For a conservative force, work done by it is independent of path. The law of conservation of mechanical energy is,
Suppose only conservative initial forces operate between parts of a system, work done by external forces is zero and the potential energy of the system (U) is defined corresponding to these forces. Then,
Also, according to Work-Energy Theorem, work done by all forces is equal to change in Kinetic Energy so
Let us take an example of a ball released from a height above Earth. For the earth-ball system,
The gravitational potential energy of the earth-ball system = mgh + C
Where h is height of the ball above the earths surface and ‘C’ is the gravitational potential energy of the system when the ball is at Earth`s surface
The Kinetic Energy of the Ball = 0.5 * m * v2
As per law of conservation of mechanical energy,
Q.1 A ball of mass 0.01 Kg is dropped from a height of 20m above the ground. Find its K.E. when it is (a) 10m above ground (b) zero m from ground. Take g = 10 m/s^2.
Q.2 A block mass ‘m’ is kept in a massless pan supported by a vertical spring of stiffness = k. The system remains upright throughout the motion. After the mass- spring system is released from its initial position, find the compression in the spring when the mass (a) is at equilibrium (b) at rest for first time after release.
Q.3 A block of mass m is kept at height of 4.9m on an incline which curves and merges with horizontal surface. At the end of the horizontal surface there is a spring of spring constant k = 400 N/m attached to wall. As the block is released it would eventually compress the spring. Find the maximum compression in the spring (g = 9.8 m/s^2).