# Physics Assignment Help With Conservation of Mechanical Energy

## Conservation of Mechanical Energy

From the previous section we know that the work done by a conservative force in terms of the change in potential energy is given by

**D***U ***= - WC (i)**

where

*U*is the potential energy and

*WC*is the work done by a conservative force.

From the

*work-energy theorem*, we know that

*Wnet*=**D**

*K*Where

*Wnet*represents the sum of work done by all the forces acting on the mass.

If a particle is subject to only

*conservative forces*, then

*WC*=*Wnet*=**D**

*K*Thus, the equation (i) becomes,

**D**

*U***= -**

**D**

*K***or**

**D**

*U***+**

**D**

*K***= 0 (ii)**

The equation (ii) tells us that the

*total change in potential energy plus the total change in kinetic energy is zero if only conservative forces are acting on the system*.

That is, there is no change in the sum of

*K*plus

*U*.

**D**

**(**

*K*+*U*) = 0 (iii)**or**

**D**

*E***= 0 where**

*E*=*K*+*U*The quantity

**is called the**

*E = K + U**total mechanical energy*.

According to equation (iii), when only conservative forces act, the change in total mechanical energy of a system is zero, in other words, If only conservative forces perform work

*on*and

*within*a system of masses,

*the total mechanical energy of the system is conserved*.

Alternatively, the equation (iii) may be written as

**(**

*Kf*+*Uf*) - (*Ki*+*Ui*) = 0**or**(iv)

*Kf*+*Uf*=*Ki*+*Ui*Since

**D**

*E***= 0,**integrating both sides,

we get

*E*= constant.

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