3. How many kilograms of air is in the room?
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1 1. Astronomers use density as a clue to the composition of distant objects. Judging by the orbits of its moons the mass of Saturn is found to be kg. (a) Use its mean radius km to determine its mean density and specific gravity. (b) The density at its core is estimated to be around 15 g/cm 3 what fraction of its total mass is Saturn s core if it is about twice the diameter of Earth? 2. Determine the density of a carbon-14 nucleus using a diameter of 5.8 fm. A neutron star is thought to be essentially a big ball of neutrons with a mass 1.4 times that of the Sun how big is it? 3. How many kilograms of air is in the room? 4. Given a tabletop that has width and length 2.0 ft by 4.0 ft, determine the force of the air on its surface. 5. A typical eardrum is about 8.0 mm in diameter. When listening to a quiet sound versus loud (75 db vs. 110 db) the amplitude of pressure change is from 0.1 Pa to about 6 Pa. (a) Find the force of air on the eardrum when there is no sound. (b) Find the change in this force at the sound levels described.
2 6. According to one source, a certain car has a weight of 4100 lb and four wheels that each have a contact patch (or tire footprint) of 37 square inches. The tires are inflated to 32 psi. (a) Calculate the normal force that acts on each tire. (b) Determine force per area for the footprint. (c) Calculate the force of the air inside the tire acting on the other side of the patch and compare. 7. While flying at an altitude around 10 km the cabin of an airplane is pressurized to 75 kpa. Given the atmospheric pressure is only 30 kpa determine the force acting on a circular window with diameter 30.0 cm to prevent it from blowing out. 8. Compare the two pumps shown, one for bicycles, the other for inflatables like a floaty. Why the big difference in diameter? Explain.
3 9. In a certain hydraulic brake system the master cylinder has a diameter of 17 mm and the wheel cylinder has a diameter of 22 mm. Suppose a force of 50.0 N is applied on the piston of the master cylinder, which increases the pressure in the hydraulic lines and moves the piston at the wheel cylinder 0.10 mm. (a) What force acts on the piston at the wheel cylinder? (b) What distance must the piston in the master cylinder move? 10. Suppose you dive to the bottom of an eight foot pool. (a) Determine the change in pressure. (b) Determine the absolute pressure at the bottom of the pool. 11. A certain pool of water is a rectangular shape with dimensions 6.0 m by 10.0 m and depth 2.0 m. Determine the force of the water acting on each wall and the bottom of the pool. 12. A submarine dives to a depth of m. Assume conditions within the sub are normal for the crew. Determine the force required to prevent a hatch of diameter 30.0 cm from imploding.
4 13. Suppose you connect an ideal pressure gauge to a rigid airtight container. Explain how it could be used to measure depth of water. Would it read positive or negative? Derive an equation for depth h in terms of gauge pressure P and any appropriate constants. A pressure reading of amount 32 psi would indicate what depth? 14. A cube of ice with sides length 3.0 cm and density 0.92 g/cm 3 is placed in a cylindrical beaker with diameter 12 cm partially filled with water. Assume that it floats with one face parallel to surface and ignore melting. (a) Determine the force of buoyancy on the cube. (b) Find the depth in the water. (c) What is the change in depth of water in the beaker? (d) Find the difference in pressure of air on top surface versus water on bottom surface. 15. A river barge is essentially a large rectangular shaped boat that can carry a load of around 1400 metric tons. Estimate the length if its width is limited to 11 m and its draft (depth in water) is 3.0 m. If the actual length is 60.0 m, what is the mass of the barge itself?
5 16. Imagine turning a student desk into a boat turn it upside down and create sides. (a) Given that the overall volume of space beneath the desk is about 0.60 m 3, how many people of mass 75 kg could it hold without sinking more than halfway into the water? (b) What if it were floating in a pool of mercury? 17. An iron (SG = 7.8) sphere of radius 5.00 cm is lifted from the ocean (density of seawater = 1020 kg/m 3 ). (a) Find the normal force if it rests on the bottom. (b) What force is needed to accelerate it upward 2.0 m/s 2? (c) What is its initial acceleration if it is dropped from rest and sinks? (d) If it falls through the water at a constant speed (terminal velocity) what is the drag acting on it? 18. It is sometimes said that if you had an ocean big enough Saturn could float in it. How deep and how wide does this ocean need to be? Density of seawater is 1020 kg/m 3. (Challenging volume determination!)
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Keshaw Classes IIT/JEE Medical Classes 5-A 11028 / 9, WEA, Sat Nagar, Karol Bagh New Delhi-110005 Mob:9910915514,9953150192 Ph:011-45660510 E-mail : keshawclasses@gmail.com Web:www.keshawclasses.com Solids