Due Monday, November 13, 1995, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1: (Case 2 from Chapter 6)
Your room in the dormitory is particularly cold at night. Here are several things that you decide to do to make life more comfortable.
(A) You tape sheets of clear plastic across the windows of your room. Why do these plastic sheets make the room warmer?
Answer: By making heat pass by convection to the plastic, by conduction through the plastic, and by convection from the plastic to the window, the sheets slow the flow of heat from the room to the cold outside air.
Why: Each impediment that heat encounters as it flows from a hot object to a cold object slows down that flow. By adding the plastic sheeting, you require the heat to pass through one more surface (conduction barrier) and one more convection cycle (convection barrier).
(B) You install curtains on the windows and draw them at night. How do the drawn curtains make your room warmer?
Answer: By making heat pass by convection to the curtains, by conduction and convection through the curtains, and then convection to the window, the curtains slow the flow of heat from the room to the cold outside air. The curtains also block direct transfer of heat by radiation.
Why: The curtains are even more insulating than the plastic sheets because they block radiation and they themselves are extremely poor conductors of heat. They trap air and use it an a thermal insulator.
(C) Your room has a high ceiling. You install a ceiling fan to push the air downward from the ceiling. Why does the fan make the air warmer near the floor?
Answer: It pushes the warm air near the ceiling back down toward the floor.
Why: Warm air rises on cool air, so that the air near the ceiling is naturally warmer than the air near the floor. By blowing that warm air back down toward the floor, the fan keeps you warmer.
(D) You put a thick, down comforter or quilt on your bed. Describe in terms of heat flow how the comforter keeps you warm in bed.
Answer: By making heat pass by convection, conduction, and radiation to the comforter, by conduction and convection through the comforter, and then by convection into the room, the comforter slows the flow of heat from you to the room. The comforter also blocks direct transfers of heat by radiation.
Why: The comforter acts like the curtains on the window. Since the comforter is thick and filled with down, it uses trapped air as its main insulator and slows the heat transfer enormously.
(E) You put an electric blanket on the bed. It uses electricity to make heat inside the blanket itself. How does this heat flow from the electric blanket to you?
Answer: By conduction and radiation.
Why: Heat can't flow downward to you by convection because heated air rises. The main heat transfer mechanisms are thus conduction (where you touch the blanket) and radiation (everywhere else). The blanket does inhibit the convection that would normally take place between your warm skin and the colder covers above you. By warming those covers, the blanket slows or stops convection.
Question 2: (Case 1 from Chapter 6)
Glass transmits the visible light radiated by the white hot sun but it absorbs the infrared light radiated by objects near room temperature. This selective absorption and transmission gives rise to the "greenhouse effect".
(A) A small patch of garden is bathed in sunlight. The sun is transferring heat to this garden by radiation but its temperature remains essentially constant. Why doesn't the garden get hotter and hotter?
Answer: It warms up until it is able to lose heat as quickly as heat arrives.
Why: The garden's temperature stabilizes when the net heat flow into it drops to zero. That occurs when the garden loses heat as quickly as it receives heat.
(B) If you cover the garden with a glass dome, what happens to the garden's ability to get rid of heat via radiation?
Answer: The garden has difficulty eliminating heat via radiation.
Why: The glass absorbs some of the infrared light emitted by the garden and reemits thermal radiation, some of which returns to the garden.
(C) How does the glass dome affect the garden's temperature?
Answer: It raises the garden's temperature
Why: By returning some of the garden's thermal radiation back to the garden, the glass makes it harder for the garden to eliminate heat. The garden's temperature rises until it is able to eliminate heat as rapidly as heat arrives.
(D) Like glass, molecules such as water vapor, carbon dioxide, and methane transmit visible light while absorbing some infrared light. How does the presence of these molecules in the earth's atmosphere affect the earth's ability to get rid of heat and the earth's temperature?
Answer: They make it more difficult for the earth to eliminate heat and thus raise its temperature.
Why: Without the atmosphere, the earth's temperature would rises only until it radiates away heat as quickly as heat reaches it from the sun. But with the atmosphere, some of the earth's thermal radiation is returned to the earth by molecules in the atmosphere. The earth's temperature must then rise even higher before it begins to lose heat as quickly as heat arrives.
(E) Why are people concerned about a large increase in the amount of carbon dioxide in the atmosphere?
Answer: It will raise the average temperature of the earth.
Why: By impeding the loss of heat by the earth's surface, the carbon dioxide will raise the earth's average surface temperature.
Question 3: (Case 4 from Chapter 6)
Baking a potato takes a long time, even in a hot oven, because the inside of a potato warms up very slowly.
