The document discusses the concepts of work, power, and energy in the context of physics, particularly focusing on mechanical energy. It defines work as the product of force and displacement, while also distinguishing between potential energy, kinetic energy, and strain energy. Additionally, it provides examples of calculations related to the kinetic energy and angular acceleration of various mechanical systems.

1. Lecture III
Work and Energy

2. Work
-Whenever a force acts on a body and the body undergoes a displacement in the
direction of the force, then work is said to be done.

3. Power
-It may be defined as the rate of doing work or work done per unit time.
Mathematically,

4. Energy
-It may be defined as the capacity to do work. The energy exists in many forms e.g.
mechanical, electrical, chemical, heat, light etc. But we are mainly concerned with
mechanical energy.
-The mechanical energy is equal to the work done on a body in altering either its
position or its velocity. The following three types of mechanical energies are
important from the subject point of view:
1. Potential Energy
2. Kinetic Energy
3. Strain Energy

5. Potential Energy
-It is the energy possessed by a body for doing work, by virtue of its position. For
example, a body raised to some height above the ground level possesses potential
energy because it can do some work by falling on earth’s surface.

6. Strain energy
● It is the potential energy stored by an elastic body when deformed. A
compressed spring possesses this type of energy, because it can do some
work in recovering its original shape. Thus if a compressed spring of stiffness
s Newton per unit deformation (i.e. extension or compression) is deformed
through a distance x by a load W, then

7. Kinetic Energy
-It is the energy possessed by a body, for doing work, by virtue of its mass and
velocity of motion. If a body of mass m attains a velocity v from rest in time t,
under the influence of a force F and moves a distance s, then

9. Worked Examples
1. The flywheel of a steam engine has a radius of gyration of 1 m and mass
2500 kg. The starting torque of the steam engine is 1500 N-m and may be
assumed constant.Determine : 1. Angular acceleration of the flywheel, and 2.
Kinetic energy of the flywheel after 10 seconds from the start.

11. 2. A road roller has a total mass of 12 tonnes. The front roller has a mass of 2
tonnes, a radius of gyration of 0.4 m and a diameter of 1.2 m. The rear axle,
together with its wheels, has a mass of 2.5 tonnes, a radius of gyration of 0.6 m
and a diameter of 1.5 m. Calculate :
1. Kinetic energy of rotation of the wheels and axles at a speed of 9 km/h,
2. Total kinetic energy of road roller
3. Braking force required to bring the roller to rest from 9 km/h in 6m on the level.