Newton’s Third law and the Conservation of Linear Momentum

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Newton’s Third law and the Conservation of Linear Momentum. Syllabus statements 2.2.14-2.3.6 due Friday (1/13). Newton’s Third Law. If body A exerts a force F on body B, then body B exerts an equal but opposite force on body A.

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### Newton’s Third law and the Conservation of Linear Momentum

Syllabus statements 2.2.14-2.3.6 due Friday (1/13)

### Newton’s Third Law

If body A exerts a force F on body B, then body B exerts an equal but opposite force on body A.

Note: this pair of forces are often called an action-reaction pair.

• The third law also works for non-contact forces: electromagnetic forces, gravitation forces, etc.

Practice

Consider an apple at rest on a table. If we call the gravitational force exerted on the apple action, what is the reaction force according to Newton’s third law?

Practice

A book of mass 2kg is allowed to fall freely. The earth exerts a force on the book, namely the gravity force. If we call this gravity force on the book the action force, what is the reaction force? How big? In what direction?

Practice

• Arnold and Susie (Arnold is considerably bigger and stronger than Susie) pull on opposite
• ends of a rope in a tug of war. The greatest force exerted on the rope is by
• a) Arnold
• b) Susie
• c) The same

Momentum of a system

Given a system of two masses and with velocities and , the total momentum of the system is defined as the vector sum of the individual momenta

In cases of more than 2 objects in the system, the total momentum is

Practice:

Two masses of 2.0 kg and 3.0 kg move to the right with speeds of 4.0 m/s and 5.0 m/s. What is the total momentum of the system?

Practice:

A mass of 2.0 kg moves to the right with a speed of 10.0 m/s and a mass of 4.0 kg moves to the left with a speed of 8.0 m/s. What is the total momentum of the system?

The total momentum of an isolated (closed) system, defined as , will remain constant. In other words, the total momentum of a system will remain the same when there is no external net force acting on the system.

### The Law of Conservation of Momentum

Practice

Two masses of 2.0 kg and 4.0 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a speed of 6.0 m/s, what is the speed of the other mass?

Practice

Jocko, who has a mass of 60 kg and stands at rest on ice, catches a 20 kg ball is thrown at him at a speed of 10 km/h. How fast does Jocko and the ball move across the ice?

Practice

• A ball is released from some height above the earth’s surface.
• Treat the ball as the entire system under consideration. As the ball falls, is the momentum of the system conserved?
• b)Treat the ball and the earth as the entire system under consideration. As the ball falls, is the momentum of the system conserved?

Warm up:

Let a mass of 3.0 kg be standing still and a second mass of 5.0 kg come along and hit it with velocity 4.0 m/s. Suppose that the smaller mass moves off with a speed of 3.0 m/s. What happens to the larger mass (what is its speed)?

Before collision

v1=4.0 m/s v2=0

After collision

u1=? u2=3.0m/s

Types of collisions:

• Elastic collisions: Objects bounce off each other undamaged.
• Inelastic collisions: Objects impact and separate, but there has been damage/deformation done to them.
• Perfectly inelastic collisions: Objects impact and STICK TOGETHER as one larger mass with the same, slower velocity.

The total momentum of the system is conserved for all three types of collisions.

But kinetic energy (which we will learn next week) is only conserved for elastic collision.

Practice:

Let two objects have masses of and and velocities and before the collision. As the result of the collision, the two objects change their velocities to and . Derive that the total momentum of the two objects remains the same before and after the collision using Newton’s second and third laws.

Let stands for the average force that A experiences during the collision, which lasts a time ∆t. Then, by Newton’s second law,

==

The force experienced by B is, by Newton’s third law, -. So

Thus