Question

The potential energy of a body is given by \(U(x)\) and it has mechanical energy is E. Then its potential energy when its velocity is zero is given by?

Answer 1

The potential energy of a body is given by \(U(x)\), and its total mechanical energy is E. When the body's velocity is zero, it means it has come to rest, and its kinetic energy is zero. In this scenario, we can determine the potential energy.
The total mechanical energy (E) of the body is the sum of its kinetic energy (K) and potential energy (U). Since the body is at rest, its kinetic energy is zero, so we can write:
\(E = K + U\)
Since K = 0, the equation simplifies to:
\(E = 0 + U\)
Therefore, the potential energy of the body when its velocity is zero is equal to its total mechanical energy (E).

The particle's potential energy becomes zero when it reaches x=2Ek​ where x>0. This occurs when the particle's kinetic energy (KE) is equal to E or half the mass (m) times the square of its velocity (v) equals E.