6

Work, Energy and Power

Top Formulae

The Scalar Product	A.B = AB cos θ
The scalar product follows the commutative law	A.B = B.A
The scalar product follows the distributive law	A. (B + C) = A.B + A.C  A. ( B) =  (A.B) Where  is a real number
Work	W = (F cos θ) d = fd
Kinetic energy	KE =1mv2  p2 2        2m
The equivalence of mass and energy	E = m c2
Average power	Pav  Wt
Instantaneous power	P  dW dt P = Fv
Unit of power	horsepower (hp) 1 hp = 746 W 1 kWhr = 1000 (watt) × 1 (hour) = 1000 watt hour = 1 kilowatt hour (kWh) = 103 (W) × 3600 (s) = 3.6 × 106 J
For conservative force	WAB. 1 = WAB. 2
For non-conservative force	WAB. 1 ≠ WAB. 2
Potential energy	(i)     Of a system is always defined corresponding to a conservative internal force. (ii)    Change in PE = Work done by the internal conservative force on the system ΔU = Uf – Ui = −Wc = F .drc
Gravitational potential energy	PE near the Earth’s surface with respect to the ground = mgh
Spring potential energy	= kx2

Top Concepts

•       Work done by a constant force is 

                          W Fs cosFs.

•       Work done can be positive, negative or zero.

•       Work done by a variable force 

s₂

          W F s ds( )      

                    s1

•       Work–energy theorem: The work W done by the net force on a particle equals the change in the particle’s kinetic energy.

² 1mu² FS mv 

1          2       

 W K f Ki

•       Gravitational potential energy does not depend on the choice of the reference surface for measuring height.

•       Gravitational potential energy: 

(a)          Energy possessed by a body changes with height with respect to the surface of the Earth.

(b)          GPE= −WGravitational Force 

•       Law of conservation of mechanical energy:

Total mechanical energy of the system always remains constant in the absence of dissipative forces.

•       Total mechanical energy of the system equals the sum of potential energy and kinetic energy. 

•       Work done on a system by conservative forces implies that the mechanical energy of the system remains constant. 

•       Work done by the conservative force is the same along any path.

•       Total work done by the gravitational force on the body moving along a closed loop is always zero.

                    W_gravity in closed loop = Zero

•       Work done on a system by non-conservative forces implies that the mechanical energy of the system is not conserved.

•       A conservative force is the negative gradient of potential energy function.  

F (x) = −U/x

•       Power is the rate at which work is done or energy is transformed.

•       The unit of power is watt.

1 watt = 1 joule/second

•       Linear momentum of an isolated system is always conserved in a collision.

•       A collision in which the total kinetic energy of the system is conserved is called elastic.  A collision in which the total kinetic energy of the system is not conserved is called inelastic. 

•       When two bodies collide, stick together and have a common final velocity, the collision is completely inelastic.