- 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

- we already have an idea that energy is associated closely with work and we have defined energy of a body as the capacity of the body to do work

- In dynamics body can do work either due to its motion ,due to its position or both due to its motion and position

- Ability of a body to do work due to its motion is called kinetic energy for example piston of a locomotive is capable of doing of work

- Ability of a body to do work due to its position or shape is called potential energy For example workdone by a body due to gravity above surface of earth

- Sum of kinetic energy and Potential energy of body is known as its mechanical energy

Thus

Mechanical Energy=Kinetic Energy+Potential Energy

- From work energy theorem , we know that

$\Delta K= W_{net}$

- Now for conservative forces , we know that

$\Delta = - F.dx

or

$W = -\Delta U$

- If only conservative forces acting on the system ,then
$\Delta K= W_{net}$

$\Delta K = - \Delta U$

$ \Delta K + \Delta U=0$

or

$K_2 - K_1 + U_2 - U_1=0$

$K_2 + U_2 = K_1 + U_1$

or

$K + U=constant$

- We already know that above quantity is called the mechanical energy of the system
- So we see that if only conservative forces are acting on the system, the total mechanical energy of the system remains constant.It does not increase or decrease and it is conserved . This is called the Principal of Conservation of Mechanical Energy
- If non-conservative forces are also present in the system such as friction, the work energy theorem is given as

$W_{net}= W_{c} + W_{nc}$

Now ,$\Delta K= W_{net}$

Therefore,

$\Delta K=W_{c} + W_{nc}$

$\Delta K -W_{c}= W_{NC}$

$\Delta K + \Delta U = W_{NC}$

- So, we see that total mechanical energy is not conserved if the non-conservative forces are present

A man throws an ball of mass .10 kg from the top of the building of height 10 m with speed of 20 m/s. Find kinetic energy and speed of the ball when it reaches the ground? (take g=10 m/s

From law of conservation of mechanical energy

(Kinetic Energy + Potential energy) at top = ( Kinetic energy ) at ground

$KE_{ground}= \frac {1}{2} mv^2 + mgH = \frac {1}{2} .1 20^2 + .1 \times 10 \times 10= 30 J$

Now

$\frac {1}{2} mv_g^2 = 30$

or

v=24.5 m/s

A object of mass 10 kg moving with a speed 5 m/s on a smooth surface and it collide with a horizontally mounted spring of spring constant 1000 N/m. What is the maximum compression of the spring ?

At maximum compression , Kinetic energy of the object converts into potential energy of the spring

From law of conservation of mechanical energy

(Kinetic Energy) initially = ( Potential Energy ) at maximum compression

$\frac {1}{2}mv^2 = \frac {1}{2}kx^2$

or

$ x= v \sqrt {\frac {m}{k}}$

or x=.5 m

Class 11 Maths Class 11 Physics Class 11 Chemistry