Forces Acting on Substances and Mechanisms

Upthrust, also known as buoyancy, is a fundamental principle that explains why objects float or sink in a fluid, such as water. It is the upward force exerted on an object submerged in a fluid, counteracting the weight of the object. This phenomenon is described by Archimedes’ principle, which states that the upthrust on an object is equal to the weight of the fluid it displaces. When an object is placed in a fluid, it displaces a volume of fluid equal to its own submerged volume.

If the upthrust is greater than or equal to the object’s weight, the object will float; if it is less, the object will sink. The concepts of upthrust and flotation are essential in understanding various applications, ranging from designing ships and submarines to understanding natural occurrences such as why certain animals can swim. Overall, these principles play a crucial role in both engineering and natural environments.

KEY IDEAS

• Archimedes’ Principle: States that the upthrust on a submerged object equals the weight of the fluid displaced.

• The upward force exerted by a fluid on an immersed object, determining whether it floats or sinks, is called Buoyant Force:

• An object floats if its density is less than the fluid’s density; it sinks if its density is greater.

• An object displaces a volume of fluid equal to its submerged volume, affecting the upthrust it experiences.

• Buoyancy principles are vital in shipbuilding, underwater exploration, and aviation design.

• Factors such as shape, material, and load distribution affect how well an object floats and its stability in the water.

Activity 5.1 Demonstrating Upthrust (buoyancy)

What you need: A clear container (like a large glass or plastic bottle), water and a small object (like a rubber ball, stone, or piece of fruit) What to do:

1. Fill the container with water until it is about three-quarters full.

2. Take the small object you have. Hold it above the water and think about how heavy it feels and what it looks like.

3. Now, gently place the object into the water. Watch closely to see what happens. Does it sink or float?

Let us talk about what you observed. The object experiences a force called upthrust from the water, which pushes it upward. If the object floats, this means the upthrust is equal to or greater than its weight. If it sinks, the weight is greater than the upthrust.

4. Try using different objects you can find around you. Note down those that float and those that sink. Think about why that might be—what do you notice about their materials or shapes?

Great job! Now you understand how upthrust works and why some objects float while others sink. Keep experimenting and observing the world around you!

Activity 5.2 Understanding Upthrust

Observe Figure 5.1 and discuss the questions with peers.

Figure 5.1: Image showing Upward Force Questions: Write your answers in your notebook.

1. What is upthrust? State one example of upthrust in action.

2. How can you observe upthrust in everyday life?

3. How does fluid density affect buoyant force?

4. What happens when an object is fully or partially submerged?

Upthrust Force

Upthrust, or buoyant force, is the upward force that a fluid (a liquid or gas) exerts on an object that is placed in it. This force works against the object’s weight and helps it float in some situations. You can see upthrust when a rubber duck floats in water, as it rises up against the downward pull of gravity.

• Higher fluid density increases the buoyant force, making it easier for objects to float. A fully submerged object experiences maximum upthrust, while a partially submerged object experiences less, affecting its ability to float.

• A boat floats because it displaces a weight of water equal to its own weight, demonstrating upthrust.

• When an object is submerged in a fluid, there is a pressure difference between the top and bottom of the object, which creates this upward force.

This phenomenon is described by Archimedes’ principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid the object displaces.

• The amount of upthrust depends on both the density of the fluid and the volume of the object that is under the fluid.

Figure 5.2: Upthrust vs. object weight in fluid When an object is placed in a fluid, it experiences both its weight pulling it down and the upthrust pushing it upward. If the upthrust is greater than the object’s weight, the object will float. If the weight is greater, the object will sink. Thus, the relationship between upthrust and an object’s weight determines whether the object will sink or float in the fluid.

Buoyancy is a force that moves an object upward — see Figure 4.2. This upward force occurs when the object is immersed (either fully or partially) in a fluid that has a measurable density. Buoyant force is measured in Newtons (N) by International System of Units (SI).

Basic understanding of buoyancy, density, fluids, and the Archimedes Principle is necessary for understanding how things float.

Question: Write your answer in your notebook.

