In previous lesson, we have discussed inertia, including what is inertia, Newton’s first law of motion, situation involving inertia, mass and inertia and reducing negative effects of inertia. In this lesson, we will discuss momentum, including the principle of conservation of momentum and its applications. Under principle of conservation of momentum, we will discuss how to solve problems related to collision and explosion.

Under momentum, we will discuss what is momentum (including its unit and formula), the principle of conservation of momentum and the applications of the principle of conservation of momentum.

Under the principle of conservation of momentum, we will discuss the formula that describes the conservation principle. We will also discuss the 2 cases of reaction: collision and explosion. Under collision, we will discuss the elastic collision and inelastic collision.

In applications, we will include rocket, jet engine, and the moving mechanism of a jelly fish.

In SPM, there are a few things that you need to know about momentum. First, you need to know the definition of momentum. Momentum is defined as the product of mass and velocity.

Second, you need to know the formula of momentum. The formula of momentum is p = mv, where p is momentum, m is mass and v is velocity.

Third, you need to know the unit of momentum. In SPM, you need to state the unit of the physical quantity of your answer. Momentum is equal to mass multiply by velocity. The SI unit of mass is kg, and the SI unit of velocity is ms^{-1}. Therefore, the unit of momentum is kgms^{-1}.

Last but not least, you need to know that momentum is a vector quantity. Therefore, you need to be caution about the direction of the motion. If an object move in opposite direction, its momentum is negative.

##### Principle of Conservation of Momentum

Let’s see this example. 2 balls of mass 4kg and 2kg, respectively, moving in the same direction in a straight line. The velocity of the ball at the back is 3 m/s, higher than the velocity of the ball in front. If the ball at the back moves faster than the ball in front, and both of the balls are moving in a straight line, collision will happen. After collision, the balls move at 1m/s and 6m/s, respectively.

Let’s calculate the momentum of the balls before and after collision. Before collision, the momentum of the 4kg ball is 4kg x 3m/s, equal to 12 kg m/s. By using the same equation, we can find the momentum of the 2kg ball, which equal to 4kgms^{-1}. The sum of momentum before collision is 12 + 4, equal to 16 kg m/s.

How about after the collision? The momentum of the 4kg ball became 4 kg m/s while the momentum of the 2 kg ball became 12 kg m/s, and the sum of momentum is 16 kg m/s.

Well, we can see that the sums of momentum before and after the collision are equal. In scientific term, we say the momentum is conserve after the collision. The word conserve means remain unchanged.

Sum of momentum before the collision is equal to the sum of momentum after the collision. This is the physics concept that we going to discuss in the principle of conservation of momentum.

The principle of conservation of momentum states that **in a system** make out of objects that react, the sum of the momentum is constant if **no external force** is acted on the system. The reaction can be a collision or explosion. The word constant means remain unchanged.

In other words, in a collision or explosion, if no external force acted on the system, the sum of the momentum before the collision or explosion will be equal to the sum of the momentum after the collision or explosion.

In SPM, there are a few things you need to know about this principle of conservation of momentum.

First, you need to remember this statement because in exam, you may be asked to state this principle of conservation of momentum.

Second, you need to know the equation that describer this principle of conservation of momentum and its applications in elastic collision, inelastic collision and explosion.

Third, you need to know the difference between elastic and elastic collision.

Forth, you need to know the application of principle of conservation of momentum in rocket and jet airplane.

##### Equation of Principle of Conservation of Momentum

If 2 balls of mass m_{1} and m_{2} collide with each other, the velocity before the collision is u_{1} and u_{2} while the velocity after the collision is v_{1} and v_{2} respectively, then the sum of momentum before the collision will be m_{1}u_{1} + m_{2}u_{2 }while the sum of momentum after the collision is m_{1}v_{1} + m_{2}v_{2},

According to the principle of conservation of momentum, the sum of momentum before reaction equal to the sum of momentum after reaction. Therefore, m_{1}u_{1} + m_{2}u_{2 }is equal to m_{1}v_{1} + m_{2}v_{2}.

We can use this equation to solve almost all the problems involving collision or explosion in SPM physics.

In SPM, almost all the numerical problems related to collision and explosion can be solved by the principle of conservation of momentum.

Let’s see this example: The diagram shows 2 objects P and Q of mass 1kg and 2kg which are about to collide. Given that object P move at 1 m/s after the collision, find the velocity of Q after the collision.

We know that a question related to collision can be solved by the equation of principle of conservation of momentum: m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}. When solving numerical problems, the first thing we need to do is to list down all the information that we have. Listing down all given information is an important step.

The mass m_{1} is 1kg, m_{2} is 2kg. The initial velocity u_{1} is 4 m/s and u_{2} is 1 m/s. Opps, wait a minute! This 1 m/s is not correct. Well, we must be very careful when writing the value of the velocity. Velocity is a vector quantity. Velocity is negative if the object moves in opposite direction. In this case, Q moves in the opposite direction. Therefore u_{2} is -1 m/s but not 1 m/s. After the collision, the velocity v_{1} become 1 m/s and we are asked to find the velocity of Q.

Plug in all these numbers into the equation. Clean up the equation, we get 4 – 2 = 1 + 2v_{2}. Therefore, v_{2} is equal to 0.5 m/s. The velocity of Q is positive. This positive value of Q shows that it moves to the right after the collision.

By definition, elastic collision is the collision where the kinetic energy is conserved after the collision. The word conserve means remain unchanged. If the kinetic energy is not conserved, then the collision is inelastic.

For example: 2 balls of mass 3kg and 1 kg move in opposite direction. Let’s say the kinetic energy of the 3kg ball is 12J while the kinetic energy of the 1 kg ball is 6J. After the collision, the kinetic energy of the 2 balls becomes 10J and 8J respectively. Do you think this collision is elastic or inelastic? Yes, you are correct. The sum of the kinetic energy before the collision is 18J and the sum of kinetic energy after the collision is also 18J. The sum of the kinetic energy before the collision equal to the sum of the kinetic energy after the collision. The kinetic energy is conserved in the collision. Therefore, this is an elastic collision. There are 2 types of collision: the elastic collision and the inelastic collision. In both collisions, the momentum is conserved. For elastic collision, the kinetic energy is conserved and the colliding objects bounce away after the collision. For inelastic collision, the kinetic energy is not conserved after the collision. In a perfectly inelastic collision, the 2 colliding objects attach and move with same speed after collision.