1. A certain sample of brass has a mass of 2 kg and a volume of 240 cm3. What is its density? Density = Mass 2 kg 2000 g = = = 8.3333g / cm 3 3 3 Volume 240 cm 240 cm 2. A 50 gram bracelet is suspected of not being pure gold. It is dropped into a glass of water and 4 cm3of water overflows. Is the bracelet pure gold? The density of the bracelet is: Density = Mass 50 g = = 12.5g / cm 3 3 Volume 4 cm The density of pure gold is 19.32 g/cm3. Since the density of the bracelet is less than the density of pure gold, the bracelet is not pure gold. 3. What volume of copper has a mass of 5 kg? The density of copper is 8930 kg/m3. Density = Mass 5kg = = 8930kg / m 3 Volume Volume Volume = 5kg = 0.0005599 m 3 = 559.9 cm 3 8930 kg / m 3 4. What mass of silver has a volume of 100 cm3? The density of silver is 10490 kg/m3 Density = Mass Mass = = 0.010490g / cm 3 3 Volume 100 cm Mass = (100 cm 3 ) ( 0.010490 g / cm 3 ) = 1.049 kg 5. A certain gas has a volume of 500 cm3. What is its volume when the pressure is tripled? P1 V 1 = P2 V 2 If P2 = 3 * P1 then, P1V1 = 3P1V2 V1 = 3V2 V2 = (1/3)V1 The volume will be one third of the original volume. (Assuming that the temperature remains constant.) 6. Consider the gas in # 5 above. What is its volume if the pressure is reduced by onethird? If the pressure is reduced by one third, then the new pressure will be 2/3 of the original pressure. As a result, the new volume will be 3/2 of the original volume. Here is how to show it with an equation: P1 V 1 = P2 V 2 P2 = (2/3)P1 P1V1 = (2/3)P2V2 V1 = (2/3)V2 V2 = (3/2)V1 7. An hydraulic car lift at the repair shop, is similar to Figure 8.31 in your text, except the area of the large piston is 100 times that of the small piston. How many N of force needs to be applied to the small piston to exactly balance a 2000 kg car? Without seeing the diagram, the assumption is that the two pistons are connected by a hydraulic hose of some sort, such that the pressure in each piston is constant. Let A represent the area of the small piston. Then 100A represents the area of the large piston. The pressure in the large piston = 2000 kg * 9.81m / s 2 196.2 N = 100A A m 2 The pressure in the smaller pistion = Force, N A Since the two pressures must be equal: Force 196.2 = A A Force = 196.2 N 8. In the example in # 7 above, what distance must the small piston move in order to raise the car 5 m? The volume of hydraulic fluid displaced by the movement of the pistons must be equal. If the large piston moves 5 m, then the total volume of fluid moved is (5 m)(100A), where A is again the area of the smaller piston. The movement of the smaller piston, with area A, is xA, where x is the distance that the smaller piston moves. Equating the two volumes gives: (5 m)(100A) = (x m)(A) x = 500 m 9. A balloon is filled with 1000 cm3of a gas weighing 1000 g. Will it rise or fall when it is released? The density of the balloon is approximately: Density = Mass 1000g = = 1.00 g / cm 3 3 Volume 1000 cm The balloon will fall. 10. For the balloon in # 9 above, whether your answer is rise or fall, why did you answer it that way? Since the density of air is about 0.00123 g/cm3, the balloon is much more dense than the surrounding air. As a result, the balloon weighs more than the air that it displaces so the balloon will fall.