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swati.07

This is my first article :

- Mechanical energy is the sum of potential & kinetic energy.

- Potential energy can be due to gravitation or in other forms

like an extended or compressed spring.

- The formula, that the potential energy of a body at a height

h = mgh where g is the acc. due to gravity which is treated as constant,is valid only when h is very small compared to

the radius of the earth.

- The potential energy at a distance r from the centre of

earth is

U(earth) = - GM(earth)*m(particle) / r

The negative sign shows that the particle is attracted by

the earth.

- The potential is - GM/(R+h) = -GM/r

As r increases,the potential & potential energy decreases.

It is zero at infinity.

- When h = 0,the potential energy = -GMm/R

( In the approx. calculations, P.E. = 0 at h = 0)

- For a spring, the potential energy = +1/2kx^2

where k is the spring constant & x is the extension

within the elastic limit.

- The P.E. of a spring or a mass oscillating in the simple

harmonic mode is always positive.

- For a mass oscillating in the simple harmonic mode, the

potential energy is +1/2m

^2x^2.

- Maximum P.E. = +1/2m

^2A^2.

- The sum of kinetic + potential energy = max K.E = max P.E.

because of conservation of energy.

Total energy = potential + kinetic

1/2m

^2A^2 = 1/2m(

)^2(x)^2 + 1/2m

^2(A^2 - x^2)

- Velocity of the particle making simple harmonic motion

=

(A^2 - x^2)

At the equilibrium position, K.E. is max as x = 0,

P.E is max at the max displacement.

- In rotation, one does not discuss P.E.. The P.E is only due to

the position of the centre of mass.

- Work done :

For translation, W = F.dx

By work energy theorm (for all types of motion) =

= final K.E. - initial K.E.

- When the P.E + K.E is constant as in the caser of a body

falling freely from a height h,

work done = initial P.E - final P.E.

- For rotation, work done =

where

is the torque applied

;

= I

where

is the angular acc.

- If rotation or circular motion is uniform, angular velocity

is a constant. The torque is not applied (neglecting friction)

;

= 0.

- Once rotation starts, in the case of uniform circular motion,

it continues without the necessity of a torque. The principle

of conservation of angular momentum is applicable. If there

is no external torque, rotation, rotation will continue in the

same way because angular momentum is conserved.

- In the same way, if there os no external force, a body in

uniform linear motion continues to move with the same

velocity because of the conservation of linear momentum.

Not copied self written !!!

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