# Work Energy and Power

## (11) Conservative Forces

• Consider the gravitational force acting on a body .If we try to move this body upwards by applying a force on it then work is done against gravitation
• Consider a block of mass m being raised to height h vertically upwards as shown in fig 8(a) .Workdone in this case is mgh
• Now we make the block travel the path given in figure 8(b) to raise its height h above the ground.In this path workdone during the horizontal motion is zero because there is no change in height of the body due to which there would be no change in gravtitaional PE of the body and if there is no change in the speed KE would also remains same
• Thus for fig 8(b) if we add up the workdone in two vertical paths the result we get is equal to mgh

• Again if we move the the block to height h above the floor through an arbitary path as shown in fig 8(c) ,the workdone can be caluctlated by breaking the path into elementary horizontal and vertical portions
• Now workdone along the horizontal path would be zero and along the vertical paths its add up to mgh
• Thus we can say that workdone in raising on object against gravity is independent of the path taken and depends only on the intial and final position of the object
• Now we are in position to define the conservative forces
" If the workdone on particle by a force is independent of how particle moves and depends only on initial and final position of the objects then such a force is called conservative force"
Gravitatinal force,electrostatic force ,elastic force and magnetic forces are conservative forces
• Total workdone by the conservative force is zero when particle moves around any closed path returning to its initial position
• Frictional forces and viscous forces are examples of non-conservative forces as these forces always oppose the motion and result in loss in KE
• Concept of PE is associated with conservative forces only .No such PE is associated with non-conservative forces like frictional forces

## (12) Power

• Power is defined as rate of doing the work
• if ΔW amount of work is done in time interval Δt ,the instantanous power delivered will be
P=ΔW/Δt or P=dW/dt
• For total workdone W in total time t,then average power
Pavg=W/t
• If P does not vary with time ,then P=Pavg
• SI unit of power is joule/sec also called watt
• Another wunit of power is horsepower(hp)
1Hp=746watt

## (13) Principle of conservation of energy

• We have already learned that KE+PE remains constant or conserved in absence of dissipative power
• As discussed in case of spring mass system in reality dissipative forces like friction and air resistance are always present and some of the energy of the system gets dissipated in the force of heat energy by increasing the internal energy of the spring
• This continues until system finally comes to rest
• If one can somehow measure this energy ,the sum of KE,PE and this internal (or energy dissipated) would remain constant .This can be extended to all types of energy
• Energy can not be created or destroyed .It can only be transferred from one form to another form.Total energy in a closed system always remains constant
• This is the law of conservation of energy although emprical one but it has never been found violated