Fluids, Density and Upthrust

Fluids

Define a fluid.

A substance that can flow. Fluids include liquids and gases.

Define density.

The mass per unit volume of a substance.

What is the equation for density?

ρ = m/V.

What does ρ represent in the density equation?

Density.

What does m represent in the density equation?

Mass.

What does V represent in the density equation?

Volume.

What is the SI unit of density?

kg m⁻³.

How can mass be calculated from density and volume?

m = ρV.

How can volume be calculated from mass and density?

V = m/ρ.

What determines the density of a substance?

The mass of its particles and how closely the particles are packed together.

Does the density equation apply only to fluids?

No. It applies to solids, liquids, gases and mixtures.

How does increasing temperature usually affect the density of a substance?

Heating usually causes a substance to expand, increasing its volume and therefore decreasing its density.

Why must temperature sometimes be stated when giving a density?

Because density can change with temperature as the volume of the substance changes.

What is the approximate density of pure water?

1000 kg m⁻³.

What is upthrust?

An upward force exerted on an object when it is partially or completely submerged in a fluid.

What causes upthrust?

The object displaces fluid, producing an upward resultant force on the object.

State Archimedes' principle.

The upthrust on an object is equal to the weight of the fluid displaced by the object.

What is another name for the fluid displaced by a submerged object?

The volume of fluid displaced is equal to the submerged volume of the object.

How can the mass of fluid displaced be calculated?

m = ρV, where ρ is the fluid density and V is the volume displaced.

How can the weight of displaced fluid be calculated?

W = mg = ρVg.

What equation can therefore be used to calculate upthrust?

U = ρVg.

What does ρ represent in the upthrust equation U = ρVg?

The density of the fluid.

What does V represent in the upthrust equation U = ρVg?

The volume of fluid displaced.

What does g represent in the upthrust equation U = ρVg?

Gravitational field strength.

What is the SI unit of upthrust?

N.

What happens if an object's weight is greater than the upthrust?

There is a resultant downward force and the object sinks.

What happens if upthrust is greater than an object's weight?

There is a resultant upward force and the object accelerates upwards.

What happens when upthrust equals an object's weight?

The resultant force is zero, so the object is in equilibrium.

Why does a brick sink in water?

Its weight is greater than the maximum upthrust produced by the water it displaces.

What happens to upthrust as an object is gradually lowered into a fluid?

Upthrust increases as a greater volume of fluid is displaced.

Why is there initially no upthrust just before an object enters a fluid?

It has not yet displaced any fluid.

What happens when a floating object sinks slightly deeper into a fluid?

It displaces more fluid, increasing the upthrust.

What condition must be satisfied for an object to float at rest?

Upthrust = weight.

What is the resultant force on an object floating at rest?

Zero.

Why does a floating object only sink partly into a fluid?

It sinks until it displaces enough fluid for the upthrust to equal its weight.

What determines how much of a floating object is submerged?

Its weight and the density of the fluid.

How does a denser fluid affect the submerged depth of a floating object?

The object needs to displace less volume, so it floats higher.

How does a less dense fluid affect the submerged depth of a floating object?

The object must displace more volume, so it sinks further into the fluid.

What relationship can be used for a floating object?

m_object g = ρ_fluid V_displaced g.

What simplified relationship applies to a floating object?

m_object = ρ_fluid V_displaced.

Why can large ships made mainly of dense materials float?

Their hollow shape gives them a large volume, so they can displace enough water for the upthrust to equal their weight.

What is a hydrometer?

An instrument used to determine the density of a fluid.

What principle does a hydrometer use?

It floats at different depths depending on the density of the fluid.

How does a hydrometer behave in a denser liquid?

It floats higher because a smaller volume needs to be displaced to produce an upthrust equal to its weight.

How does a hydrometer behave in a less dense liquid?

It sinks deeper because it must displace a larger volume to produce sufficient upthrust.

Why can a hydrometer be used to measure density?

Its submerged depth changes depending on the density of the liquid.

What force acts downward on a submerged object?

Its weight.

What force acts upward on a submerged object?

Upthrust.

How do you calculate the resultant force on a sinking object when weight is greater than upthrust?

Resultant force = weight − upthrust.

How do you calculate the resultant force when upthrust is greater than weight?

Resultant force = upthrust − weight.

What is the weight equation used in upthrust calculations?

W = mg.

What volume of fluid is displaced by a completely submerged object?

A volume equal to the total volume of the object.

What volume of fluid is displaced by a partially submerged object?

A volume equal to only the submerged part of the object.

Why is density important when determining whether an object floats?

The density determines how much mass is contained in a given volume and therefore whether sufficient upthrust can balance the object's weight.

What generally happens if an object's average density is greater than the fluid's density?

It sinks.

What generally happens if an object's average density is less than the fluid's density?

It floats.