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What are the types of Potential Energy?
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Potential energy is of 2 types
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Due to change in
shape
(deformation)
Example: stretched rubber band, bent bow, compressed spring
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Due to
position
(relative positions of objects in a system)
Example: separated magnets, separated charges, ball lifted from the Earth
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Due to change in
shape
(deformation)
- If the position is due to height above the Earth, it is called gravitational potential energy .
- This is the simplest and most common case. Lets study it.
Example — Ball and Earth
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Watch: example — Ball and Earth
![Gravitational Potential Energy - Work, Energy, and Simp - [Teachoo] - Concepts](https://cdn.teachoo.com/562d0730-576c-427c-9aee-b82523553901/animation-for-example-ball-and-earth-.-a-short-looping-gif-three-or-four-beats-drawn-in-the-flat-classroom-style-of-the-chapter.-beat-1.webp)
- Consider a ball lying on the surface of the Earth.
- The ball and the Earth together form a system.
- The Earth and the ball attract each other (gravitational force).
- To lift the ball to some height, we do work against this gravitational force.
- Once the ball is lifted and the force is removed, the ball and the Earth rush towards each other, and attain kinetic energy.
- So the ball-Earth system, when separated, stores energy due to their relative positions.
How is this related to Gravitational Potential Energy?
- This stored energy of the ball-Earth system is due to the gravitational force between them.
- Now, the Earth is much more massive than the ball.
- So the Earth hardly moves towards the ball — only the ball moves.
- Therefore, instead of saying "energy of the Earth-ball system", we simply say — the gravitational potential energy of the ball.
What is the definition of Gravitational Potential Energy?
- Gravitational potential energy of an object is the energy stored in it due to its height above the Earth's surface.
- It is equal to the work done in raising the object to that height.
- Henceforth, in this chapter, potential energy usually refers to the gravitational potential energy.
Take a heavy ball and a large container filled with loose sand.
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Watch: activity 7.1 — Let us investigate
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Step 1 — Raise the ball over the sand bed to a height of about 1 m and drop it.
- A depression is created in the sand.
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Step 2 — Raise the ball to the height of 2 m and release it at a slightly different position, so the depressions do not overlap. Repeat this step one more time from a greater height.
- Compare the depths of the depressions.
What do we observe?
- The depression is deepest when the ball is dropped from the greatest height.
- The depression is shallowest for the smallest height.
Why does this happen?
- Raising a ball to a greater height requires more work.
- So the ball possesses more energy at greater height.
- When released from a greater height, this energy creates a deeper depression.
- Conclusion — The greater the height of the ball above the Earth's surface, the greater is its potential energy .
What is the formula of Gravitational Potential Energy?
- Gravitational potential energy of an object of mass m at height h is
- U = mgh
- where g = acceleration due to gravity
- The unit of potential energy is the joule (J) — same as work and kinetic energy.
How do we derive U = mgh? (Derivation)
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We know that
- Force = mass × acceleration
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In case of gravity, we can say
- Force = mass × acceleration due to gravity
- Force = m × g … (1)
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Now we know that
- Work done = Force × Displacement
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Here, displacement is the level we raised the object above the ground. Suppose it is at height h.
- Work done = Force × h
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Putting Force from (1)
- Work done = m × g × h
- By the work-energy theorem — Work done = Energy (Gravitational potential energy)
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So we can write
- Work done = m × g × h
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as
- Gravitational potential energy = m × g × h
- U = mgh
📘 Example 7.7 (NCERT)
After taking a catch, a fielder threw the cricket ball of mass 200 g high up in the air about 10 m above the ground in celebration. How much potential energy does the ball have when the ball reaches its maximum height? Assume g = 10 m s⁻².
- Mass of the ball = 200 g = 0.2 kg
- Height = 10 m
- g = 10 m s⁻²
- U = mgh
- U = 0.2 × 10 × 10
- U = 20 J
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🤔 Pause and Ponder 6 (from the book)
Does the potential energy of an object near the surface of the Earth change if it moves with constant velocity in the horizontal direction? What if the object is gradually raised in the vertical direction?View answer
Answer-
Horizontal motion —
- U = mgh. The height h does not change in horizontal motion.
- So potential energy does NOT change .
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Raised vertically —
- The height h increases.
- So potential energy increases .
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Horizontal motion —
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📋 Revise, Reflect, Refine, Q5 (Page 137)
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.View answer
Answer-
(i) Gain in potential energy when lifted straight up
- U = mgh
- U = 50 × 10 × 72.5
- U = 36250 J
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(ii) Gain in potential energy when climbing the stairs
- The final height is the same — 72.5 m.
- U = mgh = 50 × 10 × 72.5
- U = 36250 J
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(iii) What do we conclude?
- The gain in potential energy is the same in both cases.
- Potential energy depends only on the height gained, NOT on the path taken.
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(i) Gain in potential energy when lifted straight up
📝 Important points — Gravitational Potential Energy
| Point | Detail |
|---|---|
| Gravitational PE | Stored energy of the Earth-object system, called PE "of the object" |
| Formula | U = mgh |
| Unit | joule (J) |
| Zero level | PE on the ground is taken as zero |
| Higher | More potential energy |
| Path | PE depends only on height, not on the path taken |
🚀 Ready to Go Beyond
- Expression U = mgh is valid only near the Earth's surface. Further away from the Earth's surface, the gravitational acceleration g decreases. You will learn about the gravitational potential energy of objects far from the Earth in higher grades.
- Work done on a system against its internal forces, such as gravitational, electric or magnetic forces, can result in a gain of the potential energy of the system. But this is not true for all internal forces. For example, work done against friction does not lead to a storage of energy. You will learn how to identify such forces in higher grades.
💡 Worth remembering
- U = mgh — heavier object, higher height, more stored energy.
- Only the height matters, not the path — lift, stairs or ramp, same mgh.
- Horizontal motion never changes potential energy.
✅ Quick self-check
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A 2 kg book is kept on a shelf at a height of 1.5 m. Find its potential energy. (g = 10 m s⁻²)
View Answer
- U = mgh
- U = 2 × 10 × 1.5
- U = 30 J
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A bird flies horizontally at a constant height of 20 m. Does its potential energy change?
View Answer
- Height is constant, so h does not change.
- No — its potential energy stays the same .
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A 1 kg ball is taken to a 10 m rooftop by a straight ladder, and an identical ball by a winding staircase. Which ball gains more potential energy? (g = 10 m s⁻²)
View Answer
- Both reach the same height — 10 m.
- U = mgh = 1 × 10 × 10 = 100 J for both.
- Both gain the same potential energy — path does not matter.
Key terms and units
| Term | Meaning | Unit |
|---|---|---|
| Gravitational potential energy (U) | U = mgh, near the Earth's surface | joule (J) |
