Asked by mahomes
How do collisions affect momentum in a car crash? answer in c.e.r. format
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Claim:
- In a car crash the total momentum of the vehicle system is conserved (provided external horizontal impulses are negligible during the brief collision), but each vehicle’s momentum can change; those changes are produced by internal forces during the collision and are related to impulse (force × time).
Evidence:
- Momentum definition: p = m v (vector quantity).
- Conservation law: For an isolated system, Σp_initial = Σp_final.
- Impulse–momentum theorem: Δp = J = ∫F dt ≈ F_avg · Δt (so change in momentum equals the force applied times the duration).
- Collision types:
- Perfectly inelastic (vehicles stick): final common velocity v_f = (m1 v1 + m2 v2)/(m1 + m2), which follows directly from momentum conservation.
- Elastic collision: total kinetic energy is also conserved, so velocities change differently, but momentum is still conserved.
- Real crashes are mostly inelastic: kinetic energy is converted to deformation, heat, sound; momentum remains distributed among bodies and debris.
- Example: 1000 kg car at 15 m/s hitting a 1500 kg car at rest and sticking:
v_f = (1000·15 + 1500·0)/(1000+1500) = 15000/2500 = 6 m/s, so total momentum is conserved (initial 15,000 kg·m/s = final 2500·6 = 15,000 kg·m/s).
Reasoning:
- Conservation of momentum applies because during the short time of a crash the dominant forces are internal between the vehicles; external forces from the road or friction act over much longer times or are small compared to the collision forces, so their impulse is often negligible. Thus the vector sum of individual momenta before impact equals the sum after impact. Individual vehicles experience a change in momentum (Δp) because internal contact forces act on them; the magnitude of that change depends on the force and how long it is applied (impulse). Inelastic collisions convert kinetic energy into other forms (so kinetic energy is not conserved), but that energy conversion does not violate momentum conservation. Practically, safety features (seatbelts, airbags, crumple zones) work by increasing Δt (collision time) for occupants, which reduces peak forces (F_avg = Δp / Δt) on the body for the same momentum change, reducing injury.
- In a car crash the total momentum of the vehicle system is conserved (provided external horizontal impulses are negligible during the brief collision), but each vehicle’s momentum can change; those changes are produced by internal forces during the collision and are related to impulse (force × time).
Evidence:
- Momentum definition: p = m v (vector quantity).
- Conservation law: For an isolated system, Σp_initial = Σp_final.
- Impulse–momentum theorem: Δp = J = ∫F dt ≈ F_avg · Δt (so change in momentum equals the force applied times the duration).
- Collision types:
- Perfectly inelastic (vehicles stick): final common velocity v_f = (m1 v1 + m2 v2)/(m1 + m2), which follows directly from momentum conservation.
- Elastic collision: total kinetic energy is also conserved, so velocities change differently, but momentum is still conserved.
- Real crashes are mostly inelastic: kinetic energy is converted to deformation, heat, sound; momentum remains distributed among bodies and debris.
- Example: 1000 kg car at 15 m/s hitting a 1500 kg car at rest and sticking:
v_f = (1000·15 + 1500·0)/(1000+1500) = 15000/2500 = 6 m/s, so total momentum is conserved (initial 15,000 kg·m/s = final 2500·6 = 15,000 kg·m/s).
Reasoning:
- Conservation of momentum applies because during the short time of a crash the dominant forces are internal between the vehicles; external forces from the road or friction act over much longer times or are small compared to the collision forces, so their impulse is often negligible. Thus the vector sum of individual momenta before impact equals the sum after impact. Individual vehicles experience a change in momentum (Δp) because internal contact forces act on them; the magnitude of that change depends on the force and how long it is applied (impulse). Inelastic collisions convert kinetic energy into other forms (so kinetic energy is not conserved), but that energy conversion does not violate momentum conservation. Practically, safety features (seatbelts, airbags, crumple zones) work by increasing Δt (collision time) for occupants, which reduces peak forces (F_avg = Δp / Δt) on the body for the same momentum change, reducing injury.
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