An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.

Given,

Mass (m) = 40 kg

Acceleration due to gravity = 10 ms^-2

Height (h) = 5 m

Potential energy = ?

We know,

Potential energy = m g h

Substituting we get,

P.E. = 40 × 10 × 5 = 2000 J

Height when halfway down : = $\dfrac{5}{2}$ = 2.5 m

Potential energy when halfway = ?

Substituting we get,

P.E. = 40 × 10 × 2.5 = 1000 J

According to the law of conservation of energy:

Total potential energy = potential energy halfway down + kinetic energy halfway down

2000 = 1000 + K.E. halfway down

K.E. at halfway down = 2000 - 1000 = 1000 J

Hence, Potential energy = 2000 J and kinetic energy at halfway down = 1000 joules.