A7LAM CSCA ACADEMYCSCA Academy / Physics / Mechanics
CSCA Physics · Lesson 4 of 16Momentum and impulse
Quantité de mouvement et impulsion · كمية الحركة والدفع
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Momentum measures how hard it is to stop a moving object. In a collision with no outside force, the total momentum stays the same.
Key ideas
- Momentum p = mv (kg·m/s); it is a vector.
- Impulse I = FΔt = Δp: a force acting for a time changes the momentum.
- With no external force, total momentum before = total momentum after.
- Elastic collisions also keep kinetic energy; objects that stick together lose some.
Formulas to know
- FΔt = mv − mv₀
- m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′
- They stick: m₁v₁ + m₂v₂ = (m₁ + m₂)v
Worked example
A 2 kg cart at 3 m/s hits a 1 kg cart at rest. They stick together. Final speed?
- Before: p = 2 × 3 + 1 × 0 = 6 kg·m/s
- After: p = (2 + 1)v = 3v
- Solve: 3v = 6
Answer: v = 2 m/s
Practice questions
1. A 0.5 kg ball goes from rest to 20 m/s. Impulse?
10 N·s ✓ · 40 N·s · 20 N·s · 0.025 N·s
Δp = 0.5 × 20 = 10 N·s.
2. A 1 kg ball hits a wall at 5 m/s and bounces back at 5 m/s. Size of the change in momentum?
0 · 5 kg·m/s · 10 kg·m/s ✓ · 25 kg·m/s
From +5 to −5: Δp = 10 kg·m/s.
3. A 60 kg and a 40 kg skater push off from rest. The 40 kg skater moves at 3 m/s. Speed of the 60 kg skater?
2 m/s ✓ · 3 m/s · 4.5 m/s · 1.5 m/s
40 × 3 = 60 × v, v = 2 m/s.