The owner of a company that manufactures drinking cups decides it would be impressive to build an inground swimming pool that is a scaled up version of her best selling cup. For this particular cup, the area of the circular opening at the top is 1.24 times the area of the circular bottom. Her pool contractor informs her that when the pool is full of water, the magnitude of the force acting on the top surface will be the same as the magnitude of the force acting on the bottom surface. Determine the depth of the pool. m

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density 1.30 * 10^3 kg/m3. The area of each base is 4.00 cm2, but in one vessel the liquid height is 0.854 m and in the other it is 1.560 m. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

A child playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. If the child needs to supply 5.00×102 N5.00×102 N to totally submerge the ball, calculate the diameter ?d of the ball. The density of water is ?w=1.000×103 kg/m3,ρw=1.000×103 kg/m3, the density of styrofoam is ?foam=95.0 kg/m3,ρfoam=95.0 kg/m3, and the acceleration due to gravity is ?=9.81 m/s2.

You are planning on installing a new above-ground swimming pool in your backyard. The pool will be rectangular with dimensions 31.0 m x 10.0 m. It will be filled with fresh water to a depth of 1.90 m. In order to provide the appropriate structural support, you wish to determine the following. (a) Determine the force exerted on the bottom of the pool by the water (in N). N (b) Determine the force exerted on each end of the pool by the water (in N). (Assume the end is the 10.0 m wall.) N (c) Determine the force exerted on each side of the pool by the water (in N). (Assume the side is the 31.0 m wall.) N (d) You wish to have swimming parties with your children and grandchildren. At a given time, you might have 29 people with an average mass of 75.0 kg in the pool. You need to determine if such parties will affect your calculations for the required strength of materials supporting your pool. O The parties will not affect the required strength since the forces on the surfaces will increase…

Suppose a distant world with surface gravity of 7.84 m/s2 has an atmospheric pressure of 8.44 ✕ 104 Pa at the surface. (a) What force is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of a methane ocean? N (b) What is the weight of a 10.0-m deep cylindrical column of methane with radius 2.00 m? Note: The density of liquid methane is 415 kg/m3. N (c) Calculate the pressure at a depth of 10.0 m in the methane ocean. Pa

the plunger and the needle of a hypodermic syringe have areas of 0.5 cm^2 and 0.0006 cm^2, respectively. To inject a vaccine, a nurse pushes the plunger with a force of 5.5 N. What pressure is transmitted into the vaccine?

A simplified model of how an airplane flies relies on a difference in air pressure between the top and the bottom of the wing. If a Boeing 737 has a mass of 29,000 kg and a total wing span area of 100 m2, what difference in pressure (in N/m2) is necessary for the airplane to maintain altitude? part b: in contrast, calculate the pressure difference (in N/m2) necessary for a 109 g Sharp-shinned hawk with a wing area of 0.0439 m2 to main altitude.

At a depth of 10.9 km, the Challenger Deep in the Marianas Trench of the Pacific Ocean is the deepest site in any ocean. Yet, in 1960, Donald Walsh and Jacques Piccard reached the Challenger Deep in the bathyscaph Trieste. Assuming that seawater has a uniform density of 1024 kg/m3, approximate the hydrostatic pressure (in atmospheres) that the Trieste had to withstand. (Even a slight defect in the Trieste structure would have been disastrous.)

The density of ice is 917 kg/m3, and the density of sea water is 1025 kg/m3. A swimming polar bear climbs onto a piece of floating ice that has a volume of 6.29 m3. (a) What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water? To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 5.42 × 103 kg/m3. (b) What fraction of the specimen’s apparent volume is solid?

An ice floe has a rectangular shape with dimensions of 15 x 6 x 0.15 m^3. What is the maximum mass of a polar bear that can sit on the floe before sinking?   ice density: 920 kg/m^3 sea water density: 1025 kg/m^3   1400 kg   1520 kg   1418 kg   1319 kg