- Work done Formula
- Work done by variable force
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- Kinetic energy
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- Work Energy theorem
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- Potential energy
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- Potential energy of the spring
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- Conservative Forces
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- Mechanical Energy and Conservation
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- Power definition
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- Law of Conservation of energy
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- Work Energy and Power Solved Examples

- Power is defined as rate of doing the work

- if ΔW amount of work is done in time interval Δt ,the instantaneous power delivered will be

$P=\frac {\Delta W}{ \Delta t}$

or

$P=\frac {dW}{dt}$

- For total work done W in total time t,then average power is defined

$P_{avg}=\frac {W}{t}$

- If Power (P) does not vary with time ,then $P=P_{avg}$

- the instantaneous power can also be written as

$P=\frac {dW}{dt}$

Now as dW=Fdx

$P=\frac {F dx}{dt}$

$P = F \frac {dx}{dt}$

Now velocity is given as $v= \frac {dx}{dt}$

Therefore,

$P =F.v$

This can be written in vector form as

P=**F**.**v**

This is scalar dot product of force and velocity vector.

If the Force and velocity vector are at angle,then

$P= Fvcos \theta$

- SI unit of power is joule/sec also called watt

- Power, like work and energy, is a scalar quantity. Its dimensions are $[ML^2T^{-3}]$.
- Another unit of power is horsepower(hp)

1Hp=746 watt

An elevator can carry a maximum load of 1000 kg (elevator + passengers) is moving up with a constant speed of 2 m/s. The frictional force opposing the motion is 4000 N. Determine the minimum power delivered by the motor to the elevator in watts ?

The downward force on the elevator is

$F = m g + f_{fric}$

$f = (1000 \times 10) + 4000 = 14000 N$

The motor must supply enough power to balance this force. Hence,

$P = F. v = 14000 \times 2 = 28000 W$

A truck of mass 1000 kg accelerates on the level road from 10 m/s to 20 m/s in 5 sec. The frictional force present is 4000N. Find the average power delivered by the engine.?

Acceleration of truck = $\frac {20 -10}{5} = 2 m/s^2$

So total force delivered by the engine = $ma + f_{fric} = 1000 \times 2 + 4000 = 6000 N$

Average power = F X average velocity = 6000 X 30 = 18000W

Class 11 Maths Class 11 Physics Class 11 Chemistry