• This is the energy possessed by a body by virtue of its position or shape. A body that is elevated from ground level, a compressed spring or bent bow - all these possess potential energy.
• If a body of mass m kilograms is at a height of h meters from the ground, then its potential energy `PE. = m xx g xx h` joules where g is the acceleration due to gravity at the place.
• We cannot measure the actual value of potential energy. It is always measured with respect to a particular reference level. So, we can only measure the change in potential energy of a particular body on changing its configuration and not its actual value. In our example of gravitational potential energy, the potential energy is measured taking ground level (h = 0) as the reference (where PE is assumed zero).
• This energy is potential because it has the capacity - the potential - to do work if given a chance. Thus if coconut on a coconut tree falls down say on a thin sheet of glass, it can break the glass into pieces.
• 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< < R`
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`.
`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
• This is the energy possessed by a body by virtue of its position or shape. A body that is elevated from ground level, a compressed spring or bent bow - all these possess potential energy.
• If a body of mass m kilograms is at a height of h meters from the ground, then its potential energy `PE. = m xx g xx h` joules where g is the acceleration due to gravity at the place.
• We cannot measure the actual value of potential energy. It is always measured with respect to a particular reference level. So, we can only measure the change in potential energy of a particular body on changing its configuration and not its actual value. In our example of gravitational potential energy, the potential energy is measured taking ground level (h = 0) as the reference (where PE is assumed zero).
• This energy is potential because it has the capacity - the potential - to do work if given a chance. Thus if coconut on a coconut tree falls down say on a thin sheet of glass, it can break the glass into pieces.
• 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< < R`
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`.
`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