MOD 2-Cons. & Non-Cons. Forces and Gravitation - Module 2 Conservative Non-conservative forces and Gravitation Conservative Forces A conservative

MOD 2-Cons. & Non-Cons. Forces and Gravitation - Module 2...

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Module 2 Conservative & 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 kinetic energy is decreased due to the downward pull of the earth. It reaches a definite height and then start to come down. During the downward trip, the downward pull of the earth supplies kinetic energy to the body. When it reaches the starting point, the kinetic energy becomes same as its initial kinetic energy. The potential energy of the body was zero initially, became maximum at the maximum height, and reduced to zero again. Gravitational and Spring forces are conservative force. Non conservative Forces: The work done by a non conservative force is not recoverable or expressible symbolically as a potential energy term. The work done by a non conservative force is usually dissipated as heat energy. Friction and Forces exerted by muscles are nonconservative forces . Work Done by a Constant Force: In Figure 1 a constant force F makes an angle with the x axis and acts on a particle whose displacement along the x axis is d . In this case we define the work W done by the force on the particle as the product of the component of the force along the line of motion by the distance d the body moves along that line. Then d ] cos F [ W , [1] In the terminology of vector algebra we can write [1] as d . F W , [2] 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 motion opposite 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 F that varies in magnitude only. Let the force be given as a function of position F(x) and assume that the force acts in the x-direction. Suppose a body is moved along the x-direction by this force. What is the work done by this variable force in moving the body from x 1 to x 2 ? In Figure 2 we plot F versus x. We can write the total work done by F in displacing a body from x 1 to x 2 as 2 1 ) ( 12 x x dx x F W , [3] As an example, consider a spring attached to a wall. The work done by the applied force in stretching the spring so that its endpoint moves from x 1 to x 2 is 2 1 2 1 2 1 2 2 12 2 1 2 1 ) ( ) ( x x x x kx kx dx kx dx x F W If we let x 1 =0 and x 2 =x, we obtain x kx dx kx W 0 2 2 1 ) ( , [4] Kinetic Energy: Kinetic energy is the energy of motion. An object which has motion- whether it to be vertical or horizontal motion - 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).

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