Mechanics Problem (Physics Olympiad)

Hmm I want to share about my experience when I was doing my olimpiad test in my country. I was very interesting in solving Newton`s Law Problems. It`s so fantastic, you can solve one problem with the answer until 2 full-pages. You can imagine how satisfied you are if you can do it. So that, I want to tell you the basic, and you must know this a lot and then the exercise will be add later. ^^

Tension
Tension is a general name for a force that a rope, stick, etc., exerts when it is pulled
on. Every piece of the rope feels a tension force in both directions, except the end
point, which feels a tension on one side and a force on the other side from whatever
object is attached to the end.
In some cases, the tension may vary along the rope. (The “Rope wrapped around
pole” example at the end of this section is an example of this.) In other cases, the
tension must be the same everywhere. For example, in a hanging massless rope, or
in a massless rope hanging over a frictionless pulley, the tension must be the same
at all points, because otherwise there would be a net force on at least one tiny piece,
and then F = ma would give an infinite acceleration for this tiny piece.

Normal force
This is the force perpendicular to a surface that a surface applies to an object. The
total force applied by a surface is usually a combination of the normal force and
the friction force (see below). But for “frictionless” surfaces such as greasy ones or
ice, only the normal force exists. The normal force comes about because the surface
actually compresses a tiny bit and acts like a very rigid spring; the surface gets
squeezed until the restoring force equals the force the object applies.
Remark: Technically, the only difference between a “normal force” and a “tension”
is the direction of the force. Both situations can be modeled by a spring. In the case of
a normal force, the spring (a plane, a stick, or whatever) is compressed, and the force on
the given object is directed away from the spring. In the case of a tension, the spring is
stretched, and the force on the given object is directed toward the spring. Things like sticks
can provide both normal forces and tensions. But a rope, for example, has a hard time
providing a normal force. |

Friction
Friction is the force parallel to a surface that a surface applies to an object. Some
surfaces, such as sandpaper, have a great deal of friction. Some, such as greasy ones,
have essentially no friction. There are two types of friction, called “kinetic” friction
and “static” friction.
Kinetic friction (which we won’t deal with in this chapter) deals with two objects
moving relative to each other. It is usually a good approximation to say that the
kinetic friction between two objects is proportional to the normal force between
them. We call the constant of proportionality ¹k (called the “coefficient of kinetic
friction”), where ¹k depends on the two surfaces involved. Thus, F = ¹kN. The
direction of the force is opposite to the motion.
Static friction deals with two objects at rest relative to each other. In the static
case, all we can say prior to solving a problem is that the static friction force has a
maximum value equal to Fmax = ¹sN (where ¹s is the “coefficient of static friction”).
In a given problem, it is most likely less than this. For example, if a block of large
mass M sits on a surface with coefficient of friction ¹s, and you give the block a
tiny push to the right (tiny enough so that it doesn’t move), then the friction force
is of course not ¹sN = ¹sMg to the left. Such a force would send the block sailing
off to the left. The true friction force is simply equal and opposite to the tiny force
you apply. What the coefficient ¹s tells you is that if you apply a force larger than
¹sMg (the maximum friction force), then the block will end up moving to the right.

Gravity
Consider two point objects, with masses M and m, separated by a distance R.
Newton’s law for the gravitational force says that the force between these objects is
attractive and has magnitude F = GMm=R2, where G = 6:67 ¢ 10¡11 m3=(kg ¢ s2).
As we will show in Chapter 4, the same law applies to spheres. That is, a sphere
may be treated like a point mass located at its center. Therefore, an object on the
surface of the earth feels a gravitational force equal to

F = GMm(R)^-2

where M is the mass of the earth, and R is its radius. This equation defines g.
Plugging in the numerical values, we obtain (as you can check) g ¼ 9:8 m=s2. Every
object on the surface of the earth feels a force of mg downward. If the object is not
accelerating, then there must also be other forces present (normal forces, etc.) to
make the total force zero.