work power energy

Conservative Forces:     

If workdone by the force around a closed path is zero and it is independent of path then it is a conservative force. Under conservative force

  \(F=-\frac{dU}{dx}\) where \(U\)  is Potential Energy.

\(dU=-\int{\overline{F}}.\overline{dx}\)

Ex 1: Gravitational force is a conservative force

       Ex 2: Electrostatic force betwen two stationary electric charges is a conservative force.

                  Ex 3: Magnetic force between two magnetic poles is a conservative force

                  Ex 4: Elastic force in a stretched spring is a conservative force

    Non-Conservative Forces:

          If the workdone by a force around a closed path is not equal to zero and it is dependent on the path then the force is non-conservative  force

               Ex:-Force of friction , Viscous force. Workdone by the non-conservative force will not be stored in  the form of Potential energy.

             Potential energy is undefined for a non conservative force.

      Conceptual understanding

1. Negative of work done by the conservation forces on a system is equal to

              Ans: the change in potential energy of the system.

2. In the case of conservative force

           Ans:  Work done is indepenent of the path (or)Work done in a closed loop is zero .

Ø   When a body of mass m moves with a velocity ‘v’ its kinetic energy is   \(KE=\frac{1}{2}m{{v}^{2}}\)          

          If two bodies of different masses have same velocity then \(KE\,\alpha \,m\)

ØAlso \(KE=\frac{1}{2}m{{v}^{2}}=\frac{{{m}^{2}}{{v}^{2}}}{2m}=\frac{{{\left( mv \right)}^{2}}}{2m}=\frac{{{p}^{2}}}{2m}\)

Ø If the two bodies of different masses have same momentum then lighter  body will have greater

                  K.E \(\left( \because KE\alpha \frac{1}{m} \right)\)

ØWhen a bullet is fired from a gun the momentum of the bullet and gun are equal and opposite. It can be seen from the above expression that the ratio of kinetic energics of two bodies having the same

magnitude of momenta is in the inverse ratio of their masses \(i.e\,\,\,\,\frac{K\,bullet}{K\,gun}=\frac{M\,gun}{M\,bullet}\)

          Hence, the KE of the bullet is greater than that of the gun     

Ø A body can have energy without momentum. But it can not have momentum without energy.

 ØA bullet of mass ‘m’ moving with velocity ‘v’ stops in wooden block aftger penterating through a  distance x. If F is resistance offered by the block of the bullet (Assuming F is Constant inside the block)

                 \(\frac{1}{2}m{{v}^{2}}=Fx\)

                  \(F=\frac{m{{v}^{2}}}{2x}\)

                \(\therefore \,{{v}^{2}}\alpha x\)

    Conceptual understanding

     1)  For the same kinetic energy, the momentum shall be maximum for which of the following particle?

                Ans:alpha particle

2)  If the momentum of a particle is plotted on X-axis and its kinetic energy on the Y-axis, the graph is a

              Ans:  parabola

Illustrations:

1.  A body starts from rest and moves with uniform acceleration. What is the ratio of kinetic energies at the end of 1st, 2nd and 3rd seconds of its journey?

                Ans:  1 : 4 : 9

2. A 60 kg boy lying on a surface of negligible friction throws horizontally a stone of mass 1 kg with a speed of 12 m/s away from him.  As a result with what kinetic energy he moves back?

                        Ans: 1.2 J