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Conservation of Momentum in One Dimension

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Impulse and Momentum

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Conservation of Momentum in One Dimension


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Students are introduced to the concept of momentum and its conservation in one dimension.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Describe Newton’s Third Law of Motion.
  • Explain that after a force is applied to an object, the velocity gained by that object depends on its mass.
  • Define momentum.
  • Calculate the momentum of objects.
  • Explain that the momentum of a system is conserved if no external force acts on the system.

Everything You'll Have Covered

Intuition tells us that large moving objects will be difficult to stop because the object has great momentum (p), which is the product of its velocity and its mass (p = mv). This term was first proposed by Descartes, who reasoned that the higher the velocity and the greater the mass of an object, the more "total amount of motion," or momentum, it would have. A collision between two bodies may transfer force, but it may not result in velocities of equal magnitude. In fact, the final velocities may be zero. However, Newton's Third Law of Motion states that the action force exerted by one object on another object will have an equal reaction force acting in the opposite direction.

One of the most fundamental laws in physics is the law of conservation of momentum, which derives from Newton's Third Law. For any collision in a closed system, the total momentum of the objects in the system is conserved. Therefore, if momentum is gained by one object, conservation of momentum entails that it be lost by another object. The changes in momentum are equal in magnitude and opposite in direction This does not mean that the absolute amount of motion in the system stays the same because momentum is a vector quantity, meaning it has both magnitude and direction. Two objects moving in opposite directions therefore can together have zero net momentum. However, the change in total or net momentum in a closed system, on which no outside force is acting, will always be zero.

The law of conservation of momentum is not limited to classical physics, but also applies to situations in which the laws of relativity are used.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should understand the concepts of displacement, force, friction, vector quantities, and velocity. They should be able to describe open and closed systems in terms of conservation laws.
Course Physics
Type of Tutorial Concept Development
Key Vocabulary action forces, applied forces, collisions