Hewitt asks you to outline the steps of the scientific method. Rather than do this (because there is no one scientific method), summarize what makes any scientific process "scientific." In other words, describe what makes scientific knowledge different from other kinds of knowledge.
Science is probably best described by two things: The questions it can ask, and the way it proposes answers. First, science can ask questions for which nature herself provides evidence. We can ask about the mechanics of nature, such as "How does a rock fall down?" However, we can't ask questions of nature that we can't test in a repeatable way by looking at evidence. An example of such a question might be, "Why am I here?" It's probably a very thoughtful question, but it isn't one that nature reliably gives you data for.
When we do get explanations from science, they should refer to actual events and observations that nature provides, and they should be testable. It should always be possible from a scientific test for one of our explanations to be proven wrong. Thus, when we drop a rock, we are testing to see if gravity is still behaving in the same manner. You can never prove that a scientific explanation is correct, but you can show which ones are incorrect. The explanation that survives (so far) the most number of tests and provides the most applicable description of nature is the one that we use.
If you compared your view of the sky in St. George, UT to that in Ogden, UT, how could you tell that the Earth is round? Hewitt describes a similar situation with Eratosthenes in Chapter 1.
From different points on Earth, you should have a different view of the sky. There are many ways to draw this and many examples to give. Whatever your explanation, you should show that pretty much everything that we see out in space is very far away, yet everyone on Earth points a different direction in order to face one particular object. This is because everyone's "up" and "down" is measured relative to where they stand on the planet. The curvature of the Earth makes us all face a different direction in space, so comparing observations between different observers should reflect this.
Aristotle (~350 BC) and Galileo (~1600 AD) both described motion. How would they differ in describing what causes the following motions and how the motions will continue:
a. A puck sliding across a frictionless ice sheet
Aristotle would say this is a violent motion, and that there must be some force or impetus continually poking at the puck in order to keep it moving. Galileo would claim that this constant motion is a natural tendency of all objects, and that it will remain in this motion in a straight line until something gets in the way.
b. A bowling ball falling out of the sky
Aristotle might claim that the bowling ball, being made mostly of Earth, is simply trying to return to its natural state -- the earth itself. Since the bowling ball has a large amount of earth in it, it probably returns very quickly to the Earth. Galileo instead says that all objects fall at exactly the same rate, accelerating faster and faster on their way down. How this happens is a question that isn't answered until Newton.
Runaway bowling
ballA previous class of PHSX 1010 students recorded the position and time of a bowling ball rolling across a parking lot. They made the table of data at right. Using graph paper or a graph that you make yourself, plot this table of data. Describe the motion of the bowling ball, paying special attention to its velocity and its acceleration as it rolls away.
As you might have imagined, the data that a group of physics students collects for a rolling bowling ball can be a little bit messy. But, this is just part of the scientific process; it doesn't always come out as neat and clean as it looks in a textbook. (You might be asking: "Did you really collect this data in another class?" The answer is "yes." I am just that cruel to my students.)
Once you produce this graph, the data shows some patterns that can be filled in. For example, most of the graph shows some very constant motion, as traced out with the red line (see below). This means the bowling ball has a constant velocity moving away from some start point. This also means that the acceleration is zero during this phase of the motion. After the red line, it looks as though there was an increase in velocity (more distance covered per time), followed by a decrease in velocity. (That's where the graceful professor caught up to the bowling ball and stopped it.) The increase in velocity is a positive acceleration, followed by a negative acceleration (or an acceleration in the backwards direction) which decreased the velocity. The positive acceleration was caused by a slight drop in the pavement, and the backwards acceleration was caused by the net force of the physics prof.
Imagine that you are driving down I-15 at a constant velocity. Your car is on cruise control, and you are listening to Neil Diamond, so you are not going to slow down for anything. Sketch a graph of your position versus time.
During your trip, you pass a state patrol car. The patrol car is parked under an overpass as you go by. The officer immediately accelerates from rest, passes your car, and (much to your relief) pulls over someone else further down the road. On the same graph as above, show the officer’s position vs. time. Label on the graph where you initially pass the parked officer and where the officer passes you.
