#5 #7 #12 #32 #33 #38 #41 #43 #51 #545. Gold and silver have densities of 19.3 and 10.5 grams per cubic centimeter, respectively. If you have equal masses of each, which one will occupy the larger volume?
Recall that the density of an object is its mass divided by its volume. If we have equal masses of gold and silver, the volume each occupies will be the mass times its (volume per unit mass) or mass divided by density, for that material. Since the starting masses are equal, but the density of gold is greater than silver, the volume occupied by the silver will be larger.
7. Why do pop bottles break when the pop freezes?
Most of the content of soda is water. Water is a unique material because its density as a solid is less than its liquid density. This is due to the crystal structure of ice. Since its density decreases with freezing, its volume must increase. The volume of the pop bottle does not increase along with the ice, so it breaks.
12. How do true solids and liquid solids differ?
A true solid has molecules arranged in a definite and regular fashion called a crystal structure. A liquid solid has molecules that are "frozen" into place when it cools without any real order to their arrangement.
32. What must happen to the area of a tire touching the ground if you reduce the pressure?
The weight of the car is supported on the ground by the force applied by the tires. This force is supplied to the contact area of each tire by the pressure of the air inside the tire. Recalling that pressure equals force divided by area, if pressure decreases while force is constant, the contact area must increase.
33. Why doesn't atmospheric air pressure collapse a balloon?
The atmospheric air pressure outside a balloon is balanced by the gas pressure inside the balloon.
38. Salt water is denser than fresh water. This means that the mass of 1 cubic centimeter of salt water is larger than that of 1 cubic centimeter of fresh water. Would a scuba diver have to go deeper in salt water or fresh water to reach the same pressure?
The pressure that a diver feels is the pressure of the atmosphere plus the weight of the column of water above the diver. The weight of the column of water is its mass multiplied by the acceleration of gravity. The mass of the water columns must be equal for the diver to feel the same pressure. Since the density of fresh water is less than that of salt water, the volume of the fresh water column must be larger than the salt water column. As the area of the diver is constant, the diver must go deeper in fresh water to have equal mass and so equal pressure.
41. Why can't water be "sucked" to a height greater than 10 meters even with a very good suction pump?
Water rises in a "tube" when the air is sucked out of the top because of the unbalanced force from atmospheric air pressure at the other end. Taking the areas as equal throughout the tube, the maximum height that can be reached occurs when the weight of the water column equals the air pressure times the cross-sectional area of the tube. The weight of the water column is equal to the density of water times the height of the column times its cross-sectional area times the acceleration of gravity. So, the height of the column equals atmospheric pressure divided by the density of water and divided by the acceleration of gravity. Using atmospheric pressure as 101,000 kPa and the density of water as 1 g/cc = 1000 kg/cubic meter, the maximum height of the column is about 10 m.
43. When will a helium balloon stop rising in the atmosphere?
An object has a net upward force due to buoyancy as long as its mass is less than the equivalent mass of the fluid it displaces. Another way of saying this, if we divide by the volume of the object, is that its average density is less than that of the fluid it is in. So, the helium balloon will stop rising when its average density equals that of the air at its altitude.
51. An ice cube is floating in a glass of water. Will the water level in the glass rise, go down, or stay the same as the ice cube melts?
It will stay the same. A floating object displaces a volume of fluid having a mass equal to itself. In this case, our floating ice cube will end up as liquid water as it melts. So, the space it will occupy is exactly the volume needed for its mass after it melts.
54. Why does your car get pulled sideways when a truck passes you going in the opposite direction on a two-lane highway?
A truck moving in the opposite direction in the lane next to your car causes the air on that side to have a higher relative velocity than the air on the side away from the truck. From Bernoulli's principle, the air pressure on the side by the opposing truck is lower. The higher pressure on the side away from the truck then yields a net force toward the passing truck.