Is a boat in water subject to Newtons 3rd Law

My boss has stated that balanced forces do not conform to Newton's 3rd Law and therefore a boat sitting in water does not conform, stating that the upthrust provided by the water is not a reaction force as the 2 forces are balanced.

However, my countargument is that to reach this state of balance the boat must first exert its weight force on the water displacing the fluid beneath it, at which point the upthrust begins to react pushing it bach toward the surface with equal force. So my question is does a boat sitting in water conform to Newton's 3rd Law and is upthrust a reaction force and if true how do I convince her of the fact?

• What type of work do you and your boss do? Jan 26, 2021 at 16:41

2 Answers

Let us be clear about the forces involved. There are two forces acting on the boat:

• Upthrust force (from the water acting on the boat)
• Weight force (from the Earth acting on the boat)

For equilibrium to be reached, you are right to say that the upthrust must balance the weight of the boat. However, Newton's Third Law (N3L) does not explain this balancing effect.

N3L states that if an object $$A$$ exerts a force on an object $$B$$, object $$B$$ simultaneously exerts an equal and opposite force on the object $$A$$.

For example, the gravitational force exerted from the Earth on your body is equal and opposite to the gravitational force exerted from your body on the Earth.

Note two important facts about the example:

1. N3L relates forces acting on two different objects.
2. The forces exerted are always of the same nature, in this case, gravitational force.

So why can't we apply N3L for your case with the boat? You are comparing two forces of different nature (upthrust and weight) and they are acting on the same object (the boat).

The question Why are the upthrust and weight forces balanced for a boat? is not answered through the application of Newton's Third Law. Rather, the upthrust and weight forces are balanced because they come into equilibrium with each other. The upthrust varies with the vertical position of the boat. Its sum with the weight of the boat has a stable equilibrium at a particular position, not unlike a mass on a spring resting at its equilibrium length.

Equilibrium is achieved through the physical properties of the forces involved. Newton's Third Law is never an explanation for equilibrium because equilibrium is achieved through balancing forces which can be of different nature acting on the same object.

• Your final sentence is something that would answer all the Newton's 3rd law posts on PSE. Great summary. One small quibble: the balancing forces don't need to be of a different nature, but they must be due to interactions with different objects. One could envision an equilibrium situation in which many springs are used. Jan 26, 2021 at 15:00

Newton's 3rd law states that for every force, exerted by object A towards object B, there is another force, equal in magnitude and opposite in direction, exerted by object B towards object A.

Note that there are no 'reactions' involved, both forces occur simultaneously. When I push a wall, the wall pushes me, but neither of us is 'reacting'. Both forces 'come into existence' at the same time.

All forces in Newtonian Mechanics follow Newton's 3rd Law.

The boat is subject to the force of gravity by the Earth, and its force-pair is the force of gravity done by the boat towards the Earth (of course, the Earth is so massive that this force is insignificant).

The boat also exerts a force towards the body of water, compressing it a bit and pushing some water molecules away. The force-pair of these multiple forces are done by each part of the body of water towards the boat. There is a part of these forces that has a net magnitude upwards.

The boat then feels 2 net forces, one downward caused by the Earth, and one upward caused by the body of water. They are equal in magnitude and so the boat remains at the surface of the water without sinking.

On the other hand, the Earth feels a force upwards, but it is insignificant, plus there are plenty of other forces on it in other directions, so the Earth doesn't really move. The body water also feels 'a' force, which causes it to be displaced around the boat.

The water itself is also attracted to Earth by gravity, so there is another force-pair between water and the Earth. The displaced body of water rises above its previous level. This has an effect on the entire body of water around the boat, and is part of the reason the boat is buoyant.