Referring to the figure below, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is F2 − F1 and that the ends of the cylinder have equal areas A. Note that the volume of the cylinder (and that of the fluid it displaces) equals (h2 − h1)A. (Let h1 be the depth of the top of the cylinder and h2 be the depth of the bottom of the cylinder.) **Show work**

Referring to the figure below, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant force is F2 − F1 and that the ends of the cylinder have equal areas A. Note that the volume of the cylinder (and that of the fluid it displaces) equals (h2 − h1)A. (Let h1 be the depth of the top of the cylinder and h2 be the depth of the bottom of the cylinder.) Show work

Related questions

Q: Problem 2: A liquid of density f = 850 kg/m moves from a horizontal tube of radius r; into a second…

Q: Problem 1: A person is diving in a lake in the depth of h = 15 m. The density of the water is o =…

A: Given: h=15 mρ=1.0*103 Kg/m3Po=1.0*105 PaA=0.046 m2

Q: Two horizontal fluid jets of the same density p are impinging on a fixed vertical plate from…

Q: A certain block of wood has a volume of 553 cm³ and floats on water (density = 1.0×10³ kg/m³) with…

A: Volume of wood =V=553 cm3density of waterδ=1000 kg/m3percentage of volume submerged =25%

Q: What is the volume of the professor's body? Round the final answer to two decimal places. Calculate…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: Three liquids that will not mix are poured into a cylindrical container. The volumes and densities…

Q: A platinum sphere with radius 0.0151 m is totally immersed in mercury. Find the weight of the…

Q: (a) A submersible vehicle is in a lake at a depth of 24.6 m. What is the absolute pressure (in Pa)…

Q: A circular cylinder of mass m, diameter D and length L is pulled vertically upwards within a…

Q: A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is…

A: as per our guidelines, we can answer only first question . please resubmit rest question for answer.

Q: A fluid sits in a tank whose top is open to atmosphere . This fluid has a density that increases…

A: Given: The density of the fluid is ρo+αy.

Q: Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a…

Q: A submersible vehicle is in a lake at a depth of 26.8 m. What is the absolute pressure (in Pa) at…

A: Given:The depth of the lake is 26.8 m.The density of the water is 1x103 kg/m3.The atmospheric…

Q: Bowling balls are roughly the same size but come in a variety of weights. Given that the official…

A: We have given a bowling balls are the same size and in a variety of weight and the ball have…

Q: A U-shaped tube is open to the atmosphere on both ends. Water is poured into the tube, followed by…

Q: A liquid of density Ꝭ = 850 kg/m3 moves from a horizontal tube of radius r1 into a second horizontal…

A: Given data: The relation between the radius is r2=0.5r1. The difference in pressure is…

Q: Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a…

Q: A mass m₁ = 70 kg is balanced by a mass m2 = 1200 kg on an oil hydraulic lift. The diameter of the…

A: This is a question from the Hydraulic lift system. We will elaborate more about the problem in the…

Q: (a) A submersible vehicle is in a lake at a depth of 26.0 m. What is the absolute pressure (in Pa)…

Q: The average body density of a human is 1030 kg/m3, yet we typically float in seawater when we fill…

Q: A force of 295 N is applied to a hydraulic jack piston that is 0.026 m in diameter. The second…

A: GivenF1 = 295 Nd1 = 0.026 md2 = 0.19 m

Q: If any of the combinations yield the same force, give them the same ranking. (Use only ">" or "="…

A: Pascal's Law The pressure applied to any part of an enclosed fluid at rest is transmitted…

Q: A liquid of density Ꝭ = 850 kg/m3 moves from a horizontal tube of radius r1 into a second horizontal…

Q: We have two barometers, like the one shown in the figure. One uses mercury and the other uses an…

A: Given data The relation between the height of the mercury and the unknow liquid is given as hu =…

Question

Referring to the figure below, prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle).

You may assume that the buoyant force is

F₂ − F₁

and that the ends of the cylinder have equal areas A. Note that the volume of the cylinder (and that of the fluid it displaces) equals

(h₂ − h₁)A. (Let h₁ be the depth of the top of the cylinder and h₂ be the depth of the bottom of the cylinder.)

