Concept explainers
A hollow copper (ρCu = 8.92 × 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?
(a)
The radius of the sphere.
Answer to Problem 25PQ
The radius of the sphere is
Explanation of Solution
Since the sphere is in equilibrium condition so that weight of the spherical shell is equal to the buoyant force of the water.
Here,
Write the expression for force due to gravity.
Here,
Write the expression for buoyant force.
Here,
Write the expression for volume of the spherical shell.
Here,
Conclusion:
Substitute the equation (II) and (III) in the equation (I).
Substitute equation (IV) in the above equation to solve for .
Substitute
Therefore, the radius of the sphere is
(b)
The thickness of the shell wall.
Answer to Problem 25PQ
The thickness of the shell wall is
Explanation of Solution
Write the expression for mass of the ball.
Here,
Rearrange the above equation for volume of the inner and outer radius of the sphere.
Here,
Write the expression for thickness of the shell wall.
Here,
Conclusion:
Substitute
Solve the above equation to find
Substitute
Therefore, the thickness of the shell wall is
Want to see more full solutions like this?
Chapter 15 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- (a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 030 kg/m3 and the air above exerts a pressure of 101.3 kPa. (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 m?arrow_forwardA 50.0-kg woman wearing high-heeled shoes is invited into a home in which the kitchen has vinyl floor covering. The heel on each shoe is circular and has a radius of 0.500 cm. (a) If the woman balances on one heel, what pressure does she exert on the floor? (b) Should the homeowner be concerned? Explain your answer.arrow_forwardA tank with a flat bottom of area A and vertical sides is filled to a depth h with water. The pressure is P0 at the top surface. (a) What is the absolute pressure at the bottom of the tank? (b) Suppose an object of mass M and density less than the density of water is placed into the tank and floats. No water overflows. What is the resulting increase in pressure at the bottom of the tank?arrow_forward
- A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?arrow_forward. A juniper-wood plank measuring 0.25 ft by 1 ft by 16 ft is totally submerged in water, (a) What is its weight? (b) What is the buoyant force acting on it? (c) What is the size and the direction of the net force on it?arrow_forwardIf your body has a density of 995 kg/m3, what fraction of you will be submerged when floating gently in: (a) Freshwater? (b) Salt water, which has a density of 1027 kg/m3?arrow_forward
- (a) A water hose 2.00 cm in diameter is used to fill a 20.0-L bucket. If it takes 1.00 min to fill the bucket, what is the speed v at which water moves through the hose? (Note: 1 L = 1 000 cm3.) (b) The hose has a nozzle 1.00 cm in diameter. Find the speed of the water at the nozzle.arrow_forwardA spherical weather balloon is filled with hydrogen until its radius is 3.00 m. Its total mass including the instruments it carries is 15.0 kg. (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?arrow_forwardA rectangular block of Styrofoam 25.0 cm in length, 15.0 cm in width, and 12.0 cm in height is placed in a large tub of water. Assume the density of Styrofoam is 3.00 102 kg/m3. a. What volume of the block is submerged? b. A copper block is now placed atop the Styrofoam block so that the top of the Styrofoam block is level with the surface of the water. What is the mass of the copper block?arrow_forward
- In an immersion measurement of a woman's density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 L is she able to float without treading water with her lungs filled with air?arrow_forward(a) The pressure inside an alveolus with a 2.00104 -m radius is 1.40103 Pa, due to its fluid-lined walls. Assuming the alveolus acts like a spherical bubble, what is the surface tension of the fluid? (b) Identify the likely fluid. (You may need to extrapolate between values in Table 11.3.)arrow_forwardWater is flowing through a pipe that has a constriction opening into a region with a wider cross-sectional area. If the pipe regions are cylindrical with radii of 0.10 m and 0.35 m, respectively, and the water is moving with a speed of 1.50 m/s in the wider section, what is the speed of the water in the constricted section?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning