1. A pair of eyeglass frames are made of an epoxy plastic (coefficient of linear expansion = 1.30 x 10-40C-1). At room temperature (20.0oC), the frames have circular lens holes 2.28 cm in radius. To what temperature must the frames be heated if lenses 2.29 cm in radius are to be inserted into them?
2. A small ferryboat is 4.70 m wide and 6.50 m long. When a loaded truck pulls onto it, the boat sinks an additional 3.50 cm into the river. What is the weight of the truck?
3. A 210-kg load is hung on a wire of length of 4.50 m, cross-sectional area 2.00x10-5 m2, and Young's modulus 8.00 x 1010 N/m2. What is its increase in length?
4(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 25.6 m. Assume the density of the water is 1.00 x 103 kg/m3 and the air above is at a pressure of 101.3 kPa.
(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 31.0 cm?
5. A spherical weather balloon is filled with hydrogen until its radius is 2.40 m. Its total mass including the instruments it carries is 23.0 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?
6. The four tires of an automobile are inflated to a gauge pressure of 2.3 x 105 Pa. Each tire has an area of 0.023 m2 in contact with the ground. Determine the weight of the automobile.
7. Piston (1) in the figure below has a diameter of 0.40 in.; piston (2) has a diameter of 1.1 in. In the absence of friction, determine the force F→ necessary to support the 500-lb weight. (Enter magnitude.)
8. Calculate the mass of a solid gold rectangular bar that has dimensions lwh = 4.40 cm x 14.0 cm x 24.0 cm. (The density of gold is 19.3 x 103 kg/m3.)
9. A pair of eyeglass frames are made of an epoxy plastic (coefficient of linear expansion = 1.30 x 10-40C-1). At room temperature (20.0°C), the frames have circular lens holes 2.28 cm in radius. To what temperature must the frames be heated if lenses 2.29 cm in radius are to be inserted into them?
10. The New River Gorge bridge in West Virginia is a 518-m-long steel arch. How much will its length change between temperature extremes -20°C and31°C?
11. (a) An ideal gas occupies a volume of 2.0 cm3 at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container.
(b) If the pressure of the 2.0-cm3 volume is reduced to 2.6 x 10-11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container?
12. For each of the following temperatures, find the equivalent temperature on the indicated scale.
(a) -235°C on the Fahrenheit scale
°F
(b) 99.0°F on the Celsius scale
°C
(c) 125 K on the Fahrenheit scale
°F
13. One mole of oxygen gas is at a pressure of 6.90atm and a temperature of 24.5°C.
(a) If the gas is heated at constant volume until the pressure triples, what is the final temperature?
(b) If the gas is heated so that both the pressure and volume are doubled, what is the final temperature?
14. An air bubble has a volume of 1.20 cm3 when it is released by a submarine 105 m below the surface of a lake. What is the volume of the bubble when it reaches the surface? Assume the temperature and the numbers of air molecules in the bubble remain constant during its ascent.
15. At what temperature would the rms speed of neon-20atoms equal the following speeds? (Note: The mass of a neon-20 atom is 3.32 x 10-26 kg.)
(a) the escape speed from Earth, 1.12 x 104 m/s
(b) the escape speed from the Moon, 2.37 x 103 m/s
16. What is the average kinetic energy of a molecule of oxygen at a temperature of 390 K?