**Show work**

Wob
FB
(a)
Free body
diagram
FB
Wobi
W₁
FB
(b)
Free body
diagram
Fa
W₁

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Please answer A-C
Mercury is poured into a U-tube as shown in Figure a. The left arm of the tube has cross-sectional area A1 of 10.3 cm2, and the right arm has a cross-sectional area A2 of 4.70 cm2. Two hundred grams of water are then poured into the right arm as shown in Figure b. (a) Determine the length of the water column in the right arm of the U-tube. cm(b) Given that the density of mercury is 13.6 g/cm3, what distance h does the mercury rise in the left arm? cm
X A 1m tall cylinder is filled with half water and half oil. What is the total pressure (in Pa) at the base of the cylinder? Density of water is 1000 kg/m^3 and density of oil is 900 kg/m^3. * 40,000 5,000 9,000 9,500 Correct answer
A large rectangular cube made of wood has the follow dimentions: a height, h = 2m, and an area od A = 0.25m^2. The wood that the cube is made of has a density of 800kg/m^3. The cube is then place vertically in water where it floats to rest. The density of the water is 1000kg/m^3. Then the cube is pushed down slightly (by a distance y) and released. The resulting motion is simple harmonic motion. A) Determine the mass of the cube. B) Determine the depth,d, that the cube will float. C) If the cube is pushed further down under water by a distance, y, write an expression for the net force on the block in terms of: y,A,g,p. Where g=9.8m/s^2 D)Use the expression for the net forcee found in part C), and apply newton's second law (Fnet = ma) to the situation of the cube that is being pushed down slightly to derive an equation for the vertical accerlation (ay) (hint: dont forget to pick a positive direction) Compare your results from part D) to the equation for simple harmonic motion using…
(a) If the density of an object is exactly equal to the density of a fluid, the object will (1) float, (2) sink, (3) stay at any height in the fluid, as long as it is totally immersed. (b) A cube 8.5 cm on each side has a mass of 0.65 kg. Will the cube float or sink in water? Prove your answer.
(a) A submersible vehicle is in a lake at a depth of 22.2 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the lake is 1.00 ✕ 103 kg/m3, and the air above is at a pressure of 101.3 kPa. ____ Pa (b) The submersible vehicle has a circular window with a diameter of 33.0 cm. What force (in N) is exerted by the water on the window of the vehicle at the depth from part (a)? (Enter the magnitude.) ____N
A person is diving in a lake in the depth of h = 10.5 m. The density of the water is ρ = 1.0 x103 kg/m3. The pressure of the atmosphere is P0 = 1.0 x 105 Pa. The surface area of the top of the person's head is A = 0.0335 m2. a. Express the absolute pressure at the depth of h, P, in terms of P0, ρ, and h. b. Calculate the numerical value of P in Pa. c. Express the magnitude of the force exerted by water on the top of the person's head F at the depth h in terms of P and A. d. Calculate the numerical value of F in N.
(a) A submersible vehicle is in a lake at a depth of 26.6 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the lake is 1.00 ✕ 103 kg/m3, and the air above is at a pressure of 101.3 kPa. ____Pa (b) The submersible vehicle has a circular window with a diameter of 40.0 cm. What force (in N) is exerted by the water on the window of the vehicle at the depth from part (a)? (Enter the magnitude.) ____ N
You place an open bottle filled with olive oil (density 880 kg/m^3) in a container filled with water so that the surfaces of both liquids are at the same level. The bottle has a hole in it 18cm below the surface that is initially closed with adhesive tape, as shown in (Figure 1). Determine the vertical distance Δh between the oil surface and water surface after the tape is removed and the equilibrium is reached. Assume that the volume of water is much greater than the volume of olive oil, so that the decrease in the water level is negligible.
(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 24.4 m. Assume the density of the water is 1.00 ✕ 103 kg/m3 and the air above is at a pressure of 101.3 kPa. Pa(b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 42.0 cm? N