# Newton's Third Law - Reaction and Upthrust

Newton's third law of motion states that for every force acting on an object, the object will exert an equal force on its cause but in the opposite direction'.

Another way of saying this is:

 'Whenever two bodies interact, the forces they exert on each other are equal and opposite'. OR 'To every action there is an equal and opposite reaction'

### Reaction force

When a book rests on a table the book exerts the force of its weight on the table and the table exerts an equal force (but in the opposite direction) on the book.

This force that opposes the weight is called the reaction force.

### Upthrust

If the object is 'reacting against' a solid object the reaction force is simply the upwards push of the object it is resting on - but if it is in a liquid there is a more complicated situation and upthrust comes into play.

The pressure an object experiences when immersed is greater on its base than on its top - this is because pressure increases with depth.

p = hρg

where

h = the height of the column of fluid above it (the depth )

ρ = the density of the fluid

g = gravitational field strength

This difference in pressure creates a resultant force upwards on the submerged object, and causes fluid to be displaced by the object. This force is called the upthrust.

So, when a body is wholly or partly immersed in a fluid, it experiences an upthrust or buoyant force that is equal to the weight of fluid it displaces.

Practically speaking upthrust is the difference between the object's weight in air and its 'weight' in the fluid (although it's weight (w = mg) does not actually change!).

If the upthrust is as big as the weight the object will float.

If not, it will sink, but the acceleration it will sink at will depend on the difference between the weight and the upthrust, not just its weight.... therefore the acceleration rate will be lower.