Title 6.Work, Energy and Power-f.pdf ✅

1 | P a g e 1 NEET-2022 Ultimate Crash Course NEET-2022 Ultimate Crash Course PHYSICS Work, Energy and Power
2 | P a g e 2 NEET-2022 Ultimate Crash Course POINTS TO REMEMBER • We can calculate the work done by a force on an object, but that force is not necessarily the cause of the object’s displacement. For example, if you lift can object (negative), work is done on the object by the gravitational force, although gravity is not the cause of the object moving upward • Work is defined for an internal or displacement. There is no term such as instantaneous work similar to instantaneous velocity • For a particular displacement, the work done by a force is independent of the type of motion, i.e., m whether it moves with constant velocity, constant acceleration or retardation, etc.. • For a particular displacement as work is independent of time. Work will be same for same displacement whether the time taken is small or large • When several forces act, the work done by a force for a particular displacement is independent of other forces. ➢ Work Done by Spring Force:
3 | P a g e 3 NEET-2022 Ultimate Crash Course Whenever a spring is stretched or compressed, the spring force always tends to restore it to the relaxed position. A spring stretched from its equilibrium position. F s and s are antiparallel. Fext and s are parallel. A spring is compressed from its equilibrium position. F s and s are antiparallel. Fext and s are parallel. Work done by spring force The work done by spring force is negative both in compression and extension Work done by external force The work done by external force is positive both in compressing or stretching the spring Note: • Like gravity, the work done by spring force only depends on the initial and final positions • Also, the net work done by the spring force is zero for any path that returns to the initial position ➢ Potential Energy Curve: A graph plotted between the potential energy of a particle and its displacement from the centre of force is called potential energy curve. Figure shows a graph of potential energy function U x( ) for one dimensional motion. As we know that negative gradient of the potential energy gives force. Therefore, x dU F dx = −
4 | P a g e 4 NEET-2022 Ultimate Crash Course Nature of Force: Attractive force Repulsive force Zero force On increasing x, if U increases, dU dx / is positive, then F is in negative direction i.e., force is attractive in nature. In graph, this is represented in region BC. On increasing x, if U decreases, dU dx / is negative, then F is in positive direction, i.e., force is repulsive in nature. In graph, this is represented in region AB On increasing x, if U does not change, dU dx / is o, then F is zero, i.e., no force works on the particle. Point B, C and D represent the point of zero force or these points can be termed as position of equilibrium ➢ Stable Equilibrium: The particle is in equilibrium at A, we call it “stable equilibrium”. This is the sufficient and necessary condition for “oscillations” of an object At stable equilibrium, 0 dU dx = and 2 2 0 d U dx  ➢ Unstable Equilibrium: The particle is in “unstable equilibrium” at B. As stable equilibrium, 0 dU dx = and 2 2 0 d U dx  ➢ Neutral Equilibrium: Finally, let us come the point C. At C, F = 0 as discussed earlier and the particle is in equilibrium at C. Let us displace the particle slowly in either side to (4) and (5). Since at both (4) and (5); dU dx / 0 = , we can say that the particle experiences no force when it is displaced near C. In other words, the particle will remain at rest (or move with constant velocity) at the points (4) and (5), Then we can say that the particle is simultaneously neutral and it is in equilibrium because no net force acts on the particle when it undergoes a displacement near C. Hence, at C, the particle is said to be in “neutral equilibrium”. Note: • If the work done by a force on a body depends only upon the initial final positions of that body, then the force is conservative, e.g., gravitational, electrostatic, W K K U x U x = − = − f i i f ( ) ( ) • A force is conservative if it can be derived form a scalar quantity U x( ) by the relation F x U x x ( ) = −  ( ) / or F dU dx = − / • If the work done by a force on a body that has moved in closed path and has come back to its initial position is zero, the force is conservative. ➢ Motion in a Vertical Circle: Let us consider the motion of a point mass tied to a string of length l and whirled in a vertical circle. If at any time the body is at angular position  , as shown in figure. Let the particle is given velocity v0 at lowest position. Using conservation of mechanical energy at A and (2).  +  = K U 0 ( ) 2 2 0 1 1 1 cos 2 2 mv mv mgl      − + −   ---------------(i)