Table of Contents

- 1 How does the mass of the liquid displaced compare to the mass of the object?
- 2 What is the relationship between the mass of a boat floating in water and the mass of the liquid it displaces?
- 3 What is the relation between the buoyant force on any floating object and the weight of the object?
- 4 What makes an object float in the water?

## How does the mass of the liquid displaced compare to the mass of the object?

An object heavier than the amount of the fluid it displaces, though it sinks when released, has an apparent weight loss equal to the weight of the fluid displaced. In fact, in some accurate weighing, a correction must be made in order to compensate for the buoyancy effect of the surrounding air.

**How does the mass of the wood compare with the mass of the water displaced?**

You found that the mass of the wood is equal to the mass of the water that gets displaced. If you look at a free-body diagram of a floating boat it will be clear that the weight force will have to be cancelled out by an upward force by the water. This is because of Newton’s Second Law.

**When an object floats on water it displaces a mass of water equal to the mass of the object?**

This is the weight of the object – its mass time the acceleration due to gravity (9.8 ms-2 on Earth). The buoyant force (Fb) of the water pushing up on the object. This is equal to the force of gravity acting on a mass of water equal to the amount of water the object displaces when fully immersed.

### What is the relationship between the mass of a boat floating in water and the mass of the liquid it displaces?

Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid it displaces.

**When the buoyant force on an object is greater than its weight the object?**

If the buoyant force is greater than the object’s weight, the object will rise to the surface and float. If the buoyant force is less than the object’s weight, the object will sink. If the buoyant force equals the object’s weight, the object will remain suspended at that depth.

**How does the weight of the water compare to the buoyant force?**

The buoyant force on a submerged object is equal to the weight of the fluid displaced. Since it exactly supports the volume of water, it follows that the buoyant force on any submerged object is equal to the weight of the water displaced. This is the essence of Archimedes principle.

#### What is the relation between the buoyant force on any floating object and the weight of the object?

**Does floating object affect the weight of the water?**

Yes, it will weigh more; you only need to consider the bucket-water-floater/sinker system as a whole to answer this. Whether or not the object floats simply decides which forces keep the floater/sinker in the system. The floater/sinker thrusts downwards on the water, which thrusts upwards through the buoyant force.

**Is the mass of water displaced equal to the weight of the object?**

If an object is partially submerged in water then is the weight of the object equal to the weight of water displaced by it? Yes, the mass of displaced water will be equal to the mass of the object; but, only if the object floats in water. For example, if I stood in 1.0 m deep water, obviously, the mass of water I displace will not equal my mass!

## What makes an object float in the water?

When objects float on water the force keeping the object afloat is called upthrust and this balances the weight of the object. When something is placed in the water, the water that moves out of the way. We say the object is displaced. For floating objects the weight of displaced water is equal to the weight of the object.

**How is apparent weight loss equal to fluid displacement?**

The object suffers an apparent weight loss equal to the weight of the fluid displaced. Alternatively, on balances that measure mass, the object suffers an apparent mass loss equal to the mass of fluid displaced. That is, apparent weight loss equals weight of fluid displaced, or apparent mass loss equals mass of fluid displaced.

**Why is the buoyancy of an object greater than its density?**

The reason is that the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object denser than the fluid will sink.