Physics 101 Lawrence Weinstein Homework set 1 Solutions Exercises: Chapter 2: 6: Nothing is needed to keep the asteroids moving. Objects in motion stay in motion unless a force acts on them. If there is no force acting on them, then their motion will not change. Is is also acceptable to write that "Inertia keeps them moving". 14: When your car is hit in the rear by another car, it suddenly moves forward. Your body is supported by the seat. The seat exerts a force on your body to make it move forward. If there is no headrest, then there is not much force on your head and your head will NOT move forward with the rest of your body. This means that your head moves suddenly backward with respect to the rest of your body. Ouch! A headrest will exert a force on your head to make it move forward with the rest of your body. 16: You use the brakes to slow your car to half-speed, and then take your foot off the brakes. At this time, there is very little force acting on your car. This means that it will continue with its existing motion (ie: at half speed) and gradually slow due to friction. 22: Two forces act on the monkey: 1) the force of gravity pulling down on the monkey and 2) the force of the vine pulling up on the monkey. Since the monkey is stationary, its motion is not changing. This means that the total force acting on the monkey is zero. This means that the two forces are equal in magnitude (so that their sum is zero). 26: The stage is in "mechanical equilibrium" which means that it is stationary. Therefore the total force on the stage is zero. The total upward force is 200 N + 200 N = 400 N. Therefore the total downward force must be 400 N. Since the painter weighs 250 N, the weight of the stage must be W = 400 N - 250 N = 150 N. 28: Half of Nellie's weight is supported by her left arm and half of her weight is supported by her right arm. Therefore, the scale reads half of her weight. Look at the picture on p.33 of the gymnast hanging from two rings. This is the same situation. It really does not matter that the two ropes are connected. ANother way to think about it is to envision TWO scales, one on each end of the rope. Clearly, they will show her total weight. 48: When the train is in uniform motion along a straight line, the vertically tossed coin will have the same horizontal speed that you do and will therefore land in your lap (or on your hand). If the train slows when the coin is in the air, then the coin will have a larger horizontal speed than the train and it will land in front of you. If the train turns to the right, you will also turn to the right. However, the coin will continue moving in a straight line and will therefore land to the left of you. __________________________________________________________ Problems: 1) Which of the following statements could be scientific hypotheses (ie: are falsifiable)? If a statement is falsifiable, indicate a test that the hypothesis could fail. If the statement is not falsifiable, explain. 1. Putting magnets on your body will improve your energy fields. This is NOT falsifiable and hence not a scientific hypothesis. 'Energy fields' are one of those scientific sounding but actually meaningless phrases that bogus medicine delights in. Since the term is meaningless, it cannot be measured and therefore the hypothesis does not make a testable prediction. 2. Putting magnets on your body will reduce muscle aches and pains. This is a scientific hypothesis because it makes a measurable prediction and therefore you can test it. Pain is definable and measurable (if only by people reprting how they feel). Find some people with muscles aches and pains. Put magnets on half of them and see how they feel in a week. Compare that to how the other half feel in a week. (In practice you want to be sneakier than that. Put real magnets on half of them and put fake magnets on the other half. That way all of the subjects feel like they're being given the 'special' treatment.) 3. Breaking a mirror causes seven years bad luck. This is a scientific hypothesis, although you will need to define 'bad luck'. One possible way to test it would be to take 1000 people and get a life history of their past ten years. Find out which ones had broken mirrors. Show the life histories to a group of judges and ask them to judge which ones had 'Bad luck'. See if the ones chosen by the judges were the same people who had broken a mirror. 2) Unit Conversions: a) inches in a kilometer: 1 km = 1 km (1000 m / 1 km) * (39.37 inches / 1 m) = 39370 inches = 3.937*10^4 in Note: Since this is an exact number, I will accept any answer with at least two significant figures. b) Square inches in a square kilometer: (1 km)^2 = 1 km^2 * (1000 m / 1 km) * (1000 m / 1 km) * (39.37 inches / 1 m) * (39.37 inches / 1 m) = 1.55*10^9 in^2 c) Seconds per month. Month is not well defined since it can be anywhere from 28 to 31 days. I'll use 30 days (or 3.0*10^1 in scientific notation to show that it has two significant figures). 1 month = 1 month * (30 days/month) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute) = 2.6*10^6 s --------------------------------------------------------- Estimation 1: Chapter 1 Estimation: Your chance of winning MegaMillions is about 1 in 10^8 (ie: one in one hundred million). This is the same probability as drawing the only correct card from a deck with 10^8 cards. If you stacked 10^8 cards in a single pile, how tall would that pile be (in meters)? Which distance is this closest to: a) a tall building (100 m), b) a small mountain (1000 m), c) Mt Everest (10,000 m), d) the height of the atmosphere (10^5 m), e) the distance from here to Chicago (10^6 m), f) the diameter of the Earth (10^7 m), g) the distance to the moon (4x10^8 m)? Answer: We need to know the thickness of one lottery card. There are several ways to do this. You can look at a ruler and estimate the thickness of one card. If I do this, I will get about 1/50 of an inch. But I am not very good at estimating the thickness of a single card (is it 1/16" or 1/64"?) so I'll try to estimate the thickness of a pack. One ream of copier paper (500 sheets) is about 1.5 to 2" (or about 4-5 cm). About 100 sheets of lined paper is about 0.5" (or about 1 cm), but paper is thinner than lottery tickets. A pack of 52 playing cards is also about 1 cm. That's probably closer. This means that the thickness of one ticket is t = 1 cm / 52 = 0.02 cm * (1 m / 100 cm) = 2*10^(-4) m Thus, the thickness of 10^8 tickets is T = 2*10^(-4) m * 10^8 = 2*10^4 m or 20 km If stacked horizontally, it would take you four or five hours to walk that far. If stacked vertically, it would be twice as high as Mt Everest (30,000 ft or 10,000 m or 10 km) and twice as high as jumbo jets fly. All answers within a factor of 5 are good enough (ie: between 4*10^3 m and 1*10^5 m). All answers with more than two significant figures will lose one point. (Even 2 significant figures is too many. You can't estimate the thickness of a lottery ticket that accurately.)