Maths and Science

Lesson 2

LO1: Understand and calculate density

Density Calculations• Find the density of each of these blocks.• Give your in answers in g per cubic cm

Mass

12.5kg

Volume

647 cubic cm

Side length of cube = 6cm

Mass = 143g

Side length of cube = 70mm

Mass = 343g

Gold Pine Water

Mass

12.5kg

Volume

647 cubic cm

Side length of cube = 6cm

Mass = 143g

Side length of cube = 70mm

Mass = 343g

Gold Pine Water

Archimedes

Which has the greatest mass?

• A cubic cm of iron or a cubic cm of water?

• Why?

So why do boats float?

Can you make a lump of plasticine float?

Task: Build a plasticine boat that can carry a large cargo

LO2: To understand why boats float.

Why do boats float?

Buoyancy Puzzlers

Here we have a toy submarine floating in a bathtub. It's a really fancy sub, made out of steel. The sub has a mass of 1kg. When completely submerged, it displaces 2kg of water.

What could you do to cause the sub to sink to the bottom of the tub? Add 1kg of sand to the sub's interior.

Add 1kg of sand to the sub's interior, plus a little more.

Nothing. Since the boat displaces more water than it weighs, it's already on its way down.

Buoyancy Puzzlers

Here we have a boat in a swimming pool. In the boat is an inquisitive experimenter. Also in the boat is a rock.

Our experimenter picks up the rock and tosses it into the pool. The rock sinks to the bottom. No water leaves the pool from the splash made by the rock.

Now for the question: Does the pool's water level rise, lower, or stay the same?

The water level rises.

The water level lowers.

The water level stays the same.

Add 1kg of sand

You've added 1kg of sand. The sub, which displaces two pounds of water when submerged, now weighs 2kg.

Since the weight of the water displaced by the sub equals the sub's weight, the sub is, in a sense, weightless in the water. It drifts between the surface and the bottom.

Add 1kg of sand, plus a bit more

That's right.

For the sub to sink, it needs to weigh MORE than the maximum weight it can displace.

By adding one pound of sand plus a little more, the sub's overall weight is just over two pounds.

Add nothing

The sub will not sink if left alone.

The sub is displacing half of the 2kg it would displace when completely submerged. That's why half of it is submerged and the other half is out of the water.

The water level rises?

You guessed that the pool's water level rises.

That's a good guess, but it's not the right answer.

The water level stays the same?

You guessed that the pool's water level stays the same.

That's not right, but don't be discouraged. This is the answer that most people choose.(J. Oppenheimer is supposed to have got this problem wrong).

The water level falls?

You think that the pool's water level will lower? That's absolutely right!

At any rate, the rock displaces more water when it's in the boat than when it's in the water, and so the pool's water level is lower when the rock is in the water.