The Equivalence of Mass and Energy

• Physicists believed that in every physical and chemical process, the mass of an isolated system is conserved till Albert Einstein show the relation , E = m c² where c, the speed of light in vacuum is approximately 3 ×10⁸ m s^–1.
• This equation showed that mass and energy are equivalent and are related by E = m c² .
• If there is a difference between the sum of reactants and products that differene, Dm, is called mass defect.
• In case of chemical reactions the mass defect is very small and can be neglected, but in the case of nuclear reactions this becomes significant.

Principle of Conservation of Energy

• If the forces involved are non-conservative, part of the mechanical energy may get transformed into other forms such as heat, light and sound.
• However, the total energy of an isolated system does not change.
• Since the universe as a whole may be viewed as an isolated system, the total energy of the universe is constant.

Power

• Power is defined as the time rate at which work is done or energy is transferred.

Collision in 1-D

• If the initial velocities and final velocities of both the bodies are along the same straight line, then it is called a one-dimensional collision, or head-on collision.

Elastic collision:

• With the above equations we have to solve the problem

Example: Two balls initially travelling along the x-axis with opposite velocities collide with each other obliquely, is it possible that they will move in the y-axis after collision?

Solution: Yes, it is possible, if the balls have same mass and travel with same speed. Initially their total momentum in x-direction was zero as their velocities were opposite; also in y-direction it is zero because they do not have velocity in that direction.
Now after collision if their velocities are still equal and in opposite direction, the total momentum still remains zero.