# Conservation of Momentum in 1 Dimension

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Conservation of Momentum in 1 Dimension
SPH4U – Grade 12 Physics Unit 4

Conservation of Momentum in 1 Dimension
We have already reviewed the Law of Conservation of Energy: In an isolated system, energy cannot be created or destroyed. It is only transformed from one form to another.

Conservation of Momentum in 1 Dimension
Today we will discuss the Conservation of Linear Momentum.  If the net force acting on a system of interacting objects is zero, then the linear momentum of the system before the interaction equals the linear momentum of the system after the interaction.

Conservation of Momentum in 1 Dimension
The Conservation of Linear Momentum is related to Newton’s 3rd Law. If you exert a force on an object, the object will exert a force back on you.

Classroom Demo / Discussion
Consider a situation where you are sitting on the projector stand and pushing a chair forward.

Classroom Demo / Discussion
Before you push : The system, which is made up of you (on the projector stand) and the chair has zero momentum before you push the chair. (It has zero momentum because there is no velocity). After you push the chair: The chair moves forward and you move back.

Demo / Discussion According to the Law of Conservation Linear Momentum this means that after you push the chair, the momentum of the whole system must also be zero. (We know that after you push the chair, the chair has momentum and you have momentum because there is motion…So how do we get zero momentum?) This is because the momentum is in opposite directions- so they balance each other out, and the total momentum of the system is zero.

Collisions The idea of conserved momentum is very useful to us when studying collisions. The law tells us that during an interaction between two objects on which the totally net force is zero, the change in momentum of objects 1 is equal in magnitude but opposite in direction to the change in momentum of object 2.

Thus… The prime symbols mean after the collision

We can also think of it this way: the total momentum of an isolated system before a collision is equal to the total momentum of the isolated system after the collision as long as the net force acting on the system is zero.

It is important to remember that momentum is a vector quantity; thus, any addition or subtractions in these conservation of momentum equations are vector additions or vector subtractions.

Situation where we can use the conservation of momentum
Two billiard balls on a table The two balls and the table represent an isolated system

The force exerted by the first ball on the second is equal in magnitude but opposite in direction to the force exerted by the second ball on the first. Thus, the two forces would cancel each other out and the total net force on the system would be zero.

Because the net force on the system is zero, momentum is conserved.

Situation where we cannot use the conservation of momentum
In many real life situations, which are not isolated systems, momentum will not be conserved. The influence of external factors, such as friction, can influence things since part of the energy involved gets transferred somewhere else.

Example 1 (f) If we consider Earth and the hairbrush to be initially stationary, how does Earth move as the hairbrush falls down? (g) If the hairbrush reaches a speed of 10m/s when it hits Earth (initially stationary) what is Earth’s speed at this time?

Solution

Example 2 Two ice skaters, initially stationary, push each other so that they move in opposite directions. One skater of mass of 56.9 kg has a speed of 3.28 m/s. What is the mass of the other skater if her speed is 3.69 m/s? Neglect friction. ** Note: They were stationary before,so their net force was zero. Momentum will be conserved in this system.

Solution

Example 3

Solution

Homework Read Section 5.2 in your textbook and supplement your notes with the reading. (Note: there is an interesting paragraph on explosions covered in the text, and also one on rocket propulsion that isn’t talked about in this note). Do the following questions for homework: Pg. 232 # 1, 3, 5, 7