Laws of Motion — Class 10 Science (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 10 Science, Physics — Chapter 1. The foundation of mechanics: how forces change motion, momentum, and gravitation.
1. About this chapter
This chapter explains why and how objects move when forces act on them. It builds on Newton's three laws, introduces momentum and impulse, states the law of conservation of linear momentum, and ends with Newton's universal law of gravitation and the difference between mass and weight.
2. Newton's laws of motion
- First law (law of inertia): A body continues in its state of rest or uniform motion in a straight line unless acted upon by an external force. Inertia is the resistance of a body to a change in its state; types — inertia of rest, of motion, of direction.
- Second law: The rate of change of momentum is proportional to the applied force and acts in the direction of the force. This gives F = ma.
- Third law: Every action has an equal and opposite reaction (forces act on different bodies).
3. Key terms and formulas
| Quantity | Formula | Unit |
|---|---|---|
| Linear momentum | p = m v | kg m s⁻¹ |
| Force | F = m a = Δp / Δt | newton (N) |
| Impulse | J = F × t = Δp | N s |
| Conservation of momentum | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | — |
| Universal gravitation | F = G m₁m₂ / r² | (G = 6.674×10⁻¹¹ N m² kg⁻²) |
| Acceleration due to gravity | g = G M / R² | ≈ 9.8 m s⁻² |
| Weight | W = m g | newton (N) |
- Impulse = large force acting for a short time; equals the change in momentum.
- Law of conservation of linear momentum: in the absence of external force, the total momentum of a system is constant (basis of rocket propulsion and recoil of a gun).
4. Mass and weight
- Mass is the quantity of matter (scalar, same everywhere, kg).
- Weight is the gravitational force on a body (vector, W = mg, changes with g, newton).
- Apparent weight in a lift: moving up with acceleration a → W' = m(g + a); moving down → W' = m(g − a); free fall (a = g) → apparent weight = 0 (weightlessness).
5. Worked examples
Example 1. A force of 20 N acts on a 4 kg body. Find the acceleration. a = F/m = 20/4 = 5 m s⁻².
Example 2. A 2 kg ball moving at 3 m s⁻¹ is stopped in 0.2 s. Find the average force. Impulse = Δp = m(v − u) = 2(0 − 3) = −6 N s. F = Δp/t = −6/0.2 = −30 N (30 N opposing motion).
Example 3. A gun of mass 5 kg fires a bullet of 0.02 kg at 200 m s⁻¹. Find the recoil velocity of the gun. By conservation: 0 = m_b v_b + m_g v_g → v_g = −(0.02×200)/5 = −0.8 m s⁻¹.
6. Common mistakes
- Mistake: Treating action and reaction as acting on the same body. Fix: They act on two different bodies, so they don't cancel.
- Mistake: Confusing mass and weight. Fix: Mass is in kg (constant); weight is a force in N (= mg, varies with g).
- Mistake: Forgetting units of impulse. Fix: Impulse is in N s, equal to change in momentum (kg m s⁻¹).
7. Practice (book-back style)
- State Newton's second law and derive F = ma.
- Define impulse and give its unit.
- State the law of conservation of linear momentum with one application.
- A 1000 kg car accelerates from rest to 20 m s⁻¹ in 10 s. Find the force.
- Differentiate mass and weight (any three points).
8. Answer key
- Rate of change of momentum ∝ force → F = Δp/Δt = m(v−u)/t = ma.
- Impulse = force × time = change in momentum; unit N s.
- Total momentum is conserved with no external force; e.g., recoil of a gun / rocket propulsion.
- a = (20−0)/10 = 2 m s⁻²; F = ma = 1000×2 = 2000 N.
- Mass: matter, scalar, kg, constant. Weight: force, vector, N, varies with g.
9. Quick revision
- Physics Ch 1 · Newton's three laws, momentum, impulse, gravitation.
- p = mv; F = ma = Δp/Δt; impulse J = Ft = Δp.
- Conservation of momentum: m₁u₁+m₂u₂ = m₁v₁+m₂v₂.
- F = Gm₁m₂/r²; g = GM/R²; W = mg.
- Apparent weight changes in an accelerating lift; zero in free fall.
