Physics Chapter 13

36. The top floor of a building is 20 m above the basement. Show that the water pressure in the basement is nearly 200 kPa greater than the water pressure on the top floor.

Δp = ρgΔh = 1000kg/m³ * 9.8m/s² * 20m = 196 kPa

20. Why do the gondolas of the Falkirk Wheel have the same weight whether or not they carry boats?

Because a floating object displaces a weight of fluid equal to its own weight. When one boat enters a gondola, the water overflow weights exactly as much as the boat. So the water-filled gondolas always weight the same whether or not they carry boats.

8. Why isn't there a horizontal buoyant force on a submerged object?

Buoyant force is a consequence of pressure increasing with depth. Because each side of an object, the left and the right, are at the same depth, the force vectors cancel one another, so there is no horizontal buoyant force.

22. If the pressure in a hydraulic press is increased by an additional 10 N/cm2, how much extra load will the output piston support if its cross-sectional area is 50 cm2?

500 N. An additional 10 N/cm2 means an additonal 10 N on each square centimeter. Since P= F/A, we can determine the force from F = PA = (50cm2)(10 N/cm2) = 500 N

10. How does the buoyant force on a submerged object compare with the weight of the water displaced?

An immersed object is buoyed up by a force equal to the weight of the fluid it displaces. If an object is completely submerged, the buoyant force will be the same as the weight of water displaced.

84. The relative density of water, ice, and alcohol are 1.0, 0.9, and 0.8, respectively. Do ice cubes float higher or lower in a mixed alcoholic drink? Comment on ice cubes submerged at the bottom of a cocktail.

Ice cubes will float lower in a mixed drink because the mixture of alcohol and water is less dense than water. In a less dense liquid a greater volume of liquid must be displaced to equal the weight of the floating ice. In pure alcohol, the volume of alcohol equal to that of the ice cubes weighs less than the ice cubes, and buoyancy is less than weight and ice cubes will sink. Submerged ice cubes in a cocktail indicate that it is predominantly alcohol

108. Would the water level in a canal lock go up or down if a battleship in the lock sank?

If a battleship sinks into a canal lock, the water level at the side of the lock will fall. This is because while floating the ship will displace a weight of fluid equal to its own weight, but when it sinks, it will only displace its volume, which is much less due to ship's large density. Thus while floating it displaces its weight in fluid which is considerably more than the small volume of fluid it displaces once sinks to bottom of the lock.

104. A piece of iron placed on a block of wood makes the block float lower in the water. If the iron were instead suspended beneath the wood, would the wood float as low, lower, or higher? Discuss.

The block of would would float higher if the iron were suspended beneath the wood. Either way the buoyant force doesn't change since the object remains floating. The same volume of object is submerged - since the buoyant force and hence the volume of fluid displaced remains unchanged. With the iron in the water, less wood is submerged, and hence it floats higher.

78. Why is the buoyant force on a submerged submarine appreciably greater than the buoyant force on it while it is floating?

While floating, BF equals the weight of the submarine. when submerged, BF equals the submarine's weight plus the weight of the water taken into its ballast tanks. The submerged submarine displaces a greater volume of water than the same submarine floating

54. Why is blood pressure measured in the upper arm, at the elevation of your heart?

Your arm is at the same level as your heart, so when you measure your blood pressure in your arm, it will be the same as the blood pressure in your heart because they're at the same height.

48. Think about what happens to the volume of an air-filled balloon on top of water and beneath the water. Then rank the buoyant forces on a weighted balloon in water, from greatest to least, when it is: a. barely floating with its top at the surface b. pushed 1 m beneath the surface c. pushed 2 m beneath the surface

a, b, c

42. In lab you find that a 1-kg rock suspended above water weighs 10 N. When the rock is suspended beneath the surface of the water, the scale reads 8 N. a. What is the buoyant force on the rock? b. If the container of water weighs 10 N on the weighing scale, what is the scale reading when the rock is suspended beneath the surface of the water? c. What is the scale reading when the rock is released and rests at the bottom of the container?

a. 2 N b. 12 N c. 20 N

40. A 1-m-tall barrel is closed on top except for a thin pipe extending 5 m up from the top. When the barrel is filled with water up to the base of the pipe (1 m deep), the water pressure on the bottom of the barrel is 10 kPa. What is the pressure on the bottom when water is added to fill the pipe to its top?

p = ρgh = 1000kg/m³ * 9.8m/s² * 6m = 58.8 kPa

14. Is the buoyant force on a submerged object equal to the weight of the object itself or equal to the weight of the fluid displaced by the object?

The buoyant force is equal to the weight of the fluid displaced by the object.

16. Does the buoyant force on a submerged object depend on the volume of the object or on the weight of the object?

The buoyant force on a submerged object depends on the volume of the object, because at any depth, the object can displace no greater volume of water than its own volume. The buoyant force is equal to the weight of the volume of fluid displaced.

110. Suppose that you are given the choice between two life preservers that are identical in size, the first a light one filled with Styrofoam and the second, a very heavy one, filled with gravel. If you submerged these life preservers in the water, upon which will the buoyant force be ineffective? Discuss why your answers differ.

The buoyant forces on the two preservers are the same because they displace the same amount of volume.The buoyant force will be ineffective for the gravel life preserver. The reason why Styrofoam will float is because it increases your area without increased your weight. Therefore, it decreases your density and helps your stay afloat better in water.

62. A block of aluminum with a weight of 10 N is placed in a beaker of water filled to the brim. Water overflows. The same is done in another beaker with a 10 N block of lead. Does the lead displace more, less, or the same amount of water? Why do your answers differ from answers to the preceding question?

The lead displaces less water because lead is heavier than aluminum, so it takes less lead to reach 10 N than it takes aluminum to reach 10 N. If the lead has a smaller volume, than it displaces less water, no matter what it weighs.

60. A block of aluminum with a volume of 10 cm3 is placed in a beaker of water filled to the brim .Water overflows. The same is done in another beaker with a 10-cm3 block of lead. Does the lead displace more, less, or the same amount of water?

The lead displaces the same amount of water because it has the same volume as the block of aluminum. At any depth, the blocks can displace no greater volume of water than its own volume.

2. How does pressure at the bottom of a body of water relate to the weight of water above each square meter of the bottom surface?

The pressure is higher a the bottom because liquid pressure depends on depth, and the pressure at the bottom of the water is due to the weight of the water above each square meter of the bottom of the surface.

86. When the wooden block is placed in the beaker, what happens to the scale reading? Answer the same question for an iron block.

The total weight on the scale is the same either way, so the scale reading will be the same whether or not the wooden block is outside or floating in the beaker. The same goes for an iron block.

66. When you are bathing at a stony beach, why do the stones at the bottom hurt your feet less when you're standing in deep water?

When you are immersed further into the water, the buoyant force is greater. Your BF is greater because when you're deeper in water, you displace a larger volume of water. This buoyant force holds you up and decreases your pressure on the rocks.

50. You know that a sharp knife cuts better than a dull knife. Do you know why this is so? Defend your answer.

This is because the smaller the area of contact, the greater the pressure. Pressure is force divided by area, so if you decrease the area, you increase the pressure.