Physics Principles And Problems Study Guide Answers

[Torie Crivello]

Youlike many students, may view college level physics as difficult. You, again like many students, may seem overwhelmed by new terms and equations. You may not have had extensive experience with problem-solving and may get lost when trying to apply information from your textbook and classes to an actual physics problem. We hope this pamphlet will help!

An overview of your course can help you organize your efforts and increase your efficiency. To understand and retain data or formulas, you should see the underlying principles and connecting themes. It is almost inevitable that you will sometimes forget a formula, and an understanding of the underlying principle can help you generate the formula for yourself.

When looking for relationships among topics, you may note that in many instances a specific problem is first analyzed in great detail. Then the setting of the problem is generalized into more abstract results. When such generalizations are made, you should refer back to the case that was previously cited and make sure that you understand how the general theory applies to the specific problem. Then see if you can think of other problems to which that general principle applies. Some suggestions for your physics reading:

You may now be like many students a novice problem solver. The goal of this section is to help you become an expert problem solver. Effective, expert problem solving involves answering five questions:

An important thing to remember in working physics problems is that by showing all of your work you can much more easily locate and correct mistakes. You will also find it easier to read the problems when you prepare for exams if you show all your work.

When you have completed a problem, you should be able, at some later time, to read the solution and to understand it without referring to the text. You should therefore write up the problem so as to include a description of what is wanted, the principle you have applied, and the steps you have taken. If, when you read your own answer to the problem, you come to a step that you do not understand, then you have either omitted a step that is necessary to the logical development of the solution, or you need to put down more extensive notes in your write-up to remind you of the reasons for each step.

It takes more time to write careful and complete solutions to homework problems. Writing down what you are doing and thinking slows you down, but more important it makes you behave more like an expert. You will be well paid back by the assurance that you are not overlooking essential information. These careful write-ups will provide excellent review material for exam preparation.

In 1947 Bob Feller, former Cleveland pitcher, threw a baseball across the plate at 98.6 mph or 44.1 m/s. For many years this was the fastest pitch ever measured. If Bob had thrown the pitch straight up, how high would it have gone?

Notice that the graph is fairly accurate: You can approximate the value of g as 10 m/s 2, so that the velocity decreases to zero in about 4.5 s. Therefore, even before you use your calculator, you have a good idea of about the value of t m.

Look over this problem and ask yourself if the answer makes sense. After all, throwing a ball almost 100 m in the air is basically impossible in practice, but Bob Feller did have a very fast fast ball pitch!

There is another matter: If this same problem had been given in a chapter dealing with conservation of energy, you should not solve it as outlined above. Instead, you should calculate what the initial and final kinetic energy KE and potential energy PE are in order to find the total energy. Here, the initial PE is zero, and the initial KE is m v o 2 / 2. The final PE is m g y m and the final KE is zero. Equate the initial KE to the final PE to see that the unknown mass m cancels from both sides of the equation. You can then solve for y m, and of course you will get the same answer as before but in a more sophisticated manner.

A one kilogram block rests on a plane inclined at 27 o to the horizontal. The coefficient of friction between the block and the plane is 0.19. Find the acceleration of the block down the plane.

The second principle is that the frictional force is proportional to the normal force (the component of the force on the block due to the plane that is perpendicular to the plane). The frictional force is along the plane and always opposes the motion. Since the block is initially at rest but will accelerate down the plane, the frictional force will be up along the plane. The coefficient of friction, which is used in this proportionality relation.

Note that in the vector diagram, the block has been replaced by a dot at the center of the vectors. The relevant forces are drawn in (all except the net force). Even the value assumed for the gravitational acceleration has been included. Some effort has been made to draw them to scale: The normal force is drawn equal in magnitude and opposite in direction to the component of the gravity force that is perpendicular to the plane. Also, the friction force has been drawn in parallel to the plane and opposing the motion; it has been drawn in smaller than the normal force. The angles of the normal and parallel forces have been carefully drawn in relation to the inclined plane. This sub-drawing has a title and labels, as all drawings should.

When you look over this answer to see if it makes sense, try doing the problem by substituting numbers in at each step (the concrete approach). The weight of a kilogram, for example is 9.8 N. The normal (perpendicular to the plane) component of the gravitational force is 9.8 times cos 27 o or 8.73 N. This makes sense, for if the angle were very small, the normal component of the gravitational force would be almost equal to 9.8 itself. Notice that although the final answer should be given to two significant figures, you should keep three in these intermediate calculations.

Again examine your solution. It says that the block does accelerate down the plane because the final answer is positive. The acceleration is less than g, again a reasonable result. Notice that if the angle were more than 27 o, then its sine would be larger and its cosine smaller, so the acceleration would be greater. If the angle were less than 27 o then the opposite would be true, and the acceleration, as calculated above, could become negative. But a negative value for acceleration would be wrong, because that would say that the block would accelerate up the plane because the frictional force dominates, and that is impossible. Instead, if the calculation had produced a negative value for a, you would have had to change the solution to a = 0, meaning that the frictional force was enough to prevent sliding.

For example: If velocity and acceleration principles have been emphasized in the course, look over all of your homework problems to see if they illustrate these principles, even partially. Then if you also can anticipate an emphasis on friction and inertia, once again review all of your homework problems to see if they illustrate those principles.

This is the most common of the AP Physics Multiple Choice Questions. Expect to use at least two unique thought processes to come up with the final answer. These problems can ask for comparisons during a scenario, comparisons of two scenarios when values of variables are changed, or rankings within a scenario.

This example covers the concept of conservation of energy, which is one of the most emphasized topics on the exam. Recall that the total mechanical energy is conserved in a closed system. At point A, the block has both elastic potential energy stored in the spring and gravitational potential energy due to its position. At point C, the object has potential energy, but only in the form of gravitational potential energy since there is no spring present.

Now compare the kinetic energies. The object is initially at rest at point A, so it has zero kinetic energy there. At point C, there is still some energy that was originally in the form of elastic potential energy. Since the gravitational potential energy cannot increase without an increase in height, the kinetic energy must increase in order for the system to conserve its total mechanical energy. The kinetic energy at point C is greater than that at point A, and choice B is the answer.

This is the next most common category of question type. These problems allow you to select a graph or model that matches an initial graph or scenario. Sometimes a graph is given and you pick the scenario. Know the models and how they relate to the equations for the topic.

Be sure to pay close attention to the axis labels on the graph. Is the graph velocity vs. time or position versus time? Displacement vs. time or energy vs. time? You may want to think through a description of what each section of the graph means if there are multiple sections. Here are some examples:

In this first example, there are graphs that are matched to a scenario. There are three different motions to consider. You can eliminate any answer without three different motions immediately. Acceleration is a parabola in the first section, a straight line with a positive slope in the second, and a straight line with a negative slope in the third. Know the models for graphs of motion and forces!

In our next example, a graph is matched to another graph. The answer is B again. For simple harmonic motion, the velocity is zero when the amplitude is greatest, and the speed is maximum when the position is zero. Forces are restoring forces proportion and opposite direction to displacement. You will definitely see these relationships so review them before the test.

Next, we see a different type of question where you must select the correct justification or explanation. Read the prompt and all the possible answers carefully. Those words will be clearly stated in the prompt. Many times this has an answer and an explanation. If you are sure of the answer, you will have an easy time eliminating wrong choices. Other problems ask for an explanation or justification of a statement.

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