x Icse Physics Note-4 Work, Energy & Power

WORK, ENERGY & POWER WORK If a body moves when a force is applied on it, then a work is done. If the body moves along the direction of the force, then the work done by the force is positive. If the body moves opposite to the force, then the work done by the force is negative.

Definition of work 1. Work done by force is the product of force and the displacement in the direction of force. 2. Work is the product of displacement & component of force in the direction of displacement W = F x S Cos θ,

where θ is the angle between F and S (angle between force and displacement)

Since W = F x S Cos θ. i). When θ= 0, Work done W = FS Cos 0 = FS

(maximum)

ii) When θ = 90° (displacement is perpendicular to force). Work done W = FS Cos 90 = 0 iii).When θ = 180° (displacement is opposite to force). Work done W = FS Cos 180 = - FS. (Minimum) In this case Work done by the force. Work done by Gravitational force W= mgh, when the body moves downward, and W = - mgh when the body moves upward. Examples 1. When you push a body and the body does not move, W = 0 2. When carry a load in your hand along a horizontal distance, work done by you W=0, Your are supporting the body applying a force vertically upward, while the body moves horizontally ( perpendicular to force)

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3. When move a body vertically upward through a height. Work done by you W = mgh. Work done by gravitational force of Earth W= -mgh (here gravitational force act downward while the body moves upward. 4. When a body is dropped from a height, work done by gravitational force W =mgh (positive, Gravitational force and displacement are down word.) 5. Zero work is done, by centripetal force in uniform circular motion. (Force is always perpendicular to displacement) Work is a scalar quantity. Its unit in SI system is Joule (J), which is the same as Fm. CGS unit of work is Erg. 1 J = 107 Erg Other units (i). Watt Hour 1 Wh = 3600 J = 3.6 KJ,

(ii). KiloWatt Hour 1 kWh = 3.6 x 106 J

Definition of 1 joule One joule is the amount work done in moving a body with a force of 1 N , one meter along the direction of force.

Work & Energy Energy is the capacity do work. Energy has the same unit has work, that is Joule. When a work is performed on a system, it will be converted to some form of energy and will be stored in the system.

Power Rate of doing work is power. It can also be described as right of consuming energy. Power =


  

=

     

SI unit of power is Watt = ( ) = Js-1 Definition of 1 Watt

: If one-Joule work is done in one second then the power is one watt.

Horse Power (HP) is another unit of power. 1 HP= 746 W

Different forms of Energy 1. Potential energy Energy possessed by a body due to its position or configuration 2. Gravitational potential energy When a body lifted through a height against the gravitational force mg, the work done W = Fx h= mgh. This is stored in the body as gravitational potential energy. Therefore Gravitational potential energy U = mgh. 3. Potential energy of a compressed spring U=

  

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here k is spring constant and x is the reduction in the length of spring. 2

4. Kinetic energy Energy possessed by a body due to its motion. There are 3 kinds of kinetic energies. Translational, rotational and vibrational Expression for kinetic energy(K) Consider a body of mass m at rest (u=0). Now a force F is applied on that body, till it moves through a distance “S” along the force. The body accelerates at a rate of “a” and reaches a speed “v’ by the time it moves the distance S. Then work done W = F x S= maS……..(1) But v2 = u2 + 2aS, where u = 0. Therefore v2= 2aS or aS = Substitute equation (2) in to (1), we get work done W= Kinetic Energy K =

 

………(2)

  . 

This work done will be stored in the body as kinetic energy.

=

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Momentum and Kinetic energy Momentum p = mv, therefore p2 = m2v2 or +

K= 

or

 

=

  

p = √-

Conservation of Energy Energy can neither be created nor destroyed but can be converted from one form to another. Conservation energy in free fall/ Energy transformation in free fall. 1. When a body falls from a height, its gravitational potential energy gets gradually converted in to kinetic energy. The total energy would remain the same at all the time. 2. When you move a body upward vertically, the work done by you W= mgh, will be stored in the body as gravitational potential energy. 3. When a body falls under gravity, the work done by the gravity will be stored in the body as kinetic energy. 4. When a spring is compressed, the work done will be converted in to potential energy and stored in the compressed spring.

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