Question

(a) Explain by an example what is meant by potential energy. Write down the expression for gravitational potential energy of a body of mass m placed at a height h above the surface of the earth.
(b) What is the difference between potential energy and kinetic energy?
(c) A ball of mass 0.5 kg slows down from a speed of 5 m/s so that of 3 m/s. Calculate the change in kinetic energy of the ball. State your answer giving proper units.

Answer 1

(a) An example to explain the fundamental meaning of potential energy is as follows:
A brick lying on the ground has no energy, so it cannot do any work. If we lift the brick to the roof of a house, the work done in lifting the brick against gravity gets stored in it in the form of potential energy. Thus, the energy in the brick is due to its higher position with respect to the ground, which is known as potential energy.

We can calculate the potential energy of a body of mass (m) lifted by a height (h) as,
Potential energy = (Weight of body) × (Vertical distance)
So,
P.E = m × g × h
Where,
(P.E) - Potential energy
(m) - Mass of body
(g) - Acceleration due to gravity
(h) - Height by which the body is lifted

(b) The difference between potential and kinetic energy are:

Potential Energy	Kinetic Energy
It is the energy of a body by virtue of its change in shape, size or configuration.	It is the energy of a body by virtue of its motion.
It is independent on the speed of the body.	It is directly proportional to the square of the speed of the moving body.

(c) Mass of the ball, (m) = 0.5 kg
Initial velocity, (v₁) = 5 m/s
Final velocity, (v₂) = 3 m/s
So, initial kinetic energy can be calculated as,
$K.E=\frac{1}{2}m{v}^2$
Therefore, initial kinetic energy,
$$\begin{gathered} (K.E{)}_1=\frac{1}{2}\times 0.5\times 5^2\mathrm{J} \\ =6.25\mathrm{J} \end{gathered}$$
Similarly, final kinetic energy,
$$\begin{gathered} (K.E{)}_2=\frac{1}{2}\times 0.5\times 3^2\mathrm{J} \\ =2.25\mathrm{J} \end{gathered}$$
So, Work done = Change in kinetic energy
Therefore work done,
Work done = (KE)₂ – (KE)₁
= (2.25 – 6.25) J
= – 4 J
A negative sign shows that the force applied is opposite to the direction of motion of the body.