Kinetic Energy

As noted earlier, if an object of mass m has velocity v, its kinetic energy K is 

K = $\frac{1}{2}m \mathbf{v} .\mathbf{v}=\frac{1}{2}mv^2$

Kinetic energy is a scalar quantity. The kinetic energy of an object is a measure of the work an object can do by the virtue of its motion. 

This notion has been intuitively known for a long time. The kinetic energy of a fast flowing stream has been used to grind corn. Sailing ships employ the kinetic energy of the wind. Table 6.2 lists the kinetic energies for various objects.

Fig.1: Typical kinetic energies (K)

Example 1 

In a ballistics demonstration a police officer fires a bullet of mass 50.0 g with speed 200 m s-1 (see Table 6.2) on soft plywood of thickness 2.00 cm. The bullet emerges with only 10% of its initial kinetic energy. What is the emergent speed of the bullet ?

Answer 

The initial kinetic energy of the bullet is 

mv$^{-2}$/2 = 1000 J. 

It has a final kinetic energy of 

0.1×1000 = 100 J. 

If v$_f$ is the emergent speed of the bullet, 

$\frac{1}{2}mv_f^2$ = 100 J

$v_f$ = $\sqrt{\frac{2 \times 100 \ J}{0.05 \ kg}}$ = 63.2 m.s$^{–1}$ 

The speed is reduced by approximately 68% (not 90%).