Concept #1: Intro to Buoyancy & Buoyant Force

Example #1: Comparing Buoyant Forces

Practice: When an object of unknown mass and volume is fully immersed in large oil (800 kg/m^{3} ) container and released from rest, it stays at rest. Calculate the density of this object.

Concept #2: Buoyancy / Three Common Cases

Practice: A block floats with 40% of its volume above water. When you place it on an unknown liquid, it floats with 30% of its volume above. What is the density of the unknown liquid?

Example #2: Is Crown Made of Gold? (Buoyancy)

Practice: An 8,000 cm^{3} block of wood is fully immersed in a deep water tank, then tied to the bottom. When the block is released and reaches equilibrium, you measure the tension on the string to be 12 N. What is the density of the wood?

Example #3: Maximum Load on Floating Board

Practice: You want to build a large storage container, with outer walls and an open top, as shown, so that you can load things into it, while it floats on fresh water, without any water getting inside. If the bottom face of the container measures 3.0 m by 8.0 m, how high should the side walls be, such that the combined mass of container and inside load is 100,000 kg?

A rectangular block of wood, 12 cm x 18 cm x 42 cm, has a specific gravity of 0.60. Determine the buoyant force that acts on the block when it is placed in a pool of fresh water.

Two wooden boxes of equal mass but different density are held beneath the surface of a large container of water. Box A has smaller average density than box B. When the boxes are released, they accelerate upward to the surface. Which box has the greater acceleration?
a. Box A
b. Box B
c. They are the same.
d. We need to know the actual densities of the boxes in order to answer the question.
e. It depends on the contents of the boxes.

A block of density ρ1 and volume V1 is submerged in a liquid of density ρL. A second block of density ρ2 and volume V2 is placed on top of the first block. The two blocks are floating in the manner shown in the figure below.
Find V2 such that the two blocks are just submerged, as shown in figure above.

Consider a rectangular block of ice floating in water in an open vessel. Let a denote the height of the ice block showing above the water surface, and b the height of the submerged part of the ice block.
Given a, b, the density ρwater of liquid water and the density ρice of the ice, which relationship is correct?

A slab of ice floats on a freshwater lake. What minimum volume must the slab have for a 45 kg woman to be able to stand on it without getting her feet wet?

A diver wishes to recover a treasure chest she found at the bottom of the sea, 60 m below the surface. To do this, she inflates a plastic balloon to a radius of 40 cm with the air from her compressed air tanks. The mass of the treasure chest is 200 kg and its dimensions are 20 cm x 40 cm x 10 cm. Take the density of sea water as 1025 kg/m3. How does the acceleration change (qualitatively) as the balloon and chest float to the top? Does it get larger, smaller, or stay the same? Justify your answer with equations.

A boat's hull displaces 1600 L of water when floating. What is the weight of the boat?

An object floats on the surface of water. If the object's specific gravity is 0.7, what percentage of the object's volume is above the water-line?

A boat is floating on the surface of the water when the captain throws the anchor overboard. When the anchor is thrown out of the boat, which of the following is true?
(a) The weight of the boat decreases, so the buoyant force increases
(b) The weight of the boat decreases, so the buoyant force decreases
(c) The weight of the boat increases, so the buoyant force increases
(d) The weight of the boat increases, so the buoyant force decreases

A barge is 10.0 m wide and 60.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water?
(A) 3.53 MN
(B) 6.39 MN
(C) 7.06 MN
(D) 6.82 MN
(E) 9.54 MN

A rectangular block of wood, 12 cm x 18 cm x 42 cm, has a specific gravity of 0.60. What fraction of the block is submerged?(Express your answer to two significant figures.)

A cube of side s is completely submerged in a pool of fresh water. After drawing a free-body diagram, derive an algebraic expression for the net force on the cube.a. ΣFy = Pfluidgs - Mcubegb. ΣFy = Pfluidgs3 - Mcubegc.. ΣFy = Pcubegs3 - Mfluidgd. ΣFy = Pfluidgs3

A cube of side s is completely submerged in a pool of fresh water. What is the weight of the displaced water when the cube is submerged?a. wwater = ρfluidsgb. wwater = ρcubes3gc. wwater = ρfluids3gd. wwater = mcubeg

A woman floats in a region of the Great Salt Lake where the water is about four times saltier than the ocean and has a density of about 1130 kg/m3. The woman has a mass of 56 kg, and her density is 971 kg/m3 after exhaling as much air as possible from her lungs. Determine the percentage of her volume that will be above the waterline of the Great Salt Lake. (Express your answer to three significant figures.)

A beaker of mass 1 kg containing 2.5 kg of water rests on a scale. A 3.1 kg block of a metallic alloy of density 4900 kg/m3 is suspended from a spring scale and is submerged in the water of density 1000 kg/m3 as shown in the figure.
What does the hanging scale read? The acceleration due to gravity is 9.8 m/s 2.
A. 21.3715
B. 16.043
C. 23.0577
D. 28.3774
E. 14.3733
F. 31.6615
G. 27.8826
H. 24.18
I. 23.8994
J. 27.6033

A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?
[A] 1.35 m
[B] 1.30 m
[C] 1.25 m
[D] 1.20 m
[E] 1.50 m

A solid aluminum cylinder of length L, radius r and density pal is suspended vertically from a thin wire and slowly lowered into a still lake. Let z denote the depth of the bottom of the cylinder. (When z < 0 no portion of the cylinder is submerged in water. Note that z is assumed here to increase downwards.) Assume that both the mass of the wire and the density of air are negligibly small. Let pω denote the density of water. What is the tension T in the wire
a) for z < 0?
b) for 0 < z < L?
c) for z > L?
d) Plot T(z).

A 7.4 kg solid sphere made of metal whose density is 2300 kg/m3, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 18 N. The density of the liquid is closest to:
A. 1700 kg/m3
B. 1600 kg/m3
C. 1500 kg/m3
D. 1400 kg/m3
E. 1300 kg/m3

A diver wishes to recover a treasure chest she found at the bottom of the sea, 60 m below the surface. To do this, she inflates a plastic balloon to a radius of 40 cm with the air from her compressed air tanks. The mass of the treasure chest is 200 kg and its dimensions are 20 cm x 40 cm x 10 cm. Take the density of sea water as 1025 kg/m3. The diver attaches the inflated balloon to the treasure chest using a rope. Calculate the initial acceleration of the balloon and the chest. Ignore the mass of the plastic of the balloon and of the rope connecting the balloon and the chest.

A toy floats in a swimming pool. The buoyant force exerted on the toy depends on the volume ofa. water in the pool.b. the pool.c. the toy under water.d. the toy above water.e. none of the above choices.

An object floats in water with 5/8 of its volume submerged. The ratio of the density of the object to that of water isa. 8/5.b. 5/8.c. 1/2.d. 2/1.e. 3/8.