Force of Friction

Energy

Anything which has the ability to do work possesses energy. When the work is done by such a body, it loses energy. When the work is done on the body, it gains energy. Energy is a scalar quantity and measured in joules (J).

Mechanical Energy can be of two types: Kinetic Energy and Potential Energy

Kinetic Energy (KE): It is the energy possessed by a body due to its motion.

(m : mass of the body and v : velocity)

Potential Energy (PE): When work is done on a system and the system preserves this work in such a way that it can be subsequently recovered back in form of some type of energy, the system is capable of possessing potential energy.

Types of potential energy:

In Physics, we usually come across following types of potential energies:

(i)Gravitational potential energy: It is the usual form of potential energy and is the energy associated with the state of separation between bodies that interact via gravitational force. If two particles of masses m1 and m2 are separated by a distance r, then their potential energy is

For a body of mass m at height h relative to the surface of earth (of radius R ) the above relation is reduced to

If h << R the U = mgh. Gravitational potential energy may be positive or negative.

(ii)Elastic potential energy: It is the energy associated with state of compression or expansion of an elastic spring (or spring like object) and is given by

where k is force constant and DL is the elongation or compression. Elastic potential energy is always positive.

(iii)Electric potential energy: It is associated with state of separation between charged particles interacting via electric force.

Mechanical energy: Mechanical energy (E) of a body or system is defined as the sum of its kinetic energy (K) and potential energy (U), i.e.

E = K + U

Note: Regarding mechanical energy E, we must remember that

  1. it depends on the frame of reference.
  2. a body may have mechanical energy without having either kinetic energy or potential energy. However, if both K and U are zero then the mechanical energy will also be zero.
  3. as E = K + U and K is always + ve, hence E > U.
  4. If U is +ve, E must be positive.
  5. If U is _ve and |U| < K, then mechanical energy E will be + ve.
  6. If U is _ve and |U| > K, then E = - ve.

Thus, a body can have negative mechanical energy if its potential energy U is negative and in magnitude it is more than kinetic energy K. Such a state is called the bound state e.g., and electron in an atom or a satellite revolving around a planet.

Nature of restoring force

If the length of a spring is increased or decreased by a distance x, the spring exerts a restoring force to oppose this change.

Restoring force = kx

where k: spring constant (or force constant); units of k : N/m is

To keep the spring elongated (or compressed) in this position, the applied force should also be of same magnitude.

Work done in stretching or compressing a spring by a distance x is given by

Elastic potential energy stored in a spring =

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