Energy is defined as the capacity or ability of a body to do work. Energy is scalar quantity and its units and dimensions are the same as that of work. Thus, SI unit of energy is joule. There are so many types of energy e.g. kinetic, potential, electrostatic, magnetic, geothermal, elastic, solar etc. Some of them are described below. Some other commonly used units of energy are
`1 erg = 10^-7` J
`1 cal = 4.186 J ~~ 4.2 J`
`1 kcal = 4186 J, 1 kWh = 3.6 xx 10^6 J`
and 1 electron volt `= 1 eV = 1.60 xx 10^-19 J`
`text(Kinetic Energy)`
Kinetic Energy (KE) is the capacity of a body to do work by virtue of its motion. Motion may be either transnational or rotational.
A body of mass m, moving with a velocity v, has a kinetic energy
`K =1/2 mv^2`
Thus , `K prop m`
`K prop v^2`
Kinetic energy of a body is always positive irrespective of the sign of velocity v. Negative kinetic energy is impossible.
Kinetic energy is correlated with momentum as
`K = p^2/(2m) ` or `p = sqrt( 2mK)`
Kinetic energy for a system of particle will be
`K =1/2 sum_i m_i v_i^2`
Kinetic energy depends on the frame of reference. Kinetic energy of a passenger sitting in a running train is zero in the frame of reference of the train but is finite in the frame of reference of the earth.
`text(Potential Energy)`
Potential Energy (PE) is energy of the body by virtue of its position, configuration or state of strain. The relation between potential energy and work done is
`W = - Delta U`
where, `DeltaU` is change in potential energy.
Change in potential energy of a body between any two points is equal to the negative of work done by the conservative force in displacing the body between these two points, without there being any change in kinetic energy. Thus,
`dU = - dW = - F * dr`
and `U_2 - U_1 = - W`
`= -int_(r_1)^(r_2) F * dr`
Value of the potential energy in a given position can be defined only by assigning some arbitrary value to the reference point. Generally, reference point is taken at infinity and potential energy at infinity is taken as zero. In that case,
`U = - W = - int_(oo)^r F * dr`
Potential energy is a scalar quantity but has a sign. It may be positive as well as negative.
► Generally potential energy is of three types
`text(Gravitational Potential Energy)`
It is the energy associated with the state of separation between two bodies which interact via the gravitational force. The gravitational potential energy of two particles of masses `m_1` and `m_2` separated by a distance r is
`U = (-Gm_1m_2)/r`
Generally, one of the two bodies is our earth of mass M and radius R If m is the mass of the other body, situated at a distance r(`r >= R`) from the centre of earth, the potential energy of the body
`U(r) = -(GMm)/r`
`text(Some Important Points)`
If a body of mass m is raised to a height h from the surface of earth, the change in potential energy of the system
(earth + body) comes out to be
`DeltaU=(mgh)/(1+h/R)` or `DeltaU~~mgh`, if `h<
Thus, the potential energy of a body at height h,
i.e. mgh is really the change in potential energy of the system for `h < < R`.
For the gravitational potential energy, the zero of the potential energy is chosen to be the ground.
`text(Elastic Potential Energy)`
Whenever an elastic body (say a spring) is either stretched or compressed, work is being done against the elastic spring force. The work done is `W = 1/2 kx^2`
where, k is spring constant and x is the displacement
and elastic potential energy `U = 1/2kx^2`
Elastic potential energy is always positive.
`text(Electric Potential Energy)`
The electric potential energy of two point charges `q_1` and `q_2` separated by a distance r in vacuum is given by
`U = 1/(4 pi epsi_0) (q_1q_2)/r`
where , `1/(4 piepsi_0) = 9.1 xx 10^9 N-m^2//C^2` = constant
Energy is defined as the capacity or ability of a body to do work. Energy is scalar quantity and its units and dimensions are the same as that of work. Thus, SI unit of energy is joule. There are so many types of energy e.g. kinetic, potential, electrostatic, magnetic, geothermal, elastic, solar etc. Some of them are described below. Some other commonly used units of energy are
`1 erg = 10^-7` J
`1 cal = 4.186 J ~~ 4.2 J`
`1 kcal = 4186 J, 1 kWh = 3.6 xx 10^6 J`
and 1 electron volt `= 1 eV = 1.60 xx 10^-19 J`
`text(Kinetic Energy)`
Kinetic Energy (KE) is the capacity of a body to do work by virtue of its motion. Motion may be either transnational or rotational.
A body of mass m, moving with a velocity v, has a kinetic energy
`K =1/2 mv^2`
Thus , `K prop m`
`K prop v^2`
Kinetic energy of a body is always positive irrespective of the sign of velocity v. Negative kinetic energy is impossible.
Kinetic energy is correlated with momentum as
`K = p^2/(2m) ` or `p = sqrt( 2mK)`
Kinetic energy for a system of particle will be
`K =1/2 sum_i m_i v_i^2`
Kinetic energy depends on the frame of reference. Kinetic energy of a passenger sitting in a running train is zero in the frame of reference of the train but is finite in the frame of reference of the earth.
`text(Potential Energy)`
Potential Energy (PE) is energy of the body by virtue of its position, configuration or state of strain. The relation between potential energy and work done is
`W = - Delta U`
where, `DeltaU` is change in potential energy.
Change in potential energy of a body between any two points is equal to the negative of work done by the conservative force in displacing the body between these two points, without there being any change in kinetic energy. Thus,
`dU = - dW = - F * dr`
and `U_2 - U_1 = - W`
`= -int_(r_1)^(r_2) F * dr`
Value of the potential energy in a given position can be defined only by assigning some arbitrary value to the reference point. Generally, reference point is taken at infinity and potential energy at infinity is taken as zero. In that case,
`U = - W = - int_(oo)^r F * dr`
Potential energy is a scalar quantity but has a sign. It may be positive as well as negative.
► Generally potential energy is of three types
`text(Gravitational Potential Energy)`
It is the energy associated with the state of separation between two bodies which interact via the gravitational force. The gravitational potential energy of two particles of masses `m_1` and `m_2` separated by a distance r is
`U = (-Gm_1m_2)/r`
Generally, one of the two bodies is our earth of mass M and radius R If m is the mass of the other body, situated at a distance r(`r >= R`) from the centre of earth, the potential energy of the body
`U(r) = -(GMm)/r`
`text(Some Important Points)`
If a body of mass m is raised to a height h from the surface of earth, the change in potential energy of the system
(earth + body) comes out to be
`DeltaU=(mgh)/(1+h/R)` or `DeltaU~~mgh`, if `h<
Thus, the potential energy of a body at height h,
i.e. mgh is really the change in potential energy of the system for `h < < R`.
For the gravitational potential energy, the zero of the potential energy is chosen to be the ground.
`text(Elastic Potential Energy)`
Whenever an elastic body (say a spring) is either stretched or compressed, work is being done against the elastic spring force. The work done is `W = 1/2 kx^2`
where, k is spring constant and x is the displacement
and elastic potential energy `U = 1/2kx^2`
Elastic potential energy is always positive.
`text(Electric Potential Energy)`
The electric potential energy of two point charges `q_1` and `q_2` separated by a distance r in vacuum is given by
`U = 1/(4 pi epsi_0) (q_1q_2)/r`
where , `1/(4 piepsi_0) = 9.1 xx 10^9 N-m^2//C^2` = constant