You might be expected to perform an integral or two, of the kind in Problem Set #1.

Yes. The effects you mention can greatly complicate solution of a given problem, although their inclusion does provide a more realistic model of the real world. If a rope has finite mass and a mass is suspended from it vertically, the tension in the rope is no longer the same along its length. The pieces of the rope near the bottom are under less tension than pieces near the point of suspension. A real pulley not only has friction in the bearings, it has mass and it therefore requires a force (more precisely a torque) to get it rotating. You will find in lab that the finite mass of a spring affects the application of our simple theory of simple harmonic motion for a mass on a spring. At times in this course we will attempt to include these complicating, but real, effects. At other times we will neglect them.

The spring I used to demonstrate Hooke's Law in class is a somewhat tapered spring. It is so designed to try to better approximate an ideal spring for your laboratory experiments on simple harmonic motion.

You propose a terrific problem for a future problem set perhaps. To take into account a changing mass, you need to use the form of Newton's second law that Newton in fact used. F = d(mv)/dt . If you use the product rule on this you get... F = m dv/dt + v dm/dt. The first term on the right side is ma. The second term is zero if the mass is constant. Rocket motion is another example of the motion of an object with changing mass.

Let's agree to call m(g+a) in this example... "apparent weight". It is the normal force exerted by the scale on the passenger.

The counterpart of the normal force of the table on a block, is the (downward) normal force of the block ON THE TABLE. The counterpart of the frictional force on the surface of a block in contact with the table is a frictional force ON THE TABLE surface in the opposite direction. Imagine the following example: One block is on top of a second block. The two stacked blocks sit on a frictionless table, but there is friction between the two blocks. If the top block starts out sliding to the right over the stationary bottom block, the friction force on the top block will be to the left. The NIII counterpart to that frictional force is a frictional force on the bottom block TO THE RIGHT. That force on the bottom block accelerates the bottom block to the right. Meanwhile the rightward velocity of the top block is decreasing due to friction. Eventually the two blocks come to the same final rightward velocity and coast together at constant velocity on the frictionless table.

Perfect!

Read the footnote on page 4021 carefully. The arrow in Figure 40.10 is correct if b*dz/dt is positive (upward velocity). When the velocity is negative, the actual direction of the viscous drag force will be upward because b*dz/dt is negative. When you draw a force diagram, you indicate the positive direction of the force with an arrow on the diagram and include the appropriate + or - signs in Newton's 2nd Law given that choice for positive force. If the quantity ends up being negative, that simply indicates that the force is directed opposite the direction indicated by the arrow. Buoyancy is a completely different effect, aside from the fact that viscous drag and buoyancy both require the presence of a fluid surrounding the object of interest.

I offered a verbal explanation of buoyancy in class. It arises because the pressure in a fluid increases with depth. For example, the pressure in water increases as one goes deeper in the water. Similarly, the air pressure is higher the deeper one goes in the atmosphere. We happen to reside near the bottom of the atmosphere where its pressure is greatest. It is the variation of pressure with depth (or altitude) that leads to buoyancy. An object immersed in the fluid feels a greater upward pressure from the bottom than it feels downward from above. There is therefore an upward buoyant force. Archimedes gave us the shortcut for determining that force. The buoyant force is equal to the weight of the displaced fluid.

One might expect a (very) weak effect of this sort without a fifth force. The local gravitational force is (very) slightly modified by the distribution of mass in the local vicinity. A mountain does exert its own gravitational influence on other objects adjacent to it. The fifth force was thought to modify that actual form of Newton's Universal Law of Gravitation, so that it perhaps depended on the composition of the matter doing the attraction, not just on its mass. More recent experiments have NOT provided evidence for such a force.

I do not know what t and t prime you are referring to. Are you referring to f and f prime... or perhaps T and T prime in Figure 40.7? The 3rd Law counterparts to the friction forces on the blocks due to the table are friction forces in the opposite direction ON THE TABLE.

An excellent question, although one that takes me a little out of my area of expertise. Analysis of forces on the atomic or molecular scale requires the use of quantum mechanics rather than classical mechanics. That said, one can in many cases think about atoms in a solid crystal as being connected to one anther by little springs. Likewise one can (in some contexts) think of a long molecule (polymer) like a tiny rubber band or spring. Just as a spring with a mass attached to it oscillates with a particular frequency (natural frequency), atoms in long molecules or in crystalline solids oscillate (or vibrate) with certain (natural) frequencies.

See the answer to question #9. Other effects might complicate the determination of the buoyant force, although such effects will usually be negligible. For example, the equation for buoyant force contains, as you say, the density of the fluid. But the density of the fluid is not strictly constant with depth (or altitude). What density should you use? You should use the average density in the region of the object. Since the buoyant force arises due to pressure on the surfaces of the object immersed in the fluid, and since the temperature of the fluid contributes to the pressure (pV = NRT), strong temperature variations with altitude can complicate determination of the buoyant force.

I answered this question in class. The NIII counterpart to the gravitational force on a falling object is the gravitational force ON THE EARTH due to attraction to the falling body.

