Question

What is meant by gravitational potential energy? Derive an expression for it for a body placed at a height above the ground.

April 17, 2024

Answer

The potential energy possessed by a body due to the force of attraction of the earth on it, is called the gravitational potential energy.

When a body is placed at a height above the ground then the amount of work done in lifting the body to that height against the force of gravity is called the gravitational potential energy.

When we lift a body of mass m from the ground to a height h.Then, force of gravity (mg) acts on the body acting vertically downward which must be equal to the least upward force F required to lift the body.

Work done = force of gravity (mg) × displacement (h)

⇒ W = mgh

So, the work done on the body is stored in the form of its gravitational potential energy when it is at a height h.

Hence,

Gravitational potential energy U = mgh.

💡 Some Related Questions

The figure alongside shows a simple pendulum of mass 200 g. It is displaced from the mean position A to the extreme position B. The potential energy at position A is zero. At position B the bob is raised by 5 m.
(a) What is the potential energy of the pendulum at position B ?
(b) What is the total mechanical energy at point C?
(c) What is the speed of the bob at position A when released from position B ? (Take g = 10 ms^-2)

The bob of a simple pendulum is imparted a velocity of 5 m s^-1 when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air? (Take g = 10 m s^-2).

A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce a power output of 1 MW. (Take g = 10 m s^-2).

The diagram given below shows a ski jump. A skier weighing 60kgf stands at A at the top of ski jump. He moves from A and takes off for his jump at B.

(a) Calculate the change in the gravitational potential energy of the skier between A and B.
(b) If 75% of the energy in part (a) becomes the kinetic energy at B, calculate the speed at which the skier arrives at B.
(Take g = 10 ms^-2).

A metal ball of mass 2kg is allowed to fall freely from rest from a height of 5m above the ground. Taking g = 10ms-1, calculate:
(a) the potential energy possessed by the ball when it is initially at rest.
(b) the kinetic energy of the ball just before it hits the ground?
(c) What happens to the mechanical energy after the ball hits the ground and comes to rest?

A stone of mass 500 g is thrown vertically upwards with a velocity of 15 ms^-1.
Calculate:
(a) the potential energy at the greatest height,
(b) the kinetic energy on reaching the ground
(c) the total energy at its half waypoint.

A ball of mass 0.20 kg is thrown vertically upwards with an initial velocity of 20 ms^-1. Calculate the maximum potential energy it gains as it goes up.

A pendulum is oscillating on either side of its rest position. Explain the energy changes that take place in the oscillating pendulum. How does the mechanical energy remain constant in it? Draw necessary diagram.

Show that the sum of kinetic energy and potential energy (i.e., total mechanical energy) is always conserved in the case of a freely falling body under gravity (with air resistance neglected) from a height h by finding it when
(i) the body is at the top,
(ii) the body has fallen a distance x,
(iii) the body has reached the ground.

Name the type of energy possessed by the bob of a simple pendulum when it is at
(a) the extreme position,
(b) the mean position, and
(c) between the mean and extreme positions.