1. Why do things float or sink?

An object will float when it is less dense than the fluid in which it is immersed.

This buoyant force is referred to as positive buoyancy. When an object is denser than the fluid it displaces, the object will sink because its weight is greater than the buoyant force. This buoyant force is referred to as negative buoyancy. An object is neutrally buoyant when its density is equal to the density of the fluid in which it is immersed, resulting in the buoyant force balancing the force of gravity that would otherwise cause the object to sink or rise. An object that has neutral buoyancy will neither sink nor rise. — See

Figure 4.3. Flotation is the state of an object being suspended in a fluid, neither sinking nor completely submerged.

Figure 5.3: Positive, Negative and Neutral Buoyancy

Activity 5.3 Building Examples (Prototypes) of Ships, Canoes and Boat What you need:

• Aluminium foil (large sheets)

• Modelling clay (optional)

• Shallow pan or tub filled with water

• Tape (optional)

• Scissors (optional, for cutting foil)

• Pencils or markers (optional, for decoration) What to do:

1. Take a sheet of aluminium foil and fold it lengthwise several times to form a long, strong strip.

2. Gently curve the strip upward in the centre to create the shape of a canoe, pinching the ends to make pointed tips if desired.

3. Pinch small pieces of modelling clay and place them inside the bottom of the canoe for added weight and stability, securing them with tape if needed.

4. Take another sheet of aluminium foil, fold it in half to form a square, then fold the square diagonally to create a triangle.

5. Slightly open the triangle and fold the bottom corners toward the top point to shape the hull, ensuring it has a pointed front and flat bottom.

Use tape to reinforce the folds.

6. Use markers or pens to decorate your canoe and ship with details like windows

7. Carefully place your examples (prototypes) of canoe and ship in a pan filled with water.

8. Observe whether they float and how much water they displace. Adjust the modelling clay in the canoe to see how it affects stability and try changing the ship’s body shape to see how it influences water displacement.

Figure 5.4: Example of Aluminium Foil Boat

Questions: Record your answers in your notebook.

1. How does the shape of your canoe help it float?

2. What effect does adding modelling clay have on the canoe’s stability?

3. How does modifying the body shape of your ship change its performance in the water?

4. Which design floated better, the canoe or the ship, and why do you think that is?

5. What is water displacement, and how can you observe it with your designs?

6. How do the materials used (aluminium foil, clay) influence the buoyancy of your floating models?

Concept of Buoyancy

Read these key points to help support your understanding of the concepts of buoyancy, upthrust, and design as they relate to your prototypes of ships, canoes and boats. The shape of the designs affects how water is displaced. A wider base offers more stability and buoyancy, allowing the object to float better. The canoe’s curved shape helps it slice through the water, while the ship’s hull design can affect how evenly it sits on the surface. Adding weight, such as modelling clay, can increase stability up to a point by lowering the centre of gravity. However, too much weight may cause the canoe to sink. The right amount of weight helps the canoe remain upright and balanced in the water. The performance may vary based on design and weight. Typically, if designed well, both can float effectively.

However, if one has a better shape for water displacement or more stability due to weight distribution, it will perform better. You should note how much water each design displaced when placed in the water. An object that floats in water will displace a volume of water equal to its weight. If an object sinks, less water is displaced than the object’s weight, demonstrating the principle of buoyancy. The materials (aluminium foil and modelling clay) are lightweight and can be moulded easily. Aluminium foil, being light and flexible, allowed for easy shaping into hollow forms, supporting buoyancy. Modelling clay provided additional weight and stability but needed to be balanced carefully to prevent sinking.

Activity 5.4 Exploring Buoyancy, Upthrust, Density, Mass, and Volume What you need: Blocks made of wood, metal, or plastic (hollow or solid), container filled with water, ruler and weighing scales.

What to do:

1. Use the weighing scales to find the mass of each block and write it down in a table in kilograms (kg).

2. Carefully place one block in the water and observe whether it floats or sinks. If it floats, proceed to the next steps.

