Classical mechanicsLesson 3 of 7 in the course Linear Momentum and Collisions

Linear Momentum Conservation in Interactions, Collisions, and Recoil

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

This lesson connects Newton’s third law to changes in momentum during interactions. It explains how two objects can change their individual momenta while the total momentum remains unchanged.

These forces are equal in magnitude and opposite in direction, but they act on different objects. Therefore, they do not cancel as forces acting on a single object. Each force can change the motion of the object on which it acts.

All flashcards

State Newton’s third law for two interacting objects.
Each object exerts a force on the other; the forces are equal in magnitude, opposite in direction, and act on different objects.
What is momentum?
Momentum is the vector quantity p⃗=mv⃗\vec{p}=m\vec{v}, equal to an object’s mass multiplied by its velocity.
How is force related to momentum change?
For an object, net force is the rate of change of momentum: F⃗net=dp⃗/dt\vec{F}_{\text{net}}=d\vec{p}/dt.
Why can two objects in a force pair have different accelerations?
Their masses may differ. The equal and opposite forces produce accelerations according to a⃗=F⃗/m\vec{a}=\vec{F}/m.
What is the relation between the momentum changes of two objects interacting internally?
Their changes are equal in magnitude and opposite in direction: Δp⃗1=−Δp⃗2\Delta\vec{p}_1=-\Delta\vec{p}_2.

Quiz questions

  1. What does Newton’s third law say about the forces two interacting objects exert on each other?Answer: They are equal in magnitude and opposite in direction, and act on different objects.
  2. For an object, what quantity is the time derivative of momentum?Answer: The net force acting on the object.
  3. Two objects interact only with each other in a closed system. What relation holds between their momentum changes?Answer: Δp⃗1=−Δp⃗2\Delta\vec{p}_1=-\Delta\vec{p}_2.
  4. What conditions allow a system’s total momentum to remain constant?Answer: The system has constant total mass and zero net external force.
  5. Two objects with masses m1m_1 and m2m_2 stick together after a one-dimensional collision. Which expression gives their shared final velocity if the system is closed?Answer: vf=m1v1i+m2v2im1+m2v_f=\frac{m_1v_{1i}+m_2v_{2i}}{m_1+m_2}

Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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