Upthrust
Properties of Matter | Forces and Motion

Loaded ship

for 11-14 14-16 16-19 IOP RESOURCES

In this activity, students make a model of a cargo ship and investigate how deep it sits in the water for different loads to predict when it will sink.

Learning outcome

Students can use load and depth data to predict the maximum load a ship can carry.

Preparation

Make a depth meter for each group by following the instructions on the template which can be downloaded below. You will need a laminator.

Equipment

Each group of students will need:

  • A depth meter
  • A empty 1 litre cardboard drinks container (eg juice carton)
  • A large tray or bowl with a depth at least 6 cm
  • Access to tap water
  • Scissors and sticky tape
  • 5 x 50 g slotted masses (or 12 x 20 g masses)
  • Paper towels (for spillages)
  • A few drops of blue food colouring (optional)
  • A ruler and graph paper

Procedure

Ask students to:

  1. Fill the large container with water to a depth of at least 5 cm (adding the blue food dye if available).
  2. Draw a line around the bottom of the juice carton at a height of 5 cm from the base and cut along the line to make the ‘ship’.
  3. Stick the depth meter to the side of the ship ensuring that zero on the meter is aligned to the bottom of the ship.
  4. Place the empty ship in the container and record the depth in cm.
  5. Remove the ship and add a mass of 50 g.
  6. Lower the ship into the container and adjust the positions of the mass(es) so that the ship sits level in the water.
  7. Record the new depth in cm.
  8. Repeat the steps above to obtain data for cargo mass (g) and depth (cm) up to a depth of 4 cm.
  9. Plot a graph of cargo mass (g) against depth (cm).
  10. Use their graph to predict the maximum load that their ship can carry before sinking.

Teaching notes

To aid with even loading of their ship students can use Blu-tack or a small strip of sticky tape to keep the masses in position. To predict the maximum load, they should draw a best line fit through their data and extrapolate to the height of their ship (5 cm).

The equation that describes the straight-line is:

M = ρAD – m

Where m is the mass of the empty ship, M is the cargo mass, A is the cross-sectional area of the bottom of the ship, D is the depth of the ship under water and ρ is the density of water.

Extension (16-19)

Provide the above equation and rulers so students can determine A, and challenge them to work m and ρ from their graphs.

Upthrust
is a special case of Force
appears in the relation Upthrust = Weight of Displaced Liquid
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