### Chapter 11

#### Questions:

1) Explain how the law of definite proportions supports the atomic theory.

Answer: The law of definite proportions states that a given compound (or molecule) will always have the same proportions by mass of the original ingredients. The atomic theory supports the fact that the atoms that makes up a molecule have different masses, so that a molecule will always have a definite mass proportion between the constituent atoms.

2) How does Brownian motion support the atomic theory.

Answer: By noticing that pollen floating on still water does not stand still, Einstein was able to say that in fact the water molecules must be moving and colliding with the pollen grain. Because the movement of the pollen grain can be seen, and an estimate of the pollen grain's mass can be made, a size and mass of the invisible molecules could be determined.

3) What is the principal factor that determines whether the atoms or molecules of a particular substance will form a solid, liquid, or gas at ordinary temperatures?

Answer: The strength of the forces between the atoms or molecules of the substances controls this. If the atoms or molecules are only loosely held together, then the substance will probably be a gas. If the atoms or molecules are held together more firmly, then it will probably be a liquid, and if the forces are very strong, then the atoms or molecules will be held together rigidly as a solid.

5) A kilogram of cotton compared to a kilogram of iron (a) weighs more (b) weighs less (c) has greater density (d) has less density (e) has the same density?

Answer: A kg is a kg and it has the same weight, 9.8N. The cotton has a much smaller density, so will take up a much larger volume.

6) If one material has a greater density than another, does this mean that molecules of the first are necessarily heavier? Explain.

Answer: No. Density depends on how tightly packed matter is. A light atom or molecule can be tightly packed as a solid and have a high density, and a heavy atom or molecule can be lightly packed as a gas and have a low density.

7) It is sometimes said that heavy objects sink. Is this an accurate statement? Explain.

Answer: It is not the heaviness that makes an object sink, but rather it's density. If the object has a density which is less than the liquid, it will float; if the object has a density greater than the liquid, it will sink.

8) Which has the greater mass, one cubic meter of ice or one cubic meter of water?

Answer: The cubic meter of water has more mass. Ice has a smaller density than liquid water (it floats). For the same volume, since the water is more tightly packed than the ice, more water mass can fit in the volume.

9) Which has a greater volume, 10 kg of iron or 10 kg of water?

Answer: The water will have greater volume. The density of iron is greater than water (it sinks) so the mass of iron is more tightly packed than water. It will not need as much volume to make 10kg as the water will.

#### Exercises:

3) What is the specific gravity of a material whose density is ?

7) What is the volume of 100kg of aluminum?

Answer: To answer this, we need the density of aluminum, . Then the volume is found by using

10) How many kilograms of air are there in a bedroom 3m x 4m x 3m?

Answer: We first need the volume of the bedroom, , then with the density of air , the mass of air in the room is

12) The approximate volume of the granite monolith, known as El Capitan, in Yosemite National Park is about 108m3. What is the approximate mass?

Answer: We need to use the denisty of granite, in order to find the mass of El Capitan.

### Chapter 12

#### Questions:

1) Consider what happens when you push both a pin and a stick against your skin with the same force.

Answer: A pin will make contact with a much smaller area of your skin than the stick will. Consequently, the pressure developed under the pin will be much greater than the pressure developed under the stick. It is possible that the pressure is enough to break your skin in the case of the pin, but not in the case of the stick.

3) Where is the pressure greater, at the bottom of a 1cm diameter glass tube 2m high filled with water or at the bottom of a lake 1m deep?

Answer: The water pressure will be greater in the glass tube. The water is 2m deep in the glass tube, but only 1m deep in the lake. The pressure increases with increasing depth.

6) It is sometimes said that heavy objects sink. Is this an accurate statement? Explain.

Answer: How heavy an object does not determine whether it sinks or floats. For example, a giant tree will float down the river, and a relatively light stone will sink. The important parameter is the average density of the object. If the average density is less than the liquid density then it will float. If the average density is greater than the liquid, it will sink.

7) Why is it easier to float in salt water than in fresh water?

Answer: Because saltwater has a higher density than fresh water, your body will displace a greater mass of saltwater than of freshwater. The buoyant force is the weight of the liquid displaced, so the greater the mass displaced, the greater the weight and the greater the buoyant force.

11) It is harder to pull the plug out of the drain of a full bathtub than an empty one. Why? Is this a contradiction of Archimede's principle?

Answer: The weight of the water above the plug causes extra pressure on the plug. In order to lift the plug, you must exert a force equal to the weight of the water above the plug. Obviously when the tub is empty this weight is not present. This does not contradict Archimedes principle, because one side of the plug is exposed to the air in the pipes, while the other side is in liquid. If the plug is completely in the water, it will feel a little lighter just as the Archimede's principle predicts.

12) When you are wading on a rocky beach, why do the rocks hurt your feet less when you are in deeper water?

Answer: When you are in deeper water, you are displacing more water, so the buoyant force on you (equal to the weight of the displaced water) will be larger. This means that the rocks will not need to exert as much force to hold us up, and will not hurt as much.

15) An ice cube floats in a glass of water filled to the brim. As the ice melts, does the water overflow? (Try this at home)

Answer: No the water will not overflow. The water level in the glass rises as you put the ice cube in the glass. The amount of water displaced (and the amount by which the level rises) has a mass equal to the mass of the ice in order to keep it floating. When the ice melts, it will shrink a little, and will take up the same amount of space as the water that was originally displaced.

24) Why does the canvas top of a convertible bulge out (up) when a car is traveling at high speeds?

Answer: Because of Bernoulli's principle, which states that the higher the air speed, the lower the pressure will be. The air in the car is not moving, so the pressure in the car is atmospheric pressure. Outside the car (above it), the air is rushing by and so the pressure will be lower. The canvas top is pushed upwards because the pressure in the car is greater than the pressure directly above the car.

#### Exercises:

2) What is the pressure due to water 3.0 m below the surface of a lake?

Answer: The pressure underneath the lake will be greater than the pressure at the lake's surface (atmospheric pressure) by an amount equal to .

4) What is the water pressure at a faucet if the water comes from a storage tank whose water level is 20 m above the faucet?

Answer: The pressure from the 20 m high column of water is just . This is about twice atmospheric pressure. (Remeber the rule of thumb: for every 10m of depth, there is an additional atmosphere of pressure from the water)

8) What is the difference in blood pressure between the top of the head and the bottom of the feet of a 1.60 m tall person standing erect? The density of whole blood is .

Answer: The difference in pressure is again just

19) A moon rock weighs 22.5 N in air but has an apparent weight of 16.8 N when submerged in water. (a) What is the buoyant force on the rock? (b) What must its specific gravity be?

Answer: (a)The buoyant force works against the force of gravity to make the object "feel" lighter. The amount by which the weight changes is the buoyant force. The buoyant force is: . (b) The specific gravity is the ratio of the density of the object , but it can also be found in practice by taking the ratio of the weight in air of the object to the buoyant force when the object is completely submerged. In this case, .