External forces have a big impact on how momentum works in different systems. To understand momentum better, it's important to know about conservative and non-conservative forces. This is especially true when we look at events like collisions.

What is Momentum?

Momentum, shown as $\vec{p}$, is a way to measure how much motion an object has. It’s calculated using the formula:

$$\vec{p} = m \vec{v}$$

Here, $m$ is the mass of the object, and $\vec{v}$ is its speed. Momentum has both size and direction, making it a vector. The law of momentum conservation tells us that if no outside forces are acting on a group of objects, their total momentum stays the same. But when outside forces come into play, they can change the momentum in ways we need to understand—especially in collisions and explosions.

Conservative vs. Non-Conservative Forces

Before we look at how outside forces can change momentum, let's know the difference between two types of forces:

1. Conservative Forces:

   • These forces don’t depend on how you got from one point to another.
   • The work done to move something from point A to point B is the same no matter the path taken.
   • Examples include gravity and spring force.
   • These forces keep mechanical energy in the system balanced.

2. Non-Conservative Forces:

   • The work done can change based on the path taken.
   • When these forces are involved, energy changes into different forms, like heat.
   • Examples include friction and air resistance.

Situations That Change Momentum

There are many situations where outside forces change momentum in a non-conservative way:

1. Collisions with Friction

Imagine a car hitting a wall:

• The car's speed before the crash and the impact changes its momentum.
• Friction during the crash uses up energy, turning it into heat.

In this case, the car's momentum changes in a non-conservative way because friction takes energy out of the system.

2. Air Resistance with a Skydiver

Think about a skydiver falling:

• Gravity is acting as a conservative force, constantly pulling the diver down.
• However, air resistance is a non-conservative force, slowing the diver down and turning some motion energy into heat.

Because of this air resistance, the diver's momentum changes in a non-conservative way, leading to a maximum speed called terminal velocity.

3. Explosions

During an explosion, fragments fly apart because of a fast release of energy:

• Before the explosion, the materials have a certain momentum.
• After the explosion, the forces from the explosion change the momentum of the pieces.

As the explosion pushes energy in all directions, each piece's momentum is non-conservatively affected.

4. Rocket Launch

When a rocket takes off, it pushes out gas downwards:

• This push changes the rocket's momentum.
• As the rocket burns fuel, it gets lighter, which makes calculating momentum tricky.

Here, the rocket’s momentum changes in a non-conservative way because the energy of the gas being pushed out counts as outside energy.

5. Pushing a Cart

Imagine a cart on a surface with friction. When someone pushes the cart:

• The push changes its momentum because that push is an outside force.
• The energy used to push the cart goes against friction, creating a non-conservative change in momentum.

Here, the total momentum of the cart is affected by the pushing force, leading to a non-conservative change.

Things That Affect Non-Conservative Changes

1. Size of the Force: Stronger outside forces change momentum more. For example, a hard collision will lead to a larger change in momentum.

2. Time the Force Acts: A force that works for a long time changes momentum differently than a quick force.

3. Direction of the Force: The angle at which the force is applied can determine if the momentum increases or decreases.

Laws of Conservation and Non-Conservative Forces

Even with non-conservