Wednesday, May 7, 2008

Concept Review - Chapter 4 The Forces


Force is an interaction between two objects.
Force is exerted by an object A on another object B.
Force is a vector quantity. Hence if two or more forces act on a particle, we can find the resultant force using laws of vector addition.

The SI unit for measuring the force is called a newton.

Newton's third law of motion

If a body A exerts a force F on another body B, then B exerts a force -F on A,the two forces acting along the same line.

Gravitational force

Any two bodies attract each other by virtue of their masses.

The force of attraction between two point masses is

F = Gm1m2/r²
where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

The above rule was given for point masses. But it is analytically found that the gravitational force exerted by a spherically symmetric body of mass m1 on another such body of mass m2 kept outside the first body is Gm1m2/r² where r is the distance between teh centres of such bodies.

Thus, for the calculation of gravitational force between two spherically symmetric bodies, they can be treated as point masses placed at their centres.

Gravitational force on small bodies by the earth

For earth, the value of radius R and mass M are 6400 km and 6 x 10^24 kg respectively. Hence, the force exerted by earth on a particle of mass m kept at its surface is, F = GMm/R². The direction of this force is towards the centre of the earth.

The quantity GM/R² is a constant and has the dimensions of acceleration.
It is called acceleration due to gravity and is denoted by letter g.
Hence, g and G are different.
Value of g is approximately 9.8 m/s².
In calculations, we often use 10 m/s².

Now we know that force exerted on a small body of mass m, kept near the earth's surface is mg in the vertically downward direction.

Gravitational constant is so small that the gravitational force becomes appreciable only when one of the masses has a very large mass.

HC Verma gives the example of Force exerted by a body of 10 kg on another body of 10 kg when they are separted by a distance of 0.5 m. The force comes out to be 2.7*10^-8 N which can hold only 3 microgram. Such forces can be neglected in practice.
Hence we consider only gravitational force exerted by earth

Electromagnetic force

Apart from gravitational force between any two bodies, the particles may exert upon each other electromagnetic forces.

If two particles having charges q1 and q2 are at rest with respect to the observer, the force between them has a magnitude

F = (1/4πε0)(q1q2/r^2)

Where ε0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²
The quantity (1/4πε0) = 9.0 x 10^9 N-m² /C²

q1, q2 = charges
r distance between q1 and q2

This is called coulomb force and it acts along the line joining the particles.

Atoms are composed of electrons, protons and neutrons.

Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.

In atoms, the electrons are bound by the electromagnetic force exerted on them by charge on protons. Even the combination of atoms in molecules are brought about by electromagnetic forces only. A lot of atomic and molecular phenomena result from electromagnetic forces between subatomic particles (for example, theory is put forward that charged mesons are responsible for the stability of nucleus).

Examples of electromagnetic force:

1. Bodies in contact: The contact force between bodies in contact arises out of electromagnetic forces acting between the atoms and molecules of the surfaces of the two bodies. The contact force may have a components parallel to the contact surface. This component is known as friction.

2. Tension in a string: Tension in the string is due to electromagnetic forces between atoms or electrons and protons (free electrons and nucleus in metals).

3. Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force

F = k|x-x0| = k|∆x|

k, the proportionality constant is called the spring constant. This force comes into picture due to the electromagnetic forces between the atoms of the material.

Nuclear forces

The alpha particles is a bare nucleus of Helium. It contains two protons and two neutrons. It is a stable object and once created it can remain intact until it is not made to interact with other objects.

The protons in the nucleus will repel each other due to coulomb force and try to break the nucleus. Why does the Coulomb force fail to break the nucleus.

There are forces called nucluear forces and they are exerted only if the interacting particles are protons or neutrons or both. They are largely atractive, but with a short range. They are weaker than the Coulomb force if the separation between particles is more than 10^-14 m. For separation smaller than this the nuclear force is stronger than the Coulomb force and it holds the nucleus stable.

Radioactivity, nuclear energy (fission, fusion) etc. result from nuclear force.

Weak forces

A neutron can change into proton and simulataneously emit an electron and a particle called antinutrino.

a proton can also change into neutron and simulataneously emit a positron (and a neutrino). The forces responsible for these changes are called weak forces. The effect of this force is experienced inside protons and neutrons only.

Scope of classical physics

Physics based on Newton's Laws of motion, Newton's law of gravitation, Maxwell's electromagetism, laws of thermodynamics and the Lorentz force is called classical physics. The behaviour of all the bodies of linear sizes greater than 10^-6 m are adequately described by classical physics. Grains of sands and rain drops fall into this range as well as heavenly bodies.

But sub atomic particles like atoms, nuclei, and electrons have sizes smaller than 10^-6 m and they are explained by quantum physics.

The mechanics of particles moving at velocity equal to light are explained by relativistic mechanics formulated by Einstein in 1905.

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