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 Animation for "Example — Lifting a heavy box onto a truck". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Suppose we want to lift a heavy box onto a platform (like a truck). Beat 2 — There are 2 methods. Beat 3 — Method 2 is easier — this sloping plank is an inclined plane. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
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 Animation for "Activity 7.3 — Let us experiment". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — 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. Beat 2 — 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. Beat 3 — 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. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • 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 Animation for "What happens if we make the ramp longer". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — By increasing L (making the ramp longer, with a shallower angle), the mechanical advantage L/h increases. Beat 2 — So the effort F′ required becomes even smaller. Beat 3 — 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. (Note, page 132). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • 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 Animation for "What happens if we make the ramp longer". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — By increasing L (making the ramp longer, with a shallower angle), the mechanical advantage L/h increases. Beat 2 — So the effort F′ required becomes even smaller. Beat 3 — 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. (Note, page 132). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • 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 Animation for "What happens if we make the ramp longer". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — By increasing L (making the ramp longer, with a shallower angle), the mechanical advantage L/h increases. Beat 2 — So the effort F′ required becomes even smaller. Beat 3 — 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. (Note, page 132). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
    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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