3. Use the ruler to measure how deep the floating block is submerged under the water. Calculate the volume of the water that is displaced using the formula:

Volume = Depth (m) × Width (m) × Length (m)

4. Multiply the volume of displaced water by the density of water (which is 1000 kg/m³) to find out how much mass of water has been displaced.

5. To see if the block is buoyant, compare its weight with the weight of the displaced water.

6. Use this formula to calculate weight:

Weight (N) = Mass (kg) x Acceleration due to gravity (ms⁻²)

Note

(On Earth, g = 9.81 N/kg or ms⁻²) Safety Precautions

1. Use weighing scales and tools gently to avoid breakage or injury.

2. Prevent spills and clean up any water immediately to avoid slipping.

3. Dispose of materials properly according to school rules.

Density Density is defined as mass per unit volume.

Mathematically, ρ = m/V, where ρ = density, m = mass and V = volume.

An object will float in a fluid if it is less dense than that fluid. On the other hand, it will sink if it has a higher density. When you put an object in water, it pushes some of the water out of the way (this is called displacing water). If the object is less dense than the water, the weight of the water it displaces is heavier than the object itself. This creates a buoyant force, which pushes the object up, making it float. However, if the object is denser than the water, its weight is heavier than the buoyant force, causing it to sink.

Volume Volume is the amount of space an object takes up. If an object has a larger volume, it displaces more fluid, which increases the buoyant force. So, even if an object is made from a heavy material, if it has a large volume, it can push enough fluid out of the way to create a buoyant force strong enough to support its weight. The shape and design of an object can help it increase its volume without making it too heavy, which lowers its overall density. For example, steel is normally denser than water, so a solid steel block would sink. However, a steel ship has a big hull that holds a lot of air, which increases its volume without adding much weight.

This makes the ship’s overall density less than that of water, allowing it to float.

An object will float in a fluid if its density is less than the density of the fluid.

Conversely, it will sink if its density exceeds that of the fluid. When an object is placed in a fluid, it displaces a fluid volume. If the object is less dense than the fluid, the weight of the displaced fluid is greater than the object’s weight, resulting in a net upward buoyant force that causes the object to float. If the object is denser, the weight of the object is greater than the buoyant force, and it sinks.

Questions: Write down your answers in your notebook.

1. What two forces are acting on the boat when it is floating in water, and how do they interact?

2. How does the weight of the displaced water contribute to the buoyant force that keeps the boat afloat?

3. What does the law of flotation state about the relationship between the weight of the boat and the upthrust?

The two forces acting on the boat are the weight of the boat, which acts downward due to gravity, and the upthrust (buoyant force), which is the weight of the displaced water acting upward. These forces interact such that when the upthrust equals the weight of the boat, the boat remains floating in equilibrium. The weight of the displaced water creates upthrust, or buoyant force. When the boat is placed in water, it pushes some water out of the way (displaces it). The weight of the water that is displaced acts upward against the boat, and if this upward force (upthrust) is equal to the weight of the boat, the boat will float. The law of flotation states that a floating object will remain buoyant and stable on a fluid’s surface as long as the upthrust (the weight of the displaced fluid) equals the weight of the object.

When these two forces are in balance, the object floats.

Figure 5.5: A floating object Worked Examples Calculating weight and upthrust

1. Calculate weight:

Formula: Weight (N) = Mass (kg) × Gravitational Field Strength (N/kg) Given mass = 2 kg, and g = 9.81 N/kg Weight = 2 kg × 9.81 N/kg = 19.62 N

2. Determining Volume of Water Displaced:

If the block is fully submerged (then volume of displaced water = volume of object) and measures 0.5 m (length) × 0.2 m (width) × 0.1 m (height):

Volume = Length × Width × Height = 0.5 m x 0.2 m × 0.1 m = 0.01 m³

3. Calculating mass of displaced Water:

Density of water = 1000 kg/m³ Mass of displaced water = Volume × Density = 0.01 m³ × 1000 kg/m³ = 10 kg

4. Finding upthrust:

Weight of displaced water = mass of displaced water × acceleration due to gravity (g) Weight = 10 kg × 9.81 N/kg = 98.1 N Since the weight of the block (19.62 N) is less than the upthrust (98.1 N), it will float.