(A) What makes it hard for conduction to transfer heat to the center of the potato?
Answer: The potato is a poor conductor of heat because it has no mobile electrons.
Why: Since the potato is essentially nonconducting (it has few mobile electrons and doesn't conduct electricity well at all), the potato can only conduct heat via the atom by atom bucket brigade. Heat flows slowly to the center of the potato via this mechanism.
(B) What makes it hard for convection to transfer heat to the center of the potato?
Answer: Although the potato contains lots of water, that water is trapped in cells and cannot undergo convection. Heat flows slowly to the center of the potato via this mechanism.
Why: The potato, like many plant materials, contains lots of trapped water that can't undergo convection.
(C) What makes it hard for radiation to transfer heat to the center of the potato?
Answer: Light cannot go directly from the outside of the potato to its center, but must instead go in tiny steps from one layer of the potato to the next to the next. Heat flows slowly to the center of the potato via this mechanism.
Why: The potato blocks thermal radiation at every step along the way. Thermal radiation does participate in the heating processes, but it moves only short distances before being absorbed and must then be reemitted over and over again.
(D) Why does inserting a metal skewer through the potato help it to cook quickly?
Answer: The skewer is an excellent conductor of heat (a metal with mobile electrons) and carries it quickly into the center of the potato from outside.
Why: The skewer, which has mobile electrons to carry heat through it, provides an alternate path for heat to enter the potato and flow to its center. The skewer dramatically shortens the time it takes for the potato's center to become hot.
(E) Why does a baked potato stay hot inside for such a long time, even when it's sitting on your plate?
Answer: It is such a poor conductor, convector, and radiator of heat that it not only cooks slowly in a hot environment, it also loses heat slowly in a cold environment.
Why: Anything that heats poorly when you put it in a hot environment (and is thus a good insulator) also cools slowly when you put it in a cold environment. It doesn't matter which way heat is flowing; it flows poorly through an insulator.
Question 4: (Case 2 from Chapter 5)
Modern Olympic Athletes are aided by a variety of scientific advances. Here are a few examples of how science enhances performance in athletics.
(A) A ski-jumper is suspended in a wind-tunnel, where a device measures the horizontal and vertical forces on him as air flows past. The jumper arranges his body to obtain the most favorable forces for a long flight. Describe the most favorable horizontal and vertical forces.
Answer: As little drag as possible and as much lift as possible.
Why: The only horizontal force that the jumper experiences is drag, which slows the jumper down. Minimizing this drag will allow the jumper to travel farther. The two vertical forces on the jumper are weight and lift. By maximizing the lift, the jumper is able to fly through the air and travel farther. However, lift gives rise to induced drag, so that there are limits to how perfect the jump can be. It's a careful balance act.
(B) In cross-country skiing, the skier slides forward first on one ski and then on the other. The ski bottoms are coated with special waxes so they exhibit large static frictional forces on snow but small dynamic frictional forces. How does this difference in frictional forces allow the skier to use a stationary ski to push herself forward on a sliding ski?
Answer: The skier needs a net forward force, so by obtaining a larger forward static frictional force from a stationary ski and a smaller backward sliding (dynamic) frictional force from a forward-moving ski, the skier is able to accelerate forward.
Why: If both skies experienced equal but oppositely directed sliding frictional forces, the skier would experience no net force and wouldn't accelerate. It's only by obtaining a stronger forward force than backward force that the skier is able to propel forward.
(C) Modern tracks are often constructed out of recycled rubber tires. The track surface is very resilient, deforming slightly when you push down on it and then bouncing back when you stop pushing. How does this surface improve runners' times as compared to the dirt, gravel, or cinder tracks of long ago?
Answer: The surface returns most of the runner's energy after each step on the track and thus doesn't slow the runner down as much as a dirt, gravel, or cinder track.
Why: A soft track is important to the runner because it reduces injuries. If the runner were to run on a concrete track, the runner might well damage bones and tissue during each step because of the enormous forces involved in the impact. A softer track slows the accelerations and reduces the forces involved, thus avoiding injuries. But if the track doesn't return the energy that it obtains during the impact, the runner must effectively lift him/herself out of the track with every step. That lifting uses energy that would otherwise be used for forward propulsion.
(D) Bicyclists now use aerodynamically designed bicycles and clothing to minimize air drag. Bicyclists also "draft" one another, a strategy where one bicycle follows immediately behind the previous bicycle, easing the rear bicycle's passage through the air. If the front bicycle were so aerodynamic that it experienced no air drag at all, how would this affect the strategy of drafting and why?
