Energy
Potential Energy
Potential energy of a body is the energy possessed by a body by virtue of its position or configuration
* It is measured by the work that the body can do in position or configuration.
* Potential energy is defined only for conservative forces.
It does not exist for non – conservative forces.
¶¶ Expression for gravitational potential energy :
Consider a body of mass 'm' is on the ground. It is lifted verticaly upwards through a height 'h'. Considering the height to be very small compared to the radius of the earth (R)i.e., h<<R, we can neglect the variation of g. The gravitational force 'mg' on the body can be taken to be constant. The work done by the external agency against gravitational force is
W = Fs = mgh.
\(
\left( {\because F = mg;s = h} \right)
\)
This work gets stored as potential energy of the body. Potential energy of the body
\(
\boxed{U = mgh.}
\)
The above expression actually represents the increase in the stored energy from the
reference position (earth surface) to the final position at a height 'h'.
POTENTIAL ENERGY
1.The energy possessed by a body by virtue of its state and position is called potential energy
2.The concept of potential energy exists only for conservative forces.
3.We cannot define potential energy corresponding to a non conservative internal force
4.If a body is under the influence of force of attraction or force of repulsion,it possesses the potential energy (i.e., the system)
5.The only mechanical energy a body at rest can have is potential energy.
6.The potential energy of a system of two bodies under the influence of a repulsive force is taken as positive.If the bodies attract each other,potential energy of the system is negative.
7.If a body is lifted to a height h above the ground,gravitational potential energy is mgh(if h<<R)
Here potential energy on the surface of the earth is taken is zero.
KINETIC ENERGY
1.All moving bodies posses Kinetic energy
2.In translatory motion,kinetic energy of a body is \(
\frac{1}
{2}mV^2
\)
In rotatory motion,kinetic energy of a body is \(
\frac{1}
{2}I\omega ^2
\)
3.If a body is released from certain height ,after time ‘t’ second its K.E=\(
\frac{1}
{2}m(gt)^2
\) after falling through a height y K.E=mgy
4.A body dropped from the height h above the ground when it falls through a distance y then it’s K.E=mg(h-y)
5.kinetic energy of freely falling body is directly propotional to height from which it is fallen,and propotional to square of time
MECHANICAL ENERGY
1.The sum of potential and kinetic energy of a system is known as mechanical energy E=U+K
where U is P.E and K is K.E
Here K is always positive and U may be positive or negative
2.The only mechanical energy abody at rest can have is potential energy
3.The body at rest cannot have kinetic energy and momentum
4.Mechanical energy may be positive (if K>U),negative (K<U and U is negative) or zero(if K=U and U
the inverse ratio of their masses i.e.,\(
\frac{{K_{bullet} }}
{{K_{gun} }} = \frac{{M_{gun} }}
{{M_{bullet} }}
\)
Hence, the kinetic energy of the bullet is greater than that of the gun.