Comparing Densities

You have two blocks: one made of metal (mass = 3 kg) and another made of plastic (mass = 1 kg).

Steps to Compare Densities:

Calculate the volume of each block:

Metal block: Measures 0.3 m × 0.2 m × 0.1 m Volume = 0.3 m × 0.2 m × 0.1 m = 0.006 m³ Plastic block: Measures 0.2 m × 0.2 m × 0.05 m Volume = 0.2 m × 0.2 m × 0.05 m = 0.002 m³ Calculate Density of each block:

Metal: Density = Mass______ Volume = 3/0.006 = 500 kg/m³ Plastic: Density = Mass______ Volume = 1____ .002 = 500 kg/m³ Questions: Write down your answers in your notebook.

Let us briefly revise some of the concepts we have learnt so far. Below are some multiple-choice questions focusing on the relationship between upthrust and the law of flotation. These questions can help check your comprehension of upthrust and the law of flotation. Circle the correct answer as you read.

1. What is density?

A. The amount of mass in a given volume B. The force that keeps objects afloat C. The total volume of an object D. The weight of an object

2. Which formula is used to calculate the weight of an object?

A. Weight = Mass______ Volume B. Weight = Mass × Density C. Weight = Mass × Gravitational Field Strength D. Weight = Volume × Density

3. An object will float in a fluid if its density is:

A. Greater than the fluid’s density.

B. Equal to the fluid’s density.

C. Less than the fluid’s density.

D. Always heavier than the fluid.

4. What happens to a boat that is gradually filled with cargo, as shown in Fig 5 below, in terms of its position in the water before and after being loaded?

A. Finally, if too much cargo is added, the boat may sink completely.

B. The boat will capsize if its weight exceeds the buoyant force.

C. The boat will displace more water as it fills with cargo.

D. The boat will sink lower in the water as it gains weight.

5. Which of the following statements about buoyancy is true?

A. Buoyancy depends on the volume of fluid displaced.

B. Buoyancy is always greater than weight.

C. Buoyancy is the same as mass.

D. Buoyancy only applies to solid objects.

6. If you have a block of wood and a block of metal, both with the same volume, which statement is true?

A. Both blocks have the same density.

B. The metal block is denser than the wood block.

C. The wood block has a higher density than the metal block.

D. The wood block is heavier than the metal block.

7. What does the law of flotation state?

A. All fluids have the same density.

B. All objects will sink.

C. An object will float if it is heavy.

D. An object will float when the weight of the water displaced equals its weight.

Read the scenario below and use it to answer question 8 and 9 Emmanuel has a small toy boat made of plastic that she wants to test in her pool.

The boat has a mass of 0.3 kg and dimensions of 30 cm long, 10 cm wide, and 5 cm tall. Emma places the boat in the water and observes how it floats. As the boat is placed in the pool, it displaces a certain volume of water, and Emma wonders how upthrust affects whether the boat will sink or float.

8. What is the main reason the toy boat floats in the pool?

A. The boat is heavier than the water it displaces.

B. The boat is made of plastic, which cannot sink.

C. The pool is shallow, preventing the boat from sinking.

D. The upthrust (buoyant force) acting on the boat is equal to its weight.

9. If Emma adds a weight of 0.2 kg to the boat, what will likely happen to the boat when it is placed back in the water?

A. The boat will float higher in the water.

B. The boat will remain at the same level in the water.

C. The buoyant force will increase, making the boat float better.

D. The upthrust will decrease, causing the boat to sink.

Activity 5.5 Application of The Law of Flotation in Real Life Observe Figure 5.6 below and write your answers in your notebook as you read the questions following it:

Figure 5.6: Canoe

Write your answer in your notebook and share with your peers.

1. How do canoes utilize flotation to remain on the surface? What adjustments can help maintain buoyancy

2. What impact does the canoe’s design have on its flotation and efficiency?

3. How does the canoe’s density compare to water when floating? What conditions must be satisfied for it to float?

4. Which design features enhance a canoe’s stability in the water?

5. How does weight distribution within a canoe influence its flotation?

What measures can ensure stability?