The graph is as follows. The red line shows a constant velocity, which represents you and Neil Diamond. The blue line represents the police car. See below for what each numbered point represents:
1. You are moving down the road at the time
first described in the problem.
2. The police car, at the same time as point 1, is at rest underneath the
overpass down the road.
3. You and the police car are both at the same point at the same
time. You are moving past the police car that has been waiting underneath
the overpass.
4. The police car is now moving. He is behind you, but the slope of
his line is steeper than yours, so he is catching up to you.
5. You and the police car are at the same place on the highway. The
police car's slope is steeper than yours, so he is passing you.
6. The police car is ahead of you, but he is now moving more slowly than
you are.
7. The police car is stopped, and you are passing him again.
Consider a ball that is thrown straight up into the air. At the ball’s highest point, describe as much as you can about the ball’s
a. Velocity, and
b. Acceleration.
Explain and justify your answers.
a. The ball must turn around and come back to the ground (otherwise, bummer, lost ball). For an instant, the ball must be stopped at the top of its path. Said another way: You witnessed the ball going upwards, but slower and slower and slower. The reason it doesn't go higher is because it is no longer moving upward.
b. The acceleration of the ball is constant throughout its flight (rate of gravity, g, 9.8m/s/s, etc. We'll worry about the actual value later.) The acceleration does not change at the top, even though it is stopped, since it must change from moving up to being stopped to going down again. After all, if the acceleration were zero, then the force would also have to be zero; and if the force were zero and it were stopped then it would remain stopped, and your ball would be stuck up in the air for the rest of eternity (bummer).
Once upon a time, a 7-year-old wrote to a newspaper columnist who is supposed to have "the answer" to every question. The child asked, "If the Earth stopped spinning, would we fall off of it?" It’s a good question – what is the answer? (Incidentally, the newspaper columnist got the answer wrong.) Imagine a situation in which the Earth spins on its axis once each day, and something suddenly and instantly causes the spinning to stop. Consider Newton’s Laws in your answer.
The first thing to get straight: Nothing about gravity changes. We haven't covered gravity yet, but we will show that, according to Newton's law of gravitation, the force of gravity is proportional to the two masses involved, and inversely proportional to the square of the distance between these two masses. (If that sounded like gibberish, don't worry -- we'll explain more later.) This relationship says nothing about spinning, so any change in the motion of the Earth has no effect on gravity.However, if the Earth is currently spinning, we are spinning with it. That is, standing at the equator you are moving around in a giant circle at almost 1000 mph. If the Earth stops, you will still want to keep moving forward. This is Newton's first law (as stolen from Galileo): All objects retain their state of motion unless there is an unbalanced force acting. Thus, a sudden stop of the Earth's rotation would make it seem as though we were suddenly kicked off the ground and made to fly eastward. (What actually happened is the Earth stopped and we kept going.) Trees, houses, people, etc. would all get "thrown" as though we were all getting thrown from a car that was traveling hundreds of miles per hours and ran into a brick wall. Not so good. (Of course, if you were standing at one of the poles, you'd be fine. Why?)
You are riding your tricycle down the street one day, thinking about Newton’s laws. Explain why you continue to move down the street at a constant velocity, even though you are constantly applying a force to the pedals of your vehicle. Why aren’t you accelerating in this instance, as Newton’s 2nd Law seems to suggest? Describe all the forces involved in this situation, and what kind of acceleration they produce.
You are not accelerating (constant velocity) because the net force is zero. This means that the force of the road upon the wheels pushing you forward is exactly balanced by another force (wind, frictions, etc.) pushing you backwards. With zero net force, there is zero acceleration and no change in the velocity. If the opposing force were removed, then the tricycle would continue to accelerate, going faster and faster with every moment that you were able to pedal, assuming that you could continue to pedal faster and faster.
(See selected exercise in Hewitt.) This painter is going to fall in a potentially gruesome accident if he ties one of his lines to the flagpole. Why? (Analyze the forces acting on the painter, assuming that he is at rest and not accelerating while painting.)
