Momentum and Collisions
Understanding momentum, impulse, and the conservation of momentum in collisions
Momentum is the product of mass and velocity - a key concept in understanding collisions and motion.
Momentum (p) is defined as mass multiplied by velocity: p = mv. It is measured in kg·m/s and is a vector quantity, meaning direction matters. A 1000 kg car traveling at 10 m/s has momentum of 10,000 kg·m/s.
Newton's Second Law can be written in terms of momentum: F = Δp/Δt. This shows that force equals the rate of change of momentum. The quantity impulse (FΔt)equals the change in momentum. This relationship explains why longer collision times result in smaller forces - the principle behind airbags and crumple zones.
The Law of Conservation of Momentum states that in an isolated system, total momentum before a collision equals total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. This applies to all collisions, whether elastic or inelastic.
In elastic collisions, both momentum and kinetic energy are conserved - objects bounce apart (like billiard balls). In inelastic collisions, momentum is conserved but kinetic energy is not - some energy is converted to heat, sound, or deformation (like car crashes where vehicles may stick together).
Real-world applications include car safety features: airbags increase collision time from ~0.02s to ~0.3s, reducing force on passengers by 15x. Crumple zones absorb impact energy while extending collision duration. Seatbelts prevent sudden deceleration and distribute forces across the body.
Explore momentum, collisions, impulse, and safety applications
Momentum (p = mv)
50 kg·m/s
Direction: → Right
Formula:
p = m × v = 10 × 5 = 50 kg·m/s
Example 1: Inelastic Collision
Car A (m₁ = 1000 kg) traveling at 20 m/s collides with stationary Car B (m₂ = 1500 kg). They stick together. Find the final velocity.
Using conservation: m₁u₁ + m₂u₂ = (m₁ + m₂)v
(1000)(20) + (1500)(0) = (2500)v
20000 = 2500v
v = 8 m/s
Example 2: Impulse and Force
A person catches a 0.5 kg ball traveling at 20 m/s. Compare the force with and without gloves.
Δp = mv = 0.5 × 20 = 10 kg·m/s
Without glove (Δt = 0.01 s):
F = Δp/Δt = 10/0.01 = 1000 N
With glove (Δt = 0.1 s):
F = Δp/Δt = 10/0.1 = 100 N
Example 3: Elastic Collision
Ball 1 (1 kg, 5 m/s) hits stationary Ball 2 (1 kg) elastically. Find final velocities.
For equal mass elastic collision: velocities exchange
Ball 1: v₁ = 0 m/s (stops)
Ball 2: v₂ = 5 m/s (moves)
Verify momentum: Before = 1×5 = 5, After = 1×0 + 1×5 = 5 ✓
Verify KE: Before = ½(1)(25) = 12.5 J, After = 0 + 12.5 J ✓
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Momentum (p)
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Question 1 of 8
Calculate the momentum of a 50 kg object moving at 10 m/s.