6. How do the materials used in constructing a canoe affect its buoyancy?

Canoes: stay afloat by using the principle of flotation, which requires them to maintain buoyancy. To achieve this, it’s important to load items properly and distribute the weight evenly inside the canoe. The shape and design of a canoe are essential for its buoyancy and efficiency. A wide, stable hull helps distribute the weight and keeps the canoe from sinking, while a streamlined shape allows it to move more easily through the water. For a canoe to float, its density must be lower than that of the water. It will remain on the surface for as long as the total weight of the canoe and its contents is equal to the weight of the water it displaces. Key design features that enhance stability include a wide, flat bottom and a shape that evenly distributes weight to prevent tipping. When a canoe is loaded with gear and passengers, it displaces more water because its overall weight increases. For the canoe to stay afloat, the weight of the displaced water must match the combined weight of the canoe and its cargo. The materials used to build a canoe, such as wood, fiberglass, or aluminium, also affect its buoyancy.

Lighter materials improve flotation, while heavier materials need careful design to maintain buoyancy.

Many other devices also rely on the law of flotation in real life. Table 5.1 lists some examples and Figures 5.7 to 5.9 provide diagrams.

Table 5.1: Some Water and Air Vessels That Depend on The Law of Floatation Device Link to flotation How it floats Ships and boat The design and building of ships and boats rest on the law of flotation to keep them buoyant and even in water.

Ships float due to Archimedes’ principle. When a ship enters the water, it pushes down and displaces water, creating an upward force called upthrust. Despite being made of heavy steel, ships have wide bottoms and air-filled compartments that help them displace their own weight of water to stay afloat.

Submarines Ballast tanks regulate buoyancy by changing their water volume.

Submarines utilise Archimedes’ principle to control their depth in water. They have ballast tanks on each side that can fill or empty to change how much water they displace. To sink, a submarine fills its ballast tanks with water, increasing its density, while to rise, it expels water from these tanks to become less dense and float.

Device Link to flotation How it floats Hot air balloons Hot-air balloons and airships are commonly used in air conveyance, working based on the principles of buoyancy.

A hot air balloon has three key parts: the burner, the balloon, and the basket, with the burner heating propane gas to warm the air inside the balloon. As the air expands and becomes less dense than the surrounding air, the balloon rises, while the pilot can lower it by opening a parachute valve to let cooler air in or by reducing the fuel burned to cool the air inside.

Figure 5.7: Ghana Navy- ship

Figure 5.8: Submarine Sinking and Rising

Figure 5.9: Hot Air Balloon Floating in Air

1. The volume of a small ball is calculated to be 25cm³and it weighs 30g in water. Will this ball sink or float in water. Show calculation.

2. Three identical sized blocks of lead, aluminium and zinc are submerged in water. Given that at room temperature:

Density of aluminium = 2.7g/cm³Density of lead = 11.29g/cm³Density of Zinc = 7.13g/cm³How would you compare the buoyant force on lead block, buoyant force on aluminium and buoyant force on zinc block?

3. Write down three examples of devices that use the law of flotation in real life

4. What is the function of ballast tanks in a submarine? How does changing water levels affect buoyancy?

5. How do the materials used in boat construction affect buoyancy?

6. A block of aluminium is placed into water and sinks. A second block of aluminium with the same mass is moulded into a boat, placed into water and floats. Explain why the block sinks while the boat floats.

7. A cube of steel and a hollow steel box have the same mass and are both immersed in water. Sort the statements into an explanation of why the cube sinks but the box floats.

8. In what way is upthrust different from flotation?

9. Create a brief presentation on three key factors to consider when designing a fishing canoe to ensure safety, stability, and functionality on the water.

10. An object floats if it has a lower density than the fluid it’s placed into.

Name two materials in the table that will float in water.

Densities of some substances Substance Density (kg/m3) Cardboard 700 Wood 850 Water 1000 Aluminium 2,700 Lead 11,300 Gold 19,300