Buoyancy & Buoyant Force Practice Problems

A wooden block is suspended in a tank of fresh water using a string fixed to the bottom of the tank. The tension in the string is 805 N and the block has a volume of 0.425 m³. Determine the buoyant force experienced by the block from the water and the block's mass.

Students perform an experiment using a 2.00 kg metal block. They tie the block and immerse it in water. They weigh the stone while immersed in water and find its weight to be 11.3 N. Determine the least density of a liquid that will make the block float.

A solid cylinder of diameter 10 cm and height 25 cm is placed into the container. Oil of density 850 kg/m³ and water are placed in a container. The cylinder floats at the boundary of the two liquids with 8.0 cm of its length in water. Determine the mass and density of the cylinder.

A container is filled with water and oil of density 800 kg/m³. A cylindrical wooden block of diameter 12.0 cm and height 15 cm is floating at the interface of the two liquids. If 4.0 cm of the block is in water, determine the gauge pressure at the top and lower faces of the block.

A ball is tied to the bottom of a tank containing fresh water using a string. The ball's volume is 5.56 × 10^-3 m³ while the tension in the string is 50.1 N. The thread is cut letting the ball float on the surface. At the moment the ball becomes stationary, determine the percentage of its volume submerged.

A block of ice forms in a pond during the winter. Determine the least volume of the block required to keep a 68.0 kg fisher holding a 5.00 kg load of their fishing gear without wetting their feet. 

An impure metal block has a weight of 50.4 N in air. When the block is fully submerged in oil, the string tension required to keep it suspended in the oil is 33.0 N. Determine the volume and density of the block. 

A hollow metallic container of mass 400 kg (with a square base) is floating in water. The length of the base is 1.0 m. A 70.0 kg person holding luggage of mass 20 kg jumps into the container. What extra height of the container will be submerged? 

A floating platform possesses a rectangular base with dimensions of 4 m by 8 m and a 1.5 cm thickness, made from a material with a density of 8100 kg/m³. The platform is enclosed by walls constructed from platinum, having a 0.32 cm thickness. Find the lowest height necessary for these walls to ensure the platform remains afloat in the lake. The density of water is approximately 1000 kg/m³.

A cube-shaped floating object is made of lightweight material with a density of 120 kg/m³ and a side length of 38 cm. Determine the maximum mass that can be suspended from this cubic object in water without causing it to sink. Consider that the volume of the suspended mass is negligible compared to the cube's volume.

A cylindrical object made of a material with density ρ  is partially submerged in a liquid of density σ. The object has a height of H and the portion of the cylinder that remains above the liquid's surface has a height of h as shown in the figure below. Determine the ratio of the height of the exposed surface to the entire height of the object, represented by h/H.

A specially designed underwater toy has an average density of 1210 kg/m³, which causes it to sink in water. To prevent sinking, the toy has a built-in inflatable chamber that fills with air. When inflated, the chamber contains air at a density of 1.18 kg/m³ at 25°C. What percentage should the toy's volume increase by to achieve neutral buoyancy in water?

An artifact with a radius of 3.00 cm and weighing 168.4 g exhibits neutral buoyancy in an unknown liquid. Identify the liquid in which it is submerged. Assume the shape of the artifact to be spherical.

A cylindrical copper object occupying a volume of 68cm³ is suspended from a cord, as illustrated in the figure. The object is submerged in a fluid (petrol) with a density of 730 kg/m³. Determine the tension in the cord.

In an interactive science exhibit, an aquarium contains a liquid with a density of ρ. To maintain the position of the front glass panel and avoid leakage, a spring is fastened to the panel. The spring's tension keeps the panel securely closed and counteracts torque forces that could potentially dislodge the panel. What is the minimum spring tension necessary to ensure that the panel remains in place without causing any leakage?

In an underwater-themed restaurant, a large decorative aquarium displays a captivating liquid with a density ρ. This tank has the shape of a rectangular parallelepiped, with dimensions L (length), H (height), and W (width), as shown in the figure. A spring is used to prevent the front glass panel of the aquarium from being pushed out at the bottom by counteracting the torque on the panel. Determine the minimum height above the bottom at which the spring should be fixed, given that it has the minimum tension. Note: The tank has an opening to the atmosphere. 

In a coastal engineering workshop, you are tasked with designing a floating device to hold monitoring equipment for offshore environmental assessments. The device consists of a spherical buoy made of lightweight plastic material. Determine the maximum mass of the monitoring equipment that can be placed inside the buoy without causing it to sink. The spherical buoy has a mass of 2 × 10³ kg and a diameter of 2 m.

Determine what the maximum cargo weight value is that a spherical air balloon filled with hydrogen, which has a density of 0.08375kg/m³, can lift up at 0°C and 1 atm pressure. The balloon has a radius of 8.15 m, and the combined mass of the balloon's structure and skin is 880 kg. Assume that the buoyant force on the cargo itself is negligible.

A scientist discovers a floating glacier during their trip to Alaska. Please estimate what percentage of this particular glacier is floating above the surface of the water, given that the specific gravity of the glacier is 0.927 and the specific gravity of the seawater is 2.025.

