Why a Caught Egg Survives: Impulse, Momentum, and Collisions
Lumi stands beside a low-friction air track, gently rolling two carts — labeled Cart A and Cart B, color-coded red and blue — toward each other while glowing motion arrows trail behind them across a bright classroom lab.
- Define momentum as the product of mass and velocity and calculate it for a moving object.
- Apply the impulse-momentum relationship to explain how force and contact time change an object's momentum.
- Predict the total momentum of a system before and after a collision using conservation of momentum.
- Distinguish elastic from inelastic collisions by comparing kinetic energy before and after.
Key terms
- Momentum
- The product of an object's mass and velocity, p = mv, a vector measured in kg·m/s.
- Impulse
- The product of force and the time it acts, J = FΔt, equal to the change in momentum.
- Impulse-momentum theorem
- The statement that the net impulse on an object equals its change in momentum, FΔt = Δp.
- Elastic collision
- A collision in which the total kinetic energy of the objects is conserved.
- Inelastic collision
- A collision in which some kinetic energy converts to heat, sound, or deformation while momentum is still conserved.
Impulse and Why Time Matters
The impulse-momentum theorem, FΔt = Δp, explains a huge range of safety technology. A given collision fixes the change in momentum, so the same Δp can be achieved with a large force over a short time or a small force over a long time. Extending the contact time therefore reduces the peak force on the object. Pulling your hands back to catch an egg, airbags inflating before your head hits the dashboard, and crumple zones folding slowly all stretch out Δt to lower the force and prevent injury or breakage, even though the momentum change is identical.
Conservation Across Collision Types
When no external force acts, the total momentum of an interacting system is conserved in every collision, because the equal and opposite internal forces deliver equal and opposite impulses. What distinguishes collision types is kinetic energy. In an elastic collision, kinetic energy is also conserved and objects bounce apart cleanly. In an inelastic collision, some kinetic energy becomes heat, sound, or permanent deformation; in the perfectly inelastic case the objects stick together and lose the maximum kinetic energy allowed by momentum conservation. Always reach for conservation of momentum first.
Worked examples
A 0.15 kg baseball traveling at 40 m/s is caught and brought to rest in 0.50 s. Find the average force on the ball.
- Compute the change in momentum: Δp = mΔv = (0.15 kg)(0 − 40 m/s) = −6.0 kg·m/s.
- Use the impulse-momentum theorem F = Δp / Δt.
- Substitute: F = (−6.0 kg·m/s) / (0.50 s) = −12 N.
- The negative sign shows the force opposes the ball's motion.
Answer: 12 N opposing the ball's motion (the catching hand).
A 1.0 kg cart at 4.0 m/s strikes a stationary 3.0 kg cart and they stick together. Find their common speed.
- Total momentum before: p = (1.0)(4.0) + (3.0)(0) = 4.0 kg·m/s.
- Combined mass after the perfectly inelastic collision: 1.0 + 3.0 = 4.0 kg.
- Apply conservation: 4.0 = (4.0)v.
- Solve v = 1.0 m/s.
Answer: 1.0 m/s in the original direction.
Activity
Sort each real-world collision into elastic, inelastic, or perfectly inelastic.
Practice
A 1200 kg car moving at 20 m/s crashes and stops in 0.10 s; calculate the average force exerted on the car.
Explain why bending your knees when landing from a jump reduces the force on your legs using impulse and contact time.
Common mistakes to avoid
- Pulling your hands back reduces the ball's momentum change.The momentum change is fixed by the ball stopping; pulling back increases the contact time, which lowers the force, not the momentum change.
- Momentum is lost whenever a collision destroys kinetic energy.Momentum is conserved in every collision with no external force; only kinetic energy is lost in inelastic collisions, becoming heat and sound.
Check your understanding
A 2 kg ball moves at 3 m/s. What is its momentum?
Why does pulling your hands back while catching a fast ball reduce the force on your hands?
Two ice skaters push off each other. Which quantity is conserved for the two-skater system?
Two cars crash and crumple, sticking together. Which statement is true?
Recap
Momentum p = mv measures how hard something is to stop, and impulse FΔt changes it, so extending contact time lowers force in catches, airbags, and crumple zones. Total momentum is conserved in every isolated collision, but kinetic energy is conserved only in elastic ones.
Reflect
How does understanding impulse change the way you think about everyday safety gear?