Assessment Items on Sinking and Floating

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Electronic Supplemental Materials

Assessment Items on Sinking and Floating

Item Released-Block:A block is floating on water. Sam pushes it under water as shown below. When Sam releases the block, what will happen to the block? Describe the motion (or no motion) of the block till it stops. Explain its motion.

[For the second cohort, the last sentence is rephrased as ‘Explain its motion using both the concept of density and the concept of buoyancy’.]

Item Cartesian-Diver:A Cartesian diver is simply a device of a water container with an upside down tube in it, as shown in the diagram. Predict and explain how the tube moves when you press or release the bottle.

[For the second cohort, the following additional sentence is added ‘Explain the motion of the test tube using both the concept of density and the concept of buoyancy’.]

Item Two-Ball: Ball A and ball B have the same volume. A is floating on water, B is sitting at the bottom of the water tank.

(i) Which ball has the greater buoyancy? Explain.

(ii) Which ball has the greater density? Explain.

(iii) Sam adds some amount of salt in water and let them dissolve. What happens to the buoyancy of the two balls?

(iv) What changes would you expect after Sam has added salt in the water? Explain.

Item Fish (from Conceptual Physics v.10, p.256): If a fish makes itself denser, it will sink; if it makes itself less dense, it will rise. In terms of buoyant force, why is this so?

Item Submarine:

Watch the simulation that shows how a submarine works (see the above link). Explain how the submarine moves up and down in water, using both the concept of density and the concept of buoyancy.

SPM Diagrams for the Assessment Items

a) The SPM diagram for the Item Released-Block (the linking codes are explained in the table above).

b) The SPM diagram for the Item Cartesian-Diver.

c) The SPM diagrams for the Item Two-ball (the SPM score of this item is based on the combined responses to the four subqeustions). The SPM diagrams for item fish and item submarine are similar to this one.

Knowledge Base:Key Elements of Two Exploratory Models in Explaining Sinking and Floating

Density Model / Force Model
theoretical / D0a*: The density of an object refers to the intrinsic property of how much mass the material(s) is within the object. / F0a: The buoyancy of an object in water is defined as the net force exerted by its surrounding water.
F0b: The weight of an object on the surface of the earth is defined as the gravitational force exerted by the earth.
operational / D0b: The (average) density of an object is defined as its mass over volume.
[D0c: The density of an object is a constant within the object if its mass is uniformly distributed. The density of an object has fluctuations if its mass is not uniformly distributed.] / F0c: The buoyancy of an object in water can be calculated as the integral of the pressure over the surface of the object.
F0d: The buoyancy of an object in water is equal to the weight of water displaced in terms of magnitude.
F0e: The weight of an object on the surface of the earth is equal to the product of its mass and the acceleration of gravity.
floating on water / D1a: An object floating on water has a density less than water.
[D1b: The proportion of the volume of the part of the object that is submerged under water over its whole volume is equal to the proportion of the density of the object over the density of the fluid.] / F1a: An object floating on water, suspending in water, or moving at a constant velocity in water has balanced forces acting on it (the downward weight and upward buoyancy, ignoring friction and other forces).
[F1b: The proportion of the volume of the part of the object that is submerged under water over its whole volume is equal to the ratio of the weight of the object over the weight of the water of the same size (or the ratio of the density of the object over that of the water).]
sitting at the bottom / D1c: An object sitting at the bottom of a water container has a density greater than water. / F1c: An object sitting at the bottom of a water container has a greater weight than its buoyancy. Its weight is equal to the sum of its buoyancy and the normal force exerted by the bottom surface.
[F1d: For an object sitting at the bottom of a water container, the ratio of its buoyancy over its weight equals the ratio of the density of the water over that of the object.]
suspending in water / D1d: An object suspending in water has the same density as water. / F1a: An object floating on water, suspending in water, or moving at a constant velocity in water has balanced forces acting on it (the downward weight and upward buoyancy, ignoring friction and other forces).
floating up / D2a: When put under water, an object less dense than water moves up towards the surface of the water. / F2a: An object accelerates in the direction of its net force: when its buoyancy is greater than its weight, the object is accelerating up; when its weight is greater than its buoyancy, the object is accelerating down.
sinking down / D2b: When put under water, an object denser than water moves down to the bottom of the water. / F2a: An object accelerates in the direction of its net force: when its buoyancy is greater than its weight, the object is accelerating up; when its weight is greater than its buoyancy, the object is accelerating down.
passing equilibrium / -- / F2b: An object keeps moving at the same velocity if there is no net force acting on it.