The answer to the first question is yes. F1 + f2 is the total frictional force on the table. I am not sure what you are asking in the second question. If your question is... where are the Newton's 3rd law counterparts to f1 and f2 ... there are horizontal frictional forces ON THE EARTH due to the legs of the table. They would appear in a force diagram for the earth.

You are a chapter behind. Try to keep up with the reading.

P35.1 asks you to add vectors A and B using two different methods. First, using graph paper, protractor and ruler, construct the resulting vector by making a parallelogram from A and B and finding the length and direction of its appropriate diagonal. The second (analytic) method is to determine the x and y (or east and north) components of the vectors A and B using trigonometry. A_x = A cos q_A, A_y = Asin q_A, B_x = B cos q_B, B_y = B sin q_B. The x component of A + B is A_x + B_x. Etc. Follow the example I performed in class the other day.

I know almost no biochemistry, so I cannot comment on the details of the Krebs cycle. But... I do know that the laws of physics govern the detailed interactions of atoms and molecules. In particular it is the electromagnetic interaction that determines the chemical behavior of atoms and molecules. And it is the electrostatic aspects of the electromagnetic interaction that dominate the relatively slow moving molecules in biological systems (magnetic effects are negligible). The electrostatic interaction obeys Newton's third law. When one molecule drifts into the vicinity of another, the net electric charge on parts of one molecule attract and/or repel the charged parts of the other. In the gravitational interaction two objects with mass attract each other and the force on one is equal in magnitude but opposite in direction to the force on the other. The electrostatic interaction can be either attractive or repulsive, but the force on one charged object will always be equal in magnitude but opposite in direction to the charge on another. In biochemical reactions I believe enzymes catalyze certain reactions by temporarily holding some of the reactants in the specific orientations to increase the likelihood of reaction. If the enzyme is much bigger than the molecule whose reaction it is catalyzing, when the molecule and the enzyme attract each other, it is somewhat analogous to the attraction between you and the earth. Since the earth is much more massive, it does not accelerate very much under the influence of the gravitational attraction to you, while you accelerate substantially.

We will discuss simple harmonic motion quite a bit on Friday.

The locations of the force vectors in Fig. 40.5 are intended to indicate where on the object the force is applied. Whereas the gravitational force is exerted on every piece of the object, and is usually shown in force diagrams as acting on the center of mass of object, the frictional force for example acts on the bottom surface of the block. The diagram tries to show that. However, since the block is a rigid object that force gets communicated to the entire block (via the interatomic forces that hold the block together). In drawing diagrams for problems like this I prefer to indicate all forces ass acting on the center of mass of the object. Observe my diagrams in class to see how I do this and ask questions if you do not follow.

When we start considering how objects might rotate as well as translate we will have to consider where on the object the force is acting. If you push on a door near the hinge you get a different result than if you push with the same force near the knob.

Figure 40.11 is very complete. In general when two surfaces are in contact there is a normal force (perpendicular to the surface) and a frictional force (parallel to the surface). In the example detailed in section 40.6.3, the frictional forces f' and f'' are a Newton's third law action-reaction pair (as are N' and N''). Later in the example the friction forcese are assumed to be zero, but in general, they need not be. For example, see P40.20, one of the problems assigned on PS#2.

The scale will not read your weight if you are accelerating. The scale will read the force that normal force that you are exerting on it, and by Newton's third law that equals in magnitude the normal force that it is exerting upward on you. It is this upward normal force from the floor or the scale that gives you your sensation of weight and if the floor pushes up on you with a force greater than mg then you will have an "apparent" weight greater than your actual weight.

When you consider the forces on an object sitting on a table, the normal force is indeed equal in magnitude and opposite in direction to the gravitational force on the object. But, these two forces do not need to be equal in magnitude nor opposite in direction. Consider the elevator accelerating upward. The normal force is greater than the gravitational force in that case. Consider the block on an inclined plane. The normal force is not opposite in direction to the gravitational force. Newton's third law is not violated in either of these cases, because the action and reaction forces described in NIII act on different objects. The action-reaction partner to the gravitational force on an object near the surface of the earth is the gravitational force ON THE EARTH due to the object. The action-reaction partner to the normal force on the object due to the table is the normal force (downward) ON THE TABLE due to the object.

M does indicate the mass of the block suspended by two strings in Figure 40.7. Sometimes in the text detailing that example M is also used as the name of the object in that same figure.

See answer to question #20.

This is not at all obvious unless you already know something about the microscopic makeup of matter and what governs the behavior of matter on that scale. All chemical phenomena are electromagnetic in nature. Atoms and molecules are composed of electrically charge objects... electrons and protons. It is the electromagnetic interaction of those atoms and molecules that determines the properties of materials... the friction between two surfaces... the stretchiness of a spring. It is because of the repulsion of electrons in the surfaces of two objects that a block placed on a table does not fall through the table to the center of the earth.

There are it appears only four fundamental interactions in the universe, and only two of those are apparent on the macroscopic scales we live in: gravitation and electromagnetism.