Determine the tension value that a winch cable experiences when a sailor lifts a 17,000-kg metal hull of a sunken boat out of the river and onto the riverbank.

A winch lifts an 18,000-kg metal barrel out of a river. If the barrel is fully submerged in water and is lifted at a constant speed, estimate the tension in the winch’s cable. Assume that the density of water is 1,000 kg/m³ and the density of the barrel is 7.9×10³ kg/m³.

A 3.35-kg rubber block with a specific gravity of 0.600 floats on a water pool. To make the block sink, what is the minimum mass of tin that must be hung from it using a string? [Hint: Specific gravity of Tin is 7.30].

A barge delivering vegetable oil to a remote coastal village has a horizontal cross-sectional area of 2250 m² at the waterline. How much volume of oil (m³) was delivered when the oil was unloaded, and the barge rose 9.50 m higher in the seawater? [Hint: Surface seawater density is 1025 kg/m³ and the density of vegetable oil is 915 kg/m³].

Eleven large styrofoam rods are tied together to construct a platform. Each rod measures 7.50 m in length and 46.0 cm in diameter and has a specific gravity of 0.0750. The weight of the platform is not negligible. Given that an average person has a mass of 69.0 kg, how many people at maximum can the platform support without getting their feet wet? [Hint: The density of water is 1.00 × 10³ kg/m³].

A 12.0 cm side-length plastic container floats at the interface between a swimming pool and a layer of cooking oil. The cooking oil has a density of 820 kg/m³. What is the mass of the container and the buoyant force acting on it if the container floats such that 74% of it is submerged in the water and 26% in the oil?

(a) A solid brass cylinder with a mass of 5.50 kg in air shows an apparent mass of 3.30 kg when completely submerged in a certain liquid. Calculate the density of the liquid.

(b) Using the data obtained, derive a general formula for determining the density of a liquid based on the apparent mass of a submerged object.

Use $\rho _{\text{brass }}=8500\mathrm{~kg}/\mathrm{m}^3$.

It is established that the buoyant force 𝐹_𝐵 on a floating log found in a lake acts at the center of gravity in the water which is displaced by the log itself. This specific point is referred to as the center of buoyancy. In order for the log to be in a state of stable equilibrium, should the center of buoyancy be positioned above, below, or at the same level as its center of gravity? Explain your reasoning.

A 120-m thick iceberg (density = 920 kg/m³) is floating in the ocean water around it (density = 1025 kg/m³). Estimate the height of the iceberg above the surrounding ocean water.

A block of maple wood with a mass of $0.450$ kg and a density of $7.00\times 10^2$ kg/m³ is floating in saltwater, which has a density of $1.03\times 10^3$ kg/m³. An iron weight is placed on top of the wood block. Determine the mass of the iron weight required to submerge the wood block so that its top surface is level with the saltwater surface.

A fully submerged fuel tank displaces 25 liters of freshwater. The tank's mass is 18 kg, and it holds 4.0 kg of fuel when full. Calculate the net force (magnitude and direction) on the tank when it is full and when it is empty, considering only its weight and the buoyant force. Use: The density of freshwater ${\rho }_{\text{water }}=1.0\times 10^3\frac{kg}{m^3}$.

A fish tank with water, with a density of $1.0\times 10^3\ \frac{kg}{m^3}$, weighs 150 N on a scale. A 30-N plastic toy, with a density of $1.4\times 10^3\ \frac{kg}{m^3}$, is suspended in the water by a string, not touching the bottom. Determine the new scale reading when the toy is fully submerged. Hint: Draw two free-body diagrams: one for the toy (weight, tension, buoyant force) and one for the tank + water + toy system (forces affecting the scale).

A soil scientist observes the rise of water in a narrow cylindrical tube inserted into a soil sample, which is covered with surface water. Given the density of water ρ, the surface tension of water γ, and the radius of the tube r, what is the expression for the height h (the height above the surface of the water on the soil) to which water rises in the tube? For simplicity, assume that the water wets the tube and the top water surface inside the tube is completely level.

A copper wire with length $l$ is placed on the surface of ethanol. Calculate the diameter of the copper wire that can just barely remain afloat due to surface tension. The density of copper is 8960 kg/m³ and the surface tension of ethanol is 0.022 N/m.

In a laboratory, a scientist measures the apparent mass of a copper cylinder, which reads to be 5.5000 kg when weighed in an open space filled with air. To find the true mass of the cylinder inside of a vacuum, the scientist needs to account for the buoyant force of the air. What is the true mass of the copper cylinder when it is located inside of a vacuum?

Consider a hydrogen-filled balloon that is spherical in shape and has a diameter of 50 cm. Determine the number of hydrogen-filled balloons that are needed in order to lift a box that has of mass of 55 kg up off the ground. [Hint: The density of air is ρ_air = 1.225 kg/m³ and the density of hydrogen is ρ_H2 = 0.0899 kg/m³.]

During an experiment, it is determined that a 0.65-kg object made out of plastic will float in seawater which has a specific gravity "SG" of 1.03, but will sink in kerosene which has a "SG" of 0.82. Provided that in kerosene it will have an apparent mass of 0.15 kg if it is fully submerged, determine what the "SG" of the object will be.