Collision Dynamics Lab
NGSS HS-PS2-2 — Momentum & Impulse
Launch two carts on a frictionless track and analyze the interaction. How do mass and velocity influence the outcome? Use the tools below to collect data and uncover the relationships governing these systems.
Collision Type
Elastic: carts bounce apart. Inelastic: carts stick together.
■ Cart 1 (Blue)
+ = rightward, − = leftward
■ Cart 2 (Red)
+ = rightward, − = leftward
Data Collection (kg·m/s)
| Quantity | Initial | Final |
|---|---|---|
| p₁ = m₁·v₁ | — | — |
| p₂ = m₂·v₂ | — | — |
| pₜₒₜₐₗ = p₁ + p₂ | — | — |
✓ Collision complete
Analyze the ptotal Initial and ptotal Final values. What pattern do you notice about the total system property before and after the interaction?
⚠ No Interaction
The carts did not collide. Adjust the velocities so the carts move toward each other and try again.
Track View
Arrows = momentum direction & magnitudeSystem Property Over Time
Monitor the purple dashed line (ptotal) as the collision occurs.
Foundations of Collision Physics
The Concept of "Quantity of Motion"
Early physicists like René Descartes and Isaac Newton sought to describe the "quantity of motion" an object possesses. Today we define this as momentum ($p$), the product of an object's mass and its velocity:
Because velocity is a vector, momentum is also a vector. In this 1D lab, rightward motion is positive and leftward motion is negative.
Newton's Third Law
When two carts collide, they exert forces on each other. According to Newton's Third Law, the force exerted by Cart 1 on Cart 2 ($F_{12}$) is equal in magnitude and opposite in direction to the force exerted by Cart 2 on Cart 1 ($F_{21}$):
Impulse and Change in Motion
A force applied over a duration of time ($\Delta t$) creates an impulse. This impulse causes a change in the object's momentum ($\Delta p$):
Since the collision forces are equal and opposite and act for the exact same amount of time, the impulses on the two carts are also equal and opposite. This leads to a fascinating result for the total system momentum ($p_1 + p_2$).
Types of Interactions
Physicists categorize collisions based on what happens to the system's kinetic energy. In elastic collisions, objects bounce with no permanent deformation. In perfectly inelastic collisions, the objects stick together, moving as a single mass:
Historical Context: The Vis Viva Controversy
In the 17th and 18th centuries, scientists debated what "quantity" was truly "conserved" during collisions. Gottfried Leibniz argued for vis viva ($mv^2$), while followers of Descartes argued for $mv$. It wasn't until later that physicists realized that both were useful concepts: $mv$ (momentum) is always unchanged in an isolated system, while $\frac{1}{2}mv^2$ (kinetic energy) is only unchanged in perfectly elastic interactions.
Today, these principles are used by automotive engineers to design safer vehicles. By understanding how momentum transfers during a crash, they can design crumple zones that increase the collision time ($\Delta t$), thereby reducing the peak forces ($F$) felt by passengers.