PHY003 · Mechanics · Classes 9–12
Inclined plane
Objective: To study the forces on a block on an inclined plane and find its acceleration.
🧰 Apparatus
- Inclined plane with protractor
- Wooden block
- Spring balance
- Stopwatch
- Metre scale
📐 Formulas and SI units
a = g(sin θ − μ cos θ) (m/s²)
N = mg cos θ (N)
💡 Theory
The weight mg splits into mg sin θ down the slope and mg cos θ into the surface. The normal force balances mg cos θ, friction is μ mg cos θ, so a = g(sin θ − μ cos θ). If sin θ ≤ μ cos θ the block stays at rest.
🪜 Procedure
- Set the ramp angle and measure it.
- Place the block at the top and release it.
- Time it over a measured distance s and calculate a = 2s/t².
- Repeat for several angles.
- Find the angle at which the block just starts to slide: tan θ = μ.
📋 Observations Simulated values
✅ Result and conclusion
At 30° with μ = 0.1 the block accelerates at 4.05 m/s²; it stays still when tan θ ≤ μ.
🔬 In a real lab
Static friction is larger than sliding friction, so blocks need a small push to start; the surface μ varies along the ramp.
⚠️ Safety
Keep fingers away from the bottom of the ramp; stop the block with a soft barrier.
❓ Quick check
1. With no friction, a on a 30° slope is…
2. The normal force on a slope is…
3. The block starts to slide when tan θ equals…
🏋️ Practice
Easyθ = 0°. a?
Answer: 0
Mediumμ = 0.5. Angle at which sliding starts?
Answer: ≈ 26.6°
Challengeθ = 45°, μ = 0. a?
Answer: ≈ 6.93 m/s²