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Floating and sinking — KCSE Physics

KCSE Physics · 107 practice questions · 6 syllabus objectives · 6 revision lessons

25 easy42 medium40 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

State and verify Archimedes' principle experimentally

State the law of flotation and define relative density

Describe applications of Archimedes' principle and solve numerical problems

Determine relative density of solids and liquids using Archimedes' principle and density bottles

Describe the structure, calibration and uses of a hydrometer

Explain floating and sinking in terms of density and upthrust; solve numerical problems

Revision Notes

Concise lesson notes for Floating and sinking, written to the KCSE Physics marking standard. Read the first lesson free below.

Understanding Archimedes' Principle

Archimedes' principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by that body. This principle can be verified through a simple experiment.

Experimental Verification:

  1. Materials Needed: A graduated cylinder, water, a small solid object (like a stone), and a weighing scale.
  2. Procedure:
    • Measure the weight of the solid object using the scale.
    • Fill the graduated cylinder with a known volume of water and record this volume.
    • Submerge the object in the water and note the new water level.
    • Calculate the volume of water displaced by subtracting the initial water level from the new water level.
    • Weigh the displaced water using the formula: Weight = Volume × Density (density of water = 1 g/cm³).
  3. Conclusion: The weight of the displaced water should equal the buoyant force acting on the submerged object, confirming Archimedes' principle.

This experiment demonstrates that the buoyant force is directly related to the volume of fluid displaced.

Key points to remember

  • Archimedes' principle relates buoyant force to displaced fluid weight.
  • Buoyant force equals weight of the fluid displaced.
  • Verify using a graduated cylinder and solid object.
  • Weight of displaced water confirms the principle.

Worked example

Q: State Archimedes' principle.
A: Archimedes' principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

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More lessons in this topic

Lesson 2: Understanding Flotation and Relative Density

Objective: State the law of flotation and define relative density

Law of Flotation: A body will float if the weight of the fluid displaced by it is equal to the weight of the body. This means that the upward buoyant force acting on the body is equal to its weight. Key points to remember:

  • A floating object displaces its own weight in fluid.
  • The shape and density of the object affect its ability to float.

Relative Density: Relative density (or specific gravity) is defined as the ratio of the density of a substance to the density of a reference substance, usually water. It is a dimensionless quantity. If the relative density is less than 1, the object will float; if greater than 1, it will sink.

Example of Relative Density Calculation:

  • If an object has a density of 800 kg/m³, its relative density is:
    • Relative Density = Density of Object / Density of Water = 800 kg/m³ / 1000 kg/m³ = 0.8
    • Since 0.8 < 1, the object will float.
  • A body floats if weight of fluid displaced equals its weight.
  • Buoyant force on a floating object equals its weight.
  • Relative density is the ratio of densities to water.
  • Relative density < 1 indicates floating, > 1 indicates sinking.
  • Density affects the ability of an object to float.

State the law of flotation and define relative density.

  • Law of flotation: A body floats if the weight of fluid displaced equals its weight.
  • Relative density: The ratio of the density of a substance to the density of water.
Lesson 3: Applications of Archimedes' Principle

Objective: Describe applications of Archimedes' principle and solve numerical problems

Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. This principle has several applications:

  • Ship Design: Ships are designed to displace enough water to float, ensuring they are buoyant.
  • Hydrometers: These devices measure fluid density based on buoyancy; they float at different levels in liquids of varying densities.
  • Submarines: Submarines control their buoyancy by adjusting the amount of water in their ballast tanks.

To solve numerical problems using Archimedes' principle, use the formula:

Buoyant Force (F_b) = Weight of Displaced Fluid = Volume of Fluid Displaced × Density of Fluid × g

Where:

  • g is the acceleration due to gravity (approximately 9.81 m/s²).

Example Problem: A solid cube of side 0.1 m is submerged in water. Calculate the buoyant force acting on it.

Solution:

  • Volume of the cube = (0.1 m)³ = 0.001 m³.
  • Density of water = 1000 kg/m³.
  • Buoyant Force = 0.001 m³ × 1000 kg/m³ × 9.81 m/s² = 9.81 N.

Thus, the buoyant force acting on the cube is 9.81 N.

  • Archimedes' principle explains buoyancy in fluids.
  • Applications include ship design and hydrometers.
  • Buoyant force equals weight of displaced fluid.
  • Use the formula for numerical problems.
  • Understand the role of fluid density in calculations.

A block of wood with a volume of 0.05 m³ is submerged in water. Calculate the buoyant force acting on it.

  • Buoyant Force = Volume × Density of Water × g = 0.05 m³ × 1000 kg/m³ × 9.81 m/s² = 490.5 N.
Lesson 4: Understanding Relative Density and Archimedes' Principle

Objective: Determine relative density of solids and liquids using Archimedes' principle and density bottles

Relative density (or specific gravity) is the ratio of the density of a substance to the density of water. It can be determined using Archimedes' principle, which states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced. To determine relative density using a density bottle:

  1. Fill the density bottle with water and weigh it. Record this weight.
  2. Add the solid or liquid whose relative density you want to measure, and weigh the bottle again.
  3. Calculate the volume of the displaced water by subtracting the initial weight from the new weight.
  4. Use the formula:
    • Relative Density = (Weight of substance) / (Weight of displaced water)

This method allows you to find the relative density of both solids and liquids accurately.

For solids, ensure they are fully submerged. For liquids, compare their weights directly with water to find the density ratio.

  • Relative density is the ratio of a substance's density to water's density.
  • Archimedes' principle relates to buoyant force and displaced fluid weight.
  • Use a density bottle to measure weights and calculate relative density.
  • Ensure complete submersion of solids for accurate measurement.
  • The formula for relative density is Weight of substance divided by Weight of displaced water.

A density bottle weighs 50g when filled with water and 80g when a solid is added.

  • Weight of displaced water = 80g - 50g = 30g.
  • If the solid weighs 20g, Relative Density = 20g / 30g = 0.67.

Sample Questions

Read 3 questions and answers free. Sign up to access all 107 questions with full KNEC-style marking schemes and a personalised study plan.

1
easySHORT ANSWER4 marks

State the law of flotation and explain its significance for large vessels. (4 marks)

Answer & marking scheme

Part (a) — 2 marks
A floating body displaces its own weight of the fluid in which it floats (2 mks)
Part (b) — 2 marks
It allows large vessels to carry heavy loads while floating (1 mk)
Ensures stability and safety of navigation (1 mk)
2
easySHORT ANSWER3 marks

Define relative density in the context of objects floating in seawater. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Relative density is the ratio of the density of an object to the density of seawater (1 mk)
It indicates whether the object will float or sink in seawater (1 mk)
If relative density is less than 1, the object will float (1 mk)
3
easySHORT ANSWER2 marks

Name the principle that explains why ships float on water. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Archimedes' principle (2 mks)
4

State two reasons why a solid with a relative density less than 1 will float in water. (2 marks) (b) Describe how you would use Archimedes' principle to determine the relative density of a liquid. (2 marks)

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Frequently asked questions

What does the KCSE Physics topic "Floating and sinking" cover?

Archimedes' principle, law of flotation, relative density, applications

How many practice questions are available for Floating and sinking?

HighMarks has 107 Floating and sinking practice questions for KCSE Physics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Physics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Floating and sinking for the KCSE exam?

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