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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)

2 kg
4.0 m/s

+ = rightward, − = leftward

■ Cart 2 (Red)

3 kg
-3.0 m/s

+ = rightward, − = leftward

Data Collection (kg·m/s)

Quantity Initial Final
p₁ = m₁·v₁
p₂ = m₂·v₂
pₜₒₜₐₗ = p₁ + p₂

Track View

Arrows = momentum direction & magnitude

System 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:

$$p = mv$$

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 ($F_{21}$):

$$F_{21} = -F_{12}$$

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 ($\Delta p$):

$$F \Delta t = \Delta p$$

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:

$$v_{\text{final}} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$$

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.