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A stretched slingshot, a bent bow, a compressed spring, a raised ball — none is moving, yet each is ready to do work. Where is that energy hiding?
- A stretched band, a bent bow or a compressed spring stores the work done to deform it, and releases it as kinetic energy of an object in contact.
- Energy can also be stored by arrangement : separated magnet poles or electric charges, or a ball raised above the Earth, rush together when released and gain kinetic energy.
- Potential energy is the energy stored by an object due to its deformation , or in a system of objects due to their relative positions .
- For the Earth-ball system, the stored energy is usually called the gravitational potential energy of the ball.
- To raise an object of mass m to height h , we apply a force mg over distance h : work W = mg × h = mgh .
- By the work-energy theorem this becomes the potential energy: U = mgh with unit joule (J). The higher the object, the greater its potential energy.
In this Activity, we will drop a heavy ball into sand from different heights and compare the depressions to see how potential energy depends on height.
- Take a heavy ball and a container of loose sand. Raise the ball about 1 m above the sand and drop it — a depression forms.
- Now drop it from 2 m at a fresh spot; repeat once more. Compare the depths of the depressions.
- The depression is deepest when the ball is dropped from the greatest height . Raising the ball higher takes more work, so it stores more potential energy — greater height means greater potential energy.
- Potential energy — the energy stored by an object as a result of its deformation, or in a system of objects due to their relative positions.
- Gravitational potential energy — the potential energy of the Earth-object system due to the object's height; U = mgh near the Earth's surface.
A 200 g cricket ball is thrown 10 m up. Find its potential energy at the top. Take g = 10 m s⁻².
U
= mgh
= 0.2
kg
× 10
m s
-2
× 10
m
= 20
J
.
- Energy can be stored by changing the arrangement of objects in a system. Separated unlike magnet poles, or separated electric charges, move together and gain kinetic energy when released.
- Whenever objects interact through gravitational, electric or magnetic forces, the system can store energy due to the relative positions of the objects.
- Work done against internal forces such as gravitational, electric or magnetic forces can be stored as potential energy. But this is not true for all forces — work done against friction is not stored as energy. You will learn to identify such forces in higher grades.
- The expression U = mgh is valid only near the Earth's surface . Further away, the gravitational acceleration g decreases. You will learn about potential energy far from the Earth in higher grades.
- 6. Moving horizontally at constant velocity: the height does not change, so the potential energy does not change . Being raised vertically: the height increases, so the potential energy increases (by mgh ).
NCERT Question 5 — A student is slowly lifted
A student is slowly lifted straight up in an elevator from the ground level to the top floor of a building. Later, the same student climbs the staircase, all the way to the top. Given that the height of the building is h = 72.5 m, acceleration due to gravity is g = 10 m s⁻², and student's mass is m = 50 kg. (i) Find the gain in the potential energy if the student is lifted straight up to the top. (ii) Find the gain in the potential energy when the student climbs the stairs to the same top. (iii) What do you conclude about the dependence of the potential energy on the path taken?
NCERT Question 12 — The gravitational attraction on the
The gravitational attraction on the surface of the Moon (lunar surface) is about 1/6 th of that on the surface of the Earth. An astronaut can throw a ball up to a height of 8 m from the surface of the Earth. How far up will the ball thrown with the same upward velocity travel from the surface of the Moon?
