Question

Which one among kinetic energy, potential energy and mechanical energy cannot be negative?
(A) kinetic energy
(B) potential energy
(C) mechanical energy
(D) potential energy and mechanical energy

Answer 1

The three energies which are given in the questions are having different formulas. In that formula some parameters are never negative and some parameters are negative. By checking the parameters, the solution of this question is determined.

Useful formula
The kinetic energy of the object is given by,
$KE = \dfrac{1}{2}m{v^2}$
Where, $KE$ is the kinetic energy of the object, $m$ is the mass of the object and $v$ is the velocity of the object.
The potential energy of the object is given by,
$PE = mgh$
Where, $PE$ is the potential energy of the object, $m$ is the mass of the object, $g$ is the acceleration due to gravity and $h$ is the height of the object.
The mechanical energy of the object is given by,
$ME = KE \times PE$
Where, $ME$ is the mechanical energy of the object, $KE$ is the kinetic energy of the object and $PE$ is the potential energy of the object.

Complete step by step solution
1. The kinetic energy of the object:
The kinetic energy of the object is given by,
$KE = \dfrac{1}{2}m{v^2}$
From the above equation the mass of the object and the velocity of the object both are never negative. If suppose the object is decelerating, then the velocity is said to be negative, by squaring the velocity, then the velocity will become positive. So, the Kinetic energy of the object never is negative from the above equation.

2. The potential energy of the object:
The potential energy of the object is given by,
$PE = mgh$
From the above equation, the mass and the acceleration due to gravity both are not negative. The height of the object is sometimes positive and sometimes negative. So, the potential energy has the possibility of the negative terms. So, we cannot surely tell that the potential is only positive or only negative.

3. The mechanical energy of the object:
The mechanical energy of the object is given by,
$ME = KE \times PE$
From the above equation, the kinetic energy is not negative but the potential energy has the possibility of both positive and negative, so the sign of the mechanical energy depends on the potential energy. If the potential energy is negative the mechanical energy is negative.

Hence, the option (A) is the correct answer.

Note: In some systems if the energy leaves the system, then its sign is negative. If the work is done on the system by some energy, then the sign of the energy is positive. If the work is done by the system, then the sign of the energy is negative.