Module 2Conservative & Non-conservative forces and Gravitation Conservative Forces: A conservative force is one which draws or supplies no energy from or to a body in a complete round trip. A conservative force does zero total work on any closed path.That means, when a body is thrown upward, its kineticenergy is decreased due to the downward pull of theearth. It reaches a definite height and then start to comedown. During the downward trip, the downward pull ofthe earth supplies kinetic energy to the body. When itreaches the starting point, the kinetic energy becomessame as its initial kinetic energy. The potential energy of the body was zero initially,became maximum at the maximum height, and reducedto zero again.Gravitational and Spring forces are conservativeforce.Non conservative Forces: The work done by a non conservative force is not recoverable orexpressible symbolically as a potential energy term. The work doneby a non conservative force is usually dissipated as heat energy. Friction and Forces exerted by muscles are nonconservativeforces. Work Done by a Constant Force:In Figure 1 a constant force Fmakes an angle with the x axis and acts on a particle whosedisplacement along the x axis isd. In this case we define the work W done by the force on the particleas the product of the component of the force along the line ofmotion by the distance d the body moves along that line. Thend]cosF[W, In the terminology of vector algebra we can write  as d.FW, where the dot indicates a scalar [or dot] product.1
Work can be positive or negative. If the particle on which a force acts has a component of motionopposite to the direction of the force, work done by that force is negative. Work Done by a Variable Force – One Dimensional Case:We consider first a force Fthat varies in magnitude only. Let the force be given as a function of positionF(x) and assume that the force acts in the x-direction. Suppose a body is moved along the x-direction bythis force. What is the work done by this variable force in moving the body from x1to x2?In Figure 2 we plot F versus x. We can write the total work done by F in displacing a body from x1to x2as 21)(12xxdxxFW, As an example, consider a spring attached to a wall. The workdone by the applied force in stretching the spring so that itsendpoint moves from x1to x2is 21212122122121)()(xxxxkxkxdxkxdxxFWIf we let x1=0 and x2=x, we obtainxkxdxkxW0221)(, Kinetic Energy:Kinetic energyis the energy of motion. An object which has motion- whether it to be vertical or horizontalmotion - has kinetic energy. There are many forms of kinetic energy – (i)Vibrational (the energy due to vibrational motion), (ii)Rotational (the energy due to rotational motion), and (iii)Translational (the energy due to motion from one location to another).