Refer to the table of densities in the first section of this lecture for required data.

I. Warm-up Exercises

1. An iron ball has a radius of 3.5 cm.  What is the mass of the ball? (Hint: See the table of densities in the density section of this lecture!)

2. A solid styrofoam cylinder has a height of 10.5 cm and a radius of 5.7 cm.  What is the weight of the cylinder?

3. You cut out a circle of radius 7.2 cm from a piece of paper, and place it on the table top.  What force is acting downward on the circle due to the earth’s atmospheric pressure above it?

4. You are snorkeling in the beautiful, calm Caribbean.  You notice an exotic-looking fish swimming down near the bottom, and decide to dive down to get a closer look.  What is the pressure acting on your body if you dive down to a depth of 3.4 m?

5. An iron cube of side 5.50 cm is dropped into a pool of water which is 2.70 m deep. What force is acting on the top side of the cube due to water pressure once it settles on the bottom of the pool?

II. Some Standards

6. A balloon filled with air has a total mass of 45 g.  The balloon is tied to one end of a string of length 1.2 m, the other end of which is attached to the bottom of a pool of  water of depth 4.0 m.  The balloon has a radius of 5.0 cm, and is completely submerged beneath the surface of the water.  (a) What is the value of the buoyant force acting on the balloon?  (b) What is the tension in the string? (Hint: Draw a FBD!) (c) Would the answers to (a) and (b) change if the string were only 0.2 m long? Explain your answer.

7. A cube having sides of length 7.0 cm is made of iron.  The cube is dropped into a swimming pool where it immediately sinks and then rests on the horizontal bottom surface. (a) What is the value of the normal force exerted by the pool floor on the block?  (Hint: Find  the buoyant force acting on the block, and then draw a FBD....) (b) How would the buoyant force that you found during your solution to part (a) have changed if the block had been made of copper (r = 8920 kg/m³) instead of iron?

III. So, you think you’re pretty good...?

8. A hemispherical bowl of radius 12 cm is floating on the surface of a pond. An unfortunate fish jumps out of the water and happens to land in the otherwise empty bowl.  Afterwards, the bowl just barely stays afloat, with the fish lying inside the bowl and the water outside of the bowl just up to its rim. What was the mass of the fish? (Assume that the bowl’s weight is negligible compared to that of the fish.)

9. A metal ball hangs from a string. It is lowered into a beaker of liquid so that it is completely submerged. As it is lowered, it is noticed that the string tension decreases by 3.4 N .  Find the radius of the ball if it is immersed in alcohol of density 806 kg/m³.

10. A helium balloon and its cargo weigh 1,370 N when completely empty (no helium). What diameter of the balloon (assumed spherical) is needed if it is just to be able to lift the balloon’s weight?  The density of helium is 0.18 kg/m³.

11. A sample of copper is being very accurately weighed by an analytical chemist. The very precise scale being used records the mass as 1.1200 g.  What is the sample’s actual mass? (Hint: The sample displaces its volume of air....)