Answer: Drafting would be useless if the first bicyclist didn't experience any drag because the first bicyclist would leave the air motionless behind him/her and the second bicyclist would not experience any effect of following the first bicyclist.
Why: Drafting only works because the first bicyclist pulls the air along with him/her. The second bicyclist has an advantage if he/she follows the first bicyclist in this forward-moving air pocket. The second bicyclist then experiences less drag because he/she is riding in forward moving air. If the first bicyclist doesn't experience any drag, then the air isn't being dragged along forward and the second bicyclist isn't experiencing any drag reduction.
(E) The wind is monitored during races so that a record time is labeled as "wind assisted" if the runner experienced a tail wind that was above a certain limit. Use physics to explain why a tail wind gives a runner a time advantage.
Answer: If you run in a forward-pointing wind, then you will experience either a forward drag force or a less-severe backward drag force. This diminished air resistance will help you to run faster.
Why: When you run through motionless air, you drag is along with you and experience a slowing effect. But if that air was already moving with you, you don't have to exert as much force on it to drag it along and are less taxed by the experience.
Question 5: (Case 1 from Chapter 5)
You are consulting for a screenwriter who is working on a science-fiction movie about the crew of a large, intergalactic spaceship. She wants the script to be realistic from a scientific perspective so she has asked you to check her work so far. You read through the script, which includes descriptions of special effects, and quickly find several problems with it. Here are some of the scenes that have flaws.
(A) In one scene, the spaceship must make an abrupt left turn to avoid hitting an asteroid. The crew members stand anxiously but motionlessly on the command bridge during this maneuver. In reality, what should happen to the crew members?
Answer: They would be thrown toward the right.
Why: If the ship accelerates left (turns left), the people will need forces to make them follow the ship. If they are only standing on the floor, they are likely to travel in straight lines instead and will appear to fly to the right as the ship accelerates leftward out from under them.
(B) In another scene, a guard fires a peculiar weapon at a massive alien creature. The guard does not move, but the creature is thrown backward when the weapon hits. In reality, what should happen to the guard as he fires the weapon?
Answer: The guard should also be thrown backward as he fires the weapon.
Why: The creature evidently received lots of momentum from the projectile when it hit so the projectile must have obtained that momentum from somewhere. It most likely obtained that momentum from the guard during firing, so the guard must have been left with lots of momentum in the opposite direction. Thus the guard should have flown backward. The only exception would be a rocket-propelled projectile, which obtained momentum by throwing gas backward.
(C) The main spaceship carries several small fighter spacecraft that resemble high-tech modern military fighter aircraft. In the depths of space, these fighter spacecraft dodge and turn rapidly, even though the rocket exhaust is always sent straight out of the rear of the fighter. Why can't such a spacecraft turn in space while a similar aircraft can turn near the ground?
Answer: An aircraft pushes on the air in order to turn but, in space, the spacecraft has no air to push against.
Why: An aircraft can dodge left or right by using lift to accelerate it around a turn. It tips its inside wing downward and then uses lift (now directed partly in the direction of the turn) to make it accelerate sideways. In space, there is no air to push against so the spacecraft must use rocket exhaust instead.
(D) One of the small spacecraft secretly shuttles supplies from one earth-like planet to another, completing 8 round trips without replenishing its chemical rocket fuel. You inform the writer that the spacecraft will have trouble leaving a planet even once using chemical rockets, unless that spacecraft is allowed to eject stages. Why are you right?
Answer: To reach escape velocity from a planet, a chemical rocket must eject most of its mass backward as rocket exhaust. There is no way to eject all but 5% of a rocket's mass many times in a row without refueling.
Why: To escape from a planet, a spaceship must eject the vast majority of its mass as rocket exhaust. It can't even take the fuel tanks with it during this process, so it jettisons those tanks along the way. To take off and land many times without jettisoning anything or refueling is completely out of the question.
(E) Near the end of the script, a main character falls from a cliff but is rescued only 2 meters from the ground when she lands on the wing of a passing spacecraft. You inform the writer that the impact with the wing of the spacecraft would be just as fatal as one with the ground. Why is that the case?
Answer: Once the woman is moving downward at high speed, there is no hope of stopping her from hitting the ground without injuring her just as severely. The sudden upward acceleration requires forces that are too large for her to withstand.
Why: The ground will injure the woman because it accelerates her upward too suddenly and with too large forces. The same will occur when she lands on the wing of the spacecraft. Whether she hits the ground or the wing, she's in trouble. Her only hope is if you quickly dig a hole under her and then slow her to a stop gradually, with small forces.