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.

The potential energy (PE) of an object at a height above the ground can be calculated using the formula:

PE = m x g x h

Where:
– PE is the potential energy,
– m is the mass of the object (40 kg),
– g is the acceleration due to gravity (approximately 9.81 m/s² on Earth,
– h is the height above the ground (5 m).

Let’s calculate the potential energy of the object first:

PE = 40 kg x 9.81 m/s² x 5m
PE = 1962 J

Therefore, the potential energy of the object raised to a height of 5 m above the ground is 1962 joules.

Now, to find the kinetic energy (KE) of the object when it is halfway down (at a height of 2.5 m), we’ll use the principle of conservation of mechanical energy, assuming no air resistance or other non-conservative forces.

At the midpoint, potential energy is converted entirely into kinetic energy:

KE = PE_initial – PE_final

At the midpoint:
– PE_initial = 1962 J (potential energy at the top)
– PE_final = 0 J (potential energy at the midpoint when it’s fully converted to kinetic energy)

KE = 1962 J – 0 J
KE = 1962 J

Therefore, when the object is halfway down, its kinetic energy is also 1962 joules.