7.6.2 Inclined Plane

Last updated at September 16, 2026 by

Example — Lifting a heavy box onto a truck
  • Suppose we want to lift a heavy box onto a platform (like a truck).
  • There are 2 methods
  • GIF Watch: example — Lifting a heavy box onto a truck 7.6.2 Inclined Plane - Work, Energy, and Simple Machines - [Teachoo] - Concepts
Method How Force needed
Method 1 — Lift vertically Lift the box straight up Force F equal to its full weight — difficult if the box is too heavy
Method 2 — Push up a ramp Place the box on a smooth inclined plank and push it up Smaller force — but over a longer distance
  • Method 2 is easier — this sloping plank is an inclined plane .
What is an Inclined Plane?
  • An inclined plane is a simple machine that helps move a heavy load to a higher (or lower) level .
  • It is simply a sloping surface — a ramp.
🔧 Activity 7.3 — Let us experiment
  • Take a smooth plank (say a cardboard piece) about 1.5 m long, a toy car (or cart), and a spring balance. Attach the spring balance to the cart. Arrange an elevated surface, such as the top of a low stool or a pile of books, at about 0.5 m height from the floor.
  • GIF Watch: activity 7.3 — Let us experiment part 2 - 7.6.2 Inclined Plane - Concepts - Chapter 7 - Work, Energy, and Simple Machines (Exploration) - Class 9 (Exploration)
  • Step 1 — First, lift the cart vertically, slowly and steadily, from the floor to the top of the pile of books or stool, and note the reading of the spring balance scale.
    • This reading is the force required to lift the cart vertically = weight of the cart.
  • Step 2 — Next, place the plank against the top of the pile of books or stool. Pull the cart along the plank slowly and steadily.
    • Is the reading of the spring balance (the force required) smaller than that of Step 1?
  • Step 3 — Now, reduce the angle between the plank and the base (make the plank longer/less steep) and repeat Step 2. Observe how the force required changes as the plank becomes less steep.
What do we observe?
  • The force required to pull the cart up along the plank is smaller than lifting it vertically.
  • As the plank becomes less steep , the force required decreases further.
  • However, we have to apply the force over a larger distance to bring it to the same height.
What is the Mechanical Advantage of an Inclined Plane? (Derivation)
  • Let the mass of the object be m.
  • Then the load = weight of the object = mg
  • Let F′ be the force required to push the object up the plane — this is the effort.
  • Let the length of the inclined plane = L, and the height to be reached = h.
  • Work done by us on the object (along the ramp)
    • Work = Force × Distance
    • Work = F′ × L
  • Potential energy gained by the object
    • The object rises to height h.
    • Potential energy gained = mgh
  • Apply the work-energy theorem (ignoring friction)
    • Work done by us = energy gained by the object
    • F′ × L = mgh
  • Rearranging
    • mg / F′ = L / h
  • Now, mg is the load and F′ is the effort.
  • Mechanical advantage = Load / Effort = mg / F′
  • Mechanical advantage of inclined plane = L / h
Why is the Mechanical Advantage of an inclined plane greater than 1?
  • The length of the ramp L is always larger than the height h.
  • So L / h > 1 — mechanical advantage is greater than 1.
  • This means the force F′ needed is less than the weight mg.
What happens if we make the ramp longer?
GIF Watch: what happens if we make the ramp longer part 3 - 7.6.2 Inclined Plane - Concepts - Chapter 7 - Work, Energy, and Simple Machines (Exploration) - Class 9 (Exploration)
  • By increasing L (making the ramp longer, with a shallower angle), the mechanical advantage L/h increases.
  • So the effort F′ required becomes even smaller .
Ramp Force needed Distance covered
Steep (short L) Large Small
Less steep (larger L) Smaller Larger
Very gentle (very large L) Very small Very large
  • Note — The work done, that is the product of force and displacement, is the same in all cases. If the force decreases, the displacement increases, thereby the work done remains constant.
📘 Example 7.12 (NCERT)
A person uses an inclined ramp to raise an object over a step 30 cm high. The ramp has a width of 40 cm. What is the mechanical advantage of the ramp that helps the person achieve the task?
GIF Watch: what happens if we make the ramp longer part 4 - 7.6.2 Inclined Plane - Concepts - Chapter 7 - Work, Energy, and Simple Machines (Exploration) - Class 9 (Exploration)
  • Height AB = 30 cm, width BC = 40 cm.
  • Length of the ramp AC — by the right-angled triangle property (Pythagoras theorem)
    • AC² = AB² + BC²
    • AC² = 30² + 40² = 900 + 1600 = 2500
    • AC = 50 cm
  • Mechanical advantage = L / h
  • MA = 50 / 30
  • MA = 1.67
  • 🤔 Pause and Ponder 9 (from the book)
    Explain why roads on hills are built to wind around in gentle slopes rather than going straight up?
    View answer Hide answer
    Answer
    • A winding road is like a longer inclined plane (larger L for the same height h).
    • Larger L means larger mechanical advantage L/h.
    • So vehicles need much less force to climb.
    • Going straight up would need a very large force — engines would strain, and it would be unsafe.
    • The trade-off — vehicles travel a longer distance, but the climb is easy.
  • 🤔 Pause and Ponder 10 (from the book)
    To reach a higher floor, we find climbing an inclined ladder easier in comparison to climbing a vertical ladder (Fig. 7.30). Explain why.
    GIF Watch: what happens if we make the ramp longer part 5 - 7.6.2 Inclined Plane - Concepts - Chapter 7 - Work, Energy, and Simple Machines (Exploration) - Class 9 (Exploration)
    View answer Hide answer
    Answer
    • An inclined ladder acts like an inclined plane .
    • Its length L is more than the height h — mechanical advantage L/h > 1.
    • So less force is needed at each step compared to pulling our body straight up a vertical ladder.
    • We cover a longer distance, but each step feels easier.
📝 Important points — 7.6.2 Inclined Plane
Point Detail
Inclined plane Sloping surface to move loads up or down
Effort F′, applied along the ramp
Load mg, weight of the object
Mechanical advantage L / h (always > 1, since L > h)
Longer ramp Smaller force, larger distance
Work done Same in all cases — force ↓, distance ↑
💡 Worth remembering
  • Ramp trick — trade force for distance. Less force, more distance, same work.
  • MA = L/h — just lengths, measure and divide.
  • Hill roads wind for the same reason trucks use ramps — big L, small force.
✅ Quick self-check
  1. A ramp is 4 m long and reaches a height of 1 m. Find its mechanical advantage.
    View Answer Hide Answer
    • MA = L / h
    • MA = 4 / 1
    • MA = 4
  2. A box weighs 400 N. Using the ramp of Question 1 (MA = 4), how much effort is needed to push it up? (Ignore friction)
    View Answer Hide Answer
    • MA = Load / Effort
    • 4 = 400 / Effort
    • Effort = 400 / 4
    • Effort = 100 N
  3. Does a longer ramp reduce the work needed to raise a box to the same height?
    View Answer Hide Answer
    • No. Work = mgh — it depends only on weight and height.
    • A longer ramp reduces the force , not the work. The distance increases to compensate.

Key terms and units

Term Meaning
Inclined plane Sloping surface (ramp) used as a simple machine
MA of inclined plane Length of ramp / height = L/h
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