those two boundary pushes cancel out apart from the time difference between them) I suggest he does not push against the lake, only against the water.

Acceleration provides a temporary backwards transfer of momentum to the lake, while Deceleration cancels it later with forward momentum, but the vast majority of the rower's energy is dissipated maintaining a body at constant speed through the water with no net change in momentum.

• I don't believe this to be true, a boatman's oars do not 'push water backwards', the water is essentially stationary, it provides a point at which the boatman is able to apply a force against the water (which is basically connected as a rigid system to the entire earth). The fact that to move, the boat must displace water and create waves, only increases the force that must be applied to the water to move the boat. Aug 5 '21 at 14:58
• It's over-simplified. The water is NOT stationary; you can observe it moving aft, and a nice pair of vortices at the blade edges so some of the water actually moves forwards! However the water pushed by the oar is not purely reaction mass if that's what you thought I was implying; it imperfectly transfers blade force to the "local region" of water. In a low resistance kayak paddled at v=4 (arbitrary units) you'll see the water moving aft about V=0.5 to 1 where the paddle has been. Aug 5 '21 at 15:05
• Further, a small high speed propellor (e.g. 4hp Evinrude, 170mm dia) throws water aft at several times the boat's forward velocity, while a large low speed propellor (Seagull Silver Century, 280mm dia) pushes a much larger volume more slowly, propelling the boat more efficiently. Aug 5 '21 at 15:11
• Well, I will agree that it is a continuum, there may be some movement of water aft, but that would be considered an inefficiency (represented by slippage of the oar from where it was placed in the water). As in your propeller example, the oar can be considered an even larger lower speed prop, the goal (and ultimate efficiency) being no local slippage, and thus pushing the whole lake (earth) backward. To take this back to physics, an oar is a class 2 lever with the fulcrum being where the blade contacts the water, you don't want your fulcrum moving in a lever. Aug 5 '21 at 15:24
• You're getting there. Practically the whole energy expended in moving a boat is inefficiency; form drag, surface drag * wetted area slowing the boat, and precisely the same mechanisms stealing from the oar or propellor. Yes to the oar being a larger low speed prop (ignoring the prop's greater efficiency : see Rattler vs Alecto, 1845) but no local slippage would imply a large blade area, which is not in practice the best choice. Aug 5 '21 at 15:35