Newton's three laws form the foundation of mechanics. A-Level problems involve applying F = ma to particles, with forces including weight, normal reaction, tension, and friction.
Newton's Laws
First Law
A body remains at rest or moves at constant velocity unless acted on by a resultant force.
Second Law
(resultant force = mass × acceleration).
Third Law
Every action has an equal and opposite reaction.
Common Forces
- Weight: (downward)
- Normal reaction: perpendicular to surface
- Tension: along a string
- Friction: opposes motion, along surface
Resolving Forces
On an inclined plane at angle :
- Along the plane:
- Perpendicular:
Worked Example: Example 1
5 kg mass on a smooth surface, pulled by 20 N force. m/s².
Worked Example: Example 2
Particle on a smooth slope at 30°, mass 2 kg.
Down the slope: N. m/s².
Worked Example: Connected Particles
Particles A (3 kg) and B (5 kg) connected by a string over a smooth pulley.
and . Adding: → m/s². N.
Practice Problems
- 10 kg box pushed by 50 N on a smooth surface. Find acceleration.
- 4 kg mass on 20° smooth slope. Find acceleration down the slope.
- Particles 2 kg and 7 kg on a smooth pulley. Find acceleration and tension.
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Key Takeaways
— always use resultant force.
Draw a force diagram before calculating.
Resolve forces parallel and perpendicular to motion.
Connected particles: same and same .