Note. * The codes are used to indicate the specific link between an explanatory model and a statement of state or process: the first letter indicates the type of the explanatory models (Density model or Force model); the second digit indicates if it is related to a definition (0), a state (1), or a process (2); the third digit denotes a distinctive statement within each category.

SPM Scoring Rubric and Sample Student Responses

SPM Levels / Explanation
of the Levels / Sample Student Responses / Notes
0 / No response or only irrelevant response is presented. / “I don’t know.” / --
1 / Other than the information already presented in the question, the response only contains scientifically incorrect statements regarding the key states, processes, or explanatory models. / “Buoyancy will help push the fish down when the fish is denser and push the fish up when it is less dense.”
(in response to item Fish) / This response shows the misconception that the direction of buoyancy depends on the density of the object.
2 / The response includes correct statements regarding the key states, processes, or explanatory models but does not meaningfully link them. The response may also contain some scientifically incorrect statements . / “The buoyant force on both A and B decreases because they require less force to push them up in the water because now the water has greater density because the density of the salt water is greater than the density of pure water. The balls would rise a little more from their positions.” (in response to item Two-ball) / This response correctly states that the density of salt water is greater than that of water, but unable to distinguish the two different situations for the two balls and draws incorrect conclusion about their buoyancy.
3 / The response includes correct statements regarding the key states, processes, or explanatory models and partially connects them. The response may also contain a few minor scientifically incorrect statements. / “Immediately upon release, the ball will rise upward because it is less dense than water. Inertia will cause it to continue rising upward out of the water. From here, it will sink again due to gravity and inertia, then rise again. It will continue to bobble until the buoyancy equals its weight.” (in response to item Released-block) / The response explains the rise process using the density model, but does not show a fully integration of the force model (e.g., does not explain the unbalanced forces). The last statement is incorrect.
4 / The response uses one model to fully explain the phenomenon or uses more than one explanatory models to successfully explain most of the major states and processes. / “When you squeeze the bottle, the pressure increases. Thus, more water enters the tube and the weight increases and becomes greater than its buoyancy so the tube sinks....” (in response to item Cartesian-diver) / The response correctly applies the force model to explain the movement of the tube, but does not integrate the density model.
5 / The response integrates multiple explanatory models to explain all the key states and processes successfully. / “Density equals mass/volume. The submarine sinks because the density of the sub becomes greater than the density of water. When the air is compressed, the total volume decreases and the total mass stays the same, which causes the density of the sub to be greater than the density of water and it sinks. Buoyancy is pushing the sub up and gravity is pushing the sub down. The weight of the sub is equal to the buoyancy so it is floating at the equilibrium point initially. When the water enters the tank, it displaces less water and buoyancy decreases. When the buoyancy is less than the weight, submarine sinks....” (in response to item Submarine) / The response integrates the force model and the density model to explain the movement of the submarine.

Buoyancy Lab Sequence

The buoyancy lab is a guided inquiry activity students do during the unit of sinking and floating. The goal of the buoyancy lab is to confirm the Archimedes’ Principle: i.e., the buoyancy of an object equals to the weight of water displaced. The materials for the lab (for each group) include an overflow can kit, a set of blocks with regular shapes made of different materials, a ruler, a graduated cylinder, electronic balance, and a spring scale. The lab consists of the following major steps:

Step 1: Measure the apparent weight loss of an immersed object. The apparent weight loss is defined as the difference between the measured weights when an object is in air and when it is fully immersed in water. The guiding questions include:

-How do you measure the magnitude of buoyancy? (Hint: Use force diagrams to analyse the forces and their directions acting on the object when you measure their weights in air and in water and confirm that the magnitude of buoyancy is equal to the apparent weight loss).

-How do you know the direction of the buoyancy of an immersed object?

-Does the depth of water influence the buoyancy of an immersed object?

-Does the amount of water influence the buoyancy of an immersed object?

-Does the shape of the object influence the buoyancy of an immersed object?

Step 2: Measure the weight of water displaced of the immersed object in Step 1. The guiding questions include:

-How do you measure the weight of water displaced? [At least 2 different ways and compare your results. Hint: You may measure the mass of water displaced directly using the electronic balance, or measure its volume using the graduated cylinder, given that the density of water is a constant]

-Does the depth of water influence the weight and volume of water displaced for an immersed object?

-Does the amount of water influence the weight and volume of water displaced for an immersed object?

-Does the shape of the object influence the weight and volume of water displaced for an immersed object?

Step 3: Repeat steps 1 and 2 for two other objects.

Step 4: Data analysis and discussion.

-Does your measurement support Archimedes’ principle? Why?

-Do you have any questions?