The trick here is to look at exactly what forces are acting on the painter. When the rope loops over the pulley and back to him, there are two strands of rope connected to him, so they can support the total weight of the painter by splitting it between them. When he ties the rope to the flagpole, only one rope is directly tied to him, so it must support all his weight. As is suggested by the problem, the rope might not be able to hold all this weight by itself without breaking.
It was once argued that rockets would never work because of Newton’s 3rd law: If there is nothing to push against in space, then there will be no way for a rocket to make itself go. (Certainly, your car won’t work in space, since there are no roads for the tires to push against.) So how does a rocket work? Answer the following questions:
 | Imagine that you are sitting on a raft in the middle of the ocean. All you have (besides yourself and some old Rick Springfield c.d.’s) is a ton of bananas. If you are floating on calm waters and not moving, what is the total momentum of you, the raft and the bananas (all included as one system)? How do you know? | |
| If there is no current, wind, sharks, or other external forces, what is the total momentum going to be in 10 minutes? How do you know? | |
| (Those were the easy questions. Now the hard questions.) If you throw a banana to the west with a velocity of 10 m/s (or almost 50 mph), exactly what will happen to your raft (assuming a frictionless ocean)? Assume that one banana is one one-thousandth of the mass of the raft and all its cargo. | |
| If you want to be moving at 1 m/s to the east, approximately how many bananas should you throw? |
The first couple of questions here are easy. With no motion in the beginning, all velocities are zero, which means the total momentum has got to be zero. That said, the momentum ten minutes later or ten years later (if this system isn't affected by anything external) will still be zero. We know this because momentum is conserved when no external impulses are involved.
If momentum is conserved, then any momentum that is going one direction will be exactly cancelled by some momentum in the opposite direction. If the mass of the banana is 1/1000 of the mass of the boat, then for the momentum to remain zero, the boat must "recoil" in the opposite direction of the banana at 1/1000 of the banana's speed. (In this way, the m*v of the boat is exactly the same, but in the opposite direction, as the m*v of the banana.) Thus, with each banana thrown, the boat will move at an additional 10/1000 m/s or .01 m/s. This is not very fast . . . yet.
If you throw out more bananas, then each one will boost the velocity of the raft by .01 m/s. If you want to move at 1 m/s, then you need to throw 100 bananas, since 100 * .01 m/s = 1 m/s. That's a lot of bananas, and probably not the best use of your food supply. But, it gives you the idea as to how rocket propulsion works. If you could throw the bananas much much faster, this would be more efficient, of course.
One other thing that this problem doesn't take into account is how much the mass of the boat changes each time you toss one banana overboard. Since each banana is relatively small, this isn't a big deal in the short term, but you can imagine that after you've thrown hundreds of bananas off the boat, the boat would be a lot less massive, and so it would be able to move faster and faster with each banana toss. We didn't factor this into the problem because 1. It made it harder, and 2. It wasn't too important, since you didn't change the mass of your raft too dramatically over the short term.
(Note: Rockets use the exhaust of fast moving gases instead of bananas. These gases do not have very much mass, but they have very high velocity. (Even higher than our bananas!) The rocket and its exhaust have a total momentum of zero, just like the raft and its bananas.)
A demonstration of a rocket throwing out bananas (pellets) can be found on the momentum animations page. You can vary the mass of the rocket, the mass of the thrown pellets, and the velocity of the pellets.
Two rivals (a chemist, Dr. Seager, and a physicist, Dr. Carroll) stand on a frictionless sheet of ice out in the middle of the Great Salt Lake. They are stranded for days. Finally, Dr. Seager gets tired of Dr. Carroll’s lectures and gives the physicist a push. As the physicist slides off the ice sheet, he laughs at the chemist’s foolishness. Explain why the chemist made a mistake, emphasizing Newton’s Laws and/or conservation of momentum.
The easiest way to explain this is via conservation of momentum. The physicist recognizes the fact that the two persons represent one closed system. If both are motionless, then the initial momentum is zero. If one person starts moving one way as a result of something internal to this system (a push, explosion, etc.), then something has to move the other way in order for momentum to still equal zero. Both scientists will end up wet. Perhaps the physicist is laughing because he is happy that he will get to do an experiment in buoyancy, floating in the salty water.
