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Momentum Conservation: Collisions Lab Guide

PhysicsIntermediateReading time: 3 min

Overview

Explore the law of conservation of momentum through ball collision experiments.

Background

The concept of Momentum was first proposed by Descartes, who called it 'quantity of motion'. Later, in 'Mathematical Principles of Natural Philosophy', Newton formally defined momentum as the product of mass mm and velocity vv, i.e., p=mvp = mv. Newton's second law actually describes force as the rate of change of momentum with respect to time. The law of conservation of momentum is one of the most fundamental conservation laws in physics. Its scope of application is even wider than Newton's laws, applicable not only to macroscopic low-speed objects but also to microscopic particles and high-speed relativistic systems.

Background

  • 17th Century: Descartes proposed the view of conservation of 'quantity of motion', but he did not distinguish the direction of velocity, so there were errors.
  • 1668: The Royal Society of London established a prize. Huygens, Wallis, and Wren independently gave correct answers to collision problems, establishing the vector nature of momentum conservation.
  • 1687: In 'Principia', Newton defined momentum as the product of mass and velocity and made it the core concept of the second law.

Key Concepts

Momentum

p=mvp = mv

The product of an object's mass and its velocity.

Conservation of Momentum

pinitial=pfinalp_{initial} = p_{final}

If a system is not subject to external forces or the vector sum of external forces is zero, the total momentum of the system remains constant.

Formulas & Derivation

Definition of Momentum

p=mvp = mv
Momentum equals mass times velocity

Conservation of Momentum

m1v1+m2v2=m1v1′+m2v2′m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'
Total momentum before collision equals total momentum after collision

Perfectly Inelastic Collision

m1v1+m2v2=(m1+m2)v′m_1v_1 + m_2v_2 = (m_1 + m_2)v'
After collision, two objects stick together and move

Experiment Steps

  1. 1

    Exploring Perfectly Elastic Collisions

    Set the elasticity coefficient to 11. Set the masses of the two balls to assume m1=m2=1.0kgm_1 = m_2 = 1.0kg, and initial velocities v1=5m/s,v2=0v_1 = 5m/s, v_2 = 0. What do the velocities of the two balls become after the collision? Calculate and compare pinitialp_{initial} and pfinalp_{final}. What is the relationship between them?
  2. 2

    Exploring Perfectly Inelastic Collisions

    Set the elasticity coefficient to 00. After the collision, the two balls will move with a common velocity. Record the total momentum at this time. Is momentum still conserved? Is energy (kinetic energy) conserved?
  3. 3

    The Effect of Mass on Collision

    Set m1=0.5kg,m2=5.0kgm_1 = 0.5kg, m_2 = 5.0kg (light ball hitting heavy ball). Observe how the direction of motion of ball 11 changes after the collision. Does the vector sum of momentum still remain constant?

Learning Outcomes

  • Deeply understand the vector nature of momentum.
  • Verify that the law of conservation of momentum holds true in both elastic and inelastic collisions.
  • Recognize that mechanical energy is lost in inelastic collisions, but momentum is still conserved.

Real-world Applications

  • Billiards: Collisions between billiard balls can be approximated as perfectly elastic collisions. When one ball hits another stationary ball of equal mass squarely, momentum transfer causes velocity exchange.
  • Rocket Propulsion: Rockets spray gas backwards at high speed, using the law of conservation of momentum to obtain forward propulsion (recoil motion).
  • Car Crash Safety: Car crumple zone designs utilize the principles of momentum and impulse, reducing the impact force F=Δp/ΔtF = \Delta p / \Delta t on passengers by extending the collision time Δt\Delta t.

Common Misconceptions

Misconception
Momentum and kinetic energy are the same thing
Correct
Momentum is conserved in all types of collisions (as long as there are no external forces), but kinetic energy is only conserved in perfectly elastic collisions. Inelastic collisions involve energy loss.
Misconception
Momentum is a scalar
Correct
Momentum is a vector and has directionality. In one-dimensional collisions, attention must be paid to the positive and negative signs of velocity.

Further Reading

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