1. Simple Motion
2. Accelerated Motion
3. Projectile Motion
4. Newton's Laws
5. Momentum
6. Energy
7. Heat
8. Electrostatics
9. Circuits
10. Magnetism
11. Waves5. Momentum
Overview
Momentum is a measure of mass in motion. The bigger the momentum of an object, the more work it takes to slow it down. Momentum is conserved as energy is conserved, which allows us to analyze the interaction of colliding objects through their constant total momentum.
Slides
Skills and Understanding
- Applying a net force on an object accelerates it.
- Applying a net force for a longer period of time accelerates it more.
- Momentum is conserved (in a closed system).
Equations
\[ \begin{array}{c} p = mv \quad \quad \quad \Delta p = mv_{f} - mv_{i} \quad \quad \quad \Delta p = F \Delta t \\ \end{array} \] \[ p_{i}= p_{f} \]Vocabulary
- Acceleration \(a\) is the rate at which velocity changes.
- Impulse is the change in momentum.
- Momentum \(p\) is the product of an object's mass and velocity.
5.1 Momentum
Given an object with mass \(m\) and velocity \(v\), we call the product of these two values momentum. \[ p = mv \]
5.2 Impulse
Momentum of a mass can change if the velocity changes. It is often useful to know the change in momentum \(\Delta p \). There are multiple ways we can approach working with changing momentum.\[ \Delta p = mv_{f} - mv_{i} \] \[ \Delta p = m \Delta v \] \[ \Delta p = m a \Delta t \] \[ \Delta p = F \Delta t \]
5.3 Conservation
The Law of Conservation of Momentum states that momentum is always conserved in a closed system. This means that the total momentum before collision is the same as the total momentum after collision. \[ p_{i} = p_{f} \] We will consider three cases of collision.
Elastic Collision
Two bodies collide and stay separate. \[ m_{1} \cdot v_{1i} + m_{2} \cdot v_{2i} = m_{1} \cdot v_{1f} + m_{2} \cdot v_{2f} \] That is a lot of notation, but it just says that the total momentum is the same before and after collision.
Inelastic Collision
In a perfectly inelastic collision, the colliding bodies join into one. \[ m_{1} \cdot v_{1i} + m_{2} \cdot v_{2i} = \left( m_{1} + m_{2} \right) v_{f} \]
Explosive
The explosive scenario involves an object that starts as one total mass that splits into multiple pieces. \[ \left( m_{1} + m_{2} \right) v_{i} = m_{1} \cdot v_{1f} + m_{2} \cdot v_{2f} \]