This can also be explained with Newton's 3rd law: one good push deserves another in the opposite direction. When the chemist pushes on the physicist, the chemist also receives an equal "push" in the opposite direction. Without friction to hold him down, he accelerates and slides off the opposite edge of the ice sheet.
You can demonstrate a slightly more involved version (with three objects instead of two) of this on the web by looking at the astronauts in space demo on the momentum animations page.
Two balls (red and green) of the same mass are dropped from an identical height. The red ball bounces back upwards, but the green ball hits the ground and stays there. Explain which ball had the greatest amount of force exerted on it, and explain how you know. (You probably want to think about impulse and changes in momentum.) Assume that the ground exerts a force on each ball for the same length of time.
In class we demonstrate a bouncy ball bouncing off the table and contrast it with a lump of clay with the same mass that simply sticks to the table. One way of looking at it is to consider each object's change in motion, or acceleration. The bouncy ball has about twice as much change in its motion, since it turns around and starts moving upwards, as opposed to just coming to a stop. Since its acceleration is twice as great, then the force applied must also be about twice as great.Another way to talk about this is via momentum. The happy/red ball's momentum changes the most, so its impulse must be greater. An impulse is proportional to the force acting during the collision, so this ball's force must be greater (since the times of contact is the same for each impulse).
Imagine that you are foolish enough to have a heavy bowling ball attached by a cable to the ceiling, so that the bowling ball can swing back and forth. As the bowling ball swings back and forth, describe how its kinetic, potential, and total energies change, and where each of these are at their greatest and smallest. (You might use a sketch to help your description.)
First of all, if the bowling ball system does not do or receive work from the outside, then its total energy will be conserved. It is always the same. This assumes the ideal situation where there is no friction from air resistance or other sources. Our own bowling ball pendulum is very efficient, and almost all of the energy remains in the system.
The potential energy shows up as gravitational potential energy. So, the GPE changes as the height changes. (It would also change if the mass changed, but this doesn't happen.) So, the GPE is a maximum where the height is greatest, at the top of the swing (on each side). GPE is a minimum where the height is the smallest, in the middle of the swing.
Kinetic energy (KE) depends on motion. So, where the motion is the fastest, at the middle of the swing, the KE is a maximum. At the top of the swing (on each side) the motion is zero for an instant, so the KE is also zero (a minimum).
Another way to deduce the KE's minimum and maximum is to consider the GPE. Since the total energy is the same all the time, then wherever the GPE is its greatest, the KE must be its smallest, and wherever the GPE is at its smallest, the KE is at its greatest. Imagine that energy is some kind of liquid which is stored in either a KE bucket or a GPE bucket. The total amount of liquid is the same all the time, but when it is all in the GPE bucket, the KE bucket is empty (and vice-a-versa).
Two skiers of equal mass are coasting on a flat section of frictionless snow. One skier is traveling three times as fast as the other.
a. As they begin to coast up a hill, explain how much farther one skier will
rise than the other.
b. Explain any differences if the skier who is three times as fast is also three
times as massive as the other skier.
In part (b.), while the skier with more mass has more kinetic energy, it is also true that it takes a proportionate amount of energy to get him to a certain height. That is, since both kinetic energy and potential energy or proportional to mass, the mass of the skier (under ideal, frictionless conditions) does not affect the height to which he will rise. (We did this in class, showing how the m's in both the G.P.E. term and the K.E. term will "cancel" out when one energy form is converted into another.)
(From Hewitt.) If a golf ball and a ping pong ball both move with the same kinetic energy, can you say which has the greater speed? Similarly, in a gaseous mixture of massive molecules and light molecules with the same average kinetic energy, can you say which have the greater speed? (We’ll talk about molecules and gases each in later chapters, but you can see that we’ll continue to use energy to understand these concepts.)
The ball/particle with the lesser mass will have more velocity. KE can be accounted for by both the mass and velocity of the ball, so the more mass it has, the less velocity it must have on average. Later we'll see how this applies to molecules, but basically it is the same result as a golf ball and ping pong ball with the same energy: Light molecules will have faster speeds than heavier molecules with the same KE.