Advanced Mathematics of Mechanics

Forces, Energy and Momentum

# Applying impulse, change in momentum and conservation of momentum

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Applying impulse, change in momentum and conservation of momentum

**Impulse and Change in Momentum**

**Impulse**is defined as force times time: it is the product of the average force exerted on an object and the time interval over which the force acts.- In mathematical terms, impulse is also defined as the change in momentum of an object when a force is applied.
**Momentum**is a vector quantity as it has direction as well as magnitude.- In physics, momentum is usually denoted by the letter 'p', and it is calculated by multiplying the mass of an object (m) by its velocity (v). Therefore, p=mv.
- Momentum is conserved in a closed system where external forces are not at play. This is known as the
**conservation of momentum**.

**Applying the Concept of Impulse and Change in Momentum**

- The concept of impulse can be applied to understand how the velocity of an object changes when a force is applied.
- For example, when a football is kicked, the shoe applies a force to the football over a short period of time. This force changes the football’s velocity, and hence its momentum.
- The greater the impulse, the greater the change in momentum. If the force is applied for a longer period of time, the change in the object’s momentum will be more significant.
- In an impact between two objects, the total momentum before the impact is equal to the total momentum after the impact (assuming no external forces are at work). This concept is central to the principle of conservation of momentum.

**Conservation of Momentum**

- The principle of conservation of momentum states that in a closed system, the total linear momentum of the system remains constant if no external forces act on it.
- In a collision, the total momentum of the colliding objects is the same before and after the collision.
- Therefore, if you have two objects, their combined momentum before the collision equals their combined momentum after the collision.
- This principle has significant practical applications in real-world physics including, for example, the study of vehicle collisions or the performance of rocket propulsion systems.