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š¬ Stored-up work
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?
What is potential energy?
- 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 .
What is gravitational potential energy and its formula?
- 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 \(W = mg \times h = mgh\).
- 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.
Steps
- 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.
What you observe
- 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.
Kinetic energy
Potential energy
Energy due to the motion of an object.
Energy due to position, configuration or deformation.
Depends on mass and speed: K = ½mv².
Depends on mass and height: U = mgh (near Earth).
A moving bicycle or a rolling ball.
A raised stone, a stretched bow, a compressed spring.
Important Definitions
- 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.
ā Example 7.7 — After taking a catch, a
A 200 g cricket ball is thrown 10 m up. Find its potential energy at the top. Take g = 10 m sā»².
\( U = mgh = 0.2\ \text{kg} \times 10\ \text{m s}^{-2} \times 10\ \text{m} = 20\ \text{J} \).
š¹ Ready to Go Beyond
- 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.
š¹ Ready to Go Beyond
- 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.
š¹ Ready to Go Beyond
- 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.
āøā¶ Pause and Ponder
- 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 50 kg student rises h = 72.5 m by lift, then by stairs (g = 10). PE gain each way, and what this says about path dependence.
View the answer →NCERT Question 12 — The gravitational attraction on the
Moon gravity is 1/6 of Earth's. A ball goes 8 m up on Earth — how high with the same speed on the Moon?
View the answer →