Conceptual Physics Chapter 13

15. What is the condition in which the buoyant force on an object does equal the weight of the object?

When an object floats, its buoyant force equals its weight.

75. Why will a volleyball held beneath the surface of water have more buoyant force than if it is floating?

When the ball is held beneath the surface, it will displace a greater weight of water.

59. The sketch shows a wooden reservoir reinforced with metal hoops that supplies water to a farm. (a) Why is it elevated? (b) Why are the hoops closer together near the bottom part of the tank?

(a) The reservoir is elevated so as to produce suitable water pressure in the faucets that it serves. (b) The hoops are closer together at the bottom because the water pressure is greater at the bottom. Closer to the top, the water pressure is not as great, so less reinforcement is needed there.

61. A block of aluminum with a mass of 1 kg is placed in a beaker of water filled to the brim. Water overflows. The same is done in another beaker with a 1-kg block of lead. Does the lead displace more, less, or the same amount of water?

A 1-kilogram block of aluminum is larger than a 1-kilogram block of lead. The aluminum therefore displaces more water.

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

A sharp knife cuts better than a dull knife because it has a thinner cutting area which results in more cutting pressure for a given force. Pressure is force divided by area, so if you decrease the area, you increase the pressure.

23. What geometrical shape has the smallest surface area for a given volume?

A sphere has the smallest surface area for a given volume.

91. We say that the shape of a liquid is the same as the shape of its container. But, with no container and no gravity, what is the natural shape of a blob of water? Why?

Because of surface tension, which tends to minimize the surface area of a blob of water, its shape without gravity and other distorting forces is a sphere—the shape with the smallest surface area for a given volume.

9. How does the volume of a completely submerged object compare with the volume of water displaced?

Both volumes are the same.

7. Why does buoyant force act upward on an object submerged in water?

Buoyant force acts upward because there is more force beneath an object due to greater pressure at greater depth.

67. If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? Explain.

Buoyant force is the result of differences in pressure; if there are no pressure differences, there is no buoyant force. This can be illustrated by the following example: A Ping-Pong ball pushed beneath the surface of water will normally float back to the surface when released. If the container of water is in free fall, however, a submerged Ping-Pong ball will fall with the container and make no attempt to reach the surface. In this case there is no buoyant force acting on the ball because there are no pressure differences—the local effects of gravity are absent.

39. A 12-kg piece of metal displaces 2 L of water when submerged. Show that its density is 6000 kg/m3. How does this compare with the density of water?

Density = m/V = 12kg/2L = 6 kg/L (Since there are 1000 liters in 1 cubic meter, density may be expressed in units kg/m^3.) Density = 6 kg/L X 1000 L/m^3 = 6,000 kg/m^3 (That's six times the density of water.)

21. What happens to the pressure in all parts of a confined fluid if the pressure in one part is increased?

If the pressure in one part is increased, the same increase in pressure is transmitted to all parts.

89. A small aquarium half-filled with water is on a spring scale. Will the reading of the scale increase or remain the same if a fish is placed in the aquarium? (Will your answer be different if the aquarium is initially filled to the brim?)

If water doesn't overflow, the reading on the scale will increase by the ordinary weight of the fish. However, if the aquarium is brim filled, so that a volume of water equal to the volume of the fish overflows, then the reading will not change. We correctly assume here that the fish and water have the same density.

3. What is the relationship between liquid pressure and the depth of a liquid? Between liquid pressure and weight density?

Liquid pressure is proportional to depth and to weight density.

57. If water faucets upstairs and downstairs are turned fully on, will more water per second flow out of the upstairs faucets or the downstairs faucets?

More water will flow from open faucets downstairs because of the greater pressure. Since pressure depends on depth, a downstairs faucet is effectively "deeper" than an upstairs faucet. The pressure downstairs is greater by an amount = weight density × depth, where the depth is the vertical distance between faucets.

35. The depth of water behind the Hoover Dam is 220 m. Show that the water pressure at the base of this dam is 2200 kPa.

Pressure = weight density X depth = 10,000 N/m^3 X 220 m = 2,200,000 N/m^2 = 2,200 kPa

1. How does pressure relate to force?

Pressure is force per area.

79. Will a rock gain or lose buoyant force as it sinks deeper in water? Or will the buoyant force remain the same at greater depths? Defend your answer.

The buoyant force will remain unchanged on the sinking rock because it displaces the same volume and weight of water at any depth.

70. A can of diet soda floats in water, whereas a can of regular soda sinks. Explain this phenomenon first in terms of density and then in terms of weight versus buoyant force.

The diet drink is less dense than water, whereas the regular drink is denser than water (water with dissolved sugar is denser than pure water) also, the weight of the can is less than the buoyant force that would act on it if totally submerged. So it floats, where buoyant force equals the weight of the can

87. One gondola in the Falkirk Wheel carries a 50-ton boat, while the other carries a 100-ton boat. Why do the gondolas nevertheless weigh the same?

The gondolas weigh the same because they're brim full, and whatever the weight of a floating boat, that same weight of water was displaced when the boat entered the gondola.

51. Which is more likely to hurt: being stepped on by a 200-lb man wearing loafers or being stepped on by a 100-lb woman wearing high heels?

The pressure of the woman is appreciably greater because of the relatively small area of contact at the heel, which would hurt you more.

5. How does the water pressure 1 m below the surface of a small pond compare with the water pressure 1 m below the surface of a huge lake?

The pressures are the same at the same depth.

85. When an ice cube in a glass of water melts, does the water level in the glass rise, fall, or remain unchanged? Does your answer change if the ice cube has many air bubbles in it? How about if the ice cube contains many grains of heavy sand?

When the ice cube melts, the water level at the side of the glass does not change (ignoring temperature effects). To see this, suppose the ice cube is a 5-gram cube; while floating, it displaces 5 grams of water. But when melted, it becomes the same 5 grams of water. Hence the water level is unchanged. The same occurs when the ice cube with the air bubbles melts. Whether the ice cube is hollow or solid, it displaces as much water floating as when melted. If the ice cube contains grains of heavy sand, however, upon melting, the water level at the edge of the glass drops.

81. The density of a rock doesn't change when it is submerged in water, but your density changes when you are submerged. Explain.

You are compressible, whereas a rock is not, so when you are submerged, the water pressure tends to squeeze in on you and reduce your volume. This increases your density. (Be careful when swimming—at shallow depths you may still be less dense than water and be buoyed to the surface without effort, but at greater depths you may be pressed to a density greater than water and you'll have to swim to the surface.)

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

Your upper arm is at the same level as your heart, so the blood pressure in your upper arms will be the same as the blood pressure in your heart.

17. Fill in the blanks: An object denser than water will _______ in water. An object less dense than water will _______ in water. An object that has the same density as water will ______ in water.

sink; float; neither sink nor float