Physics

Example : 12
A bullet of mass 100 gm is fired with a velocity 50 m/s from a gun. Calculate the kinetic energy of the bullet.
Solution. Kinetic energy is given by
K.E. = mv²
Here m = 100 gm = 0.1 kg; v = 500 m/s
K.E. = × 0.1 × (50)²
= × 0.1 × 50 × 50 = 125 J

Example : 13
A 4 kg body is dropped from the top of a building of height 2.5 m. With what velocity will it strike the ground ? What is its kinetic energy when it strikes the ground ?
(Takes g = 9.8 m/s²)
Solution. Velocity of the body with which it strikes the ground can be calculated by using the equation, v² = u² + 2gh
Here, u = 0; g = 9.8 m/s² ; h = 2.5 m
Substituting these values, we get
v² = 0² + 2 × 9.8 × 2.5 = 49
or v = 7 m/s
Thus, the speed of the body with which it strikes the ground = 7 m/s.
Example : 14
Calculate the velocity of 4 kg mass with kinetic energy of 128 J.
Solution. The formula for kinetic energy is given by
K.E. = mv²
Here K.E. = 128 J; m = 4 kg
∴ 128 = × 4 × v²
or v² = 64; or v = 8 m/s

Example : 15
Which would have a greater effect on the kinetic energy of an object, doubling the mass or doubling the velocity ?
Solution. (i) The kinetic energy of a body is directly proportional to its "mass" (m). So, if we double the mass (so that it becomes 2m), then the kinetic energy will also get doubled.
(ii) On the other hand, kinetic energy of a body is directly proportional to the "square of its velocity" (v²). So, if we double the velocity (so that it becomes 2v), then the kinetic energy will become four times. This is because : (2v)² = 4v².
It is clear from the above discussion that doubling the velocity has a greater effect on the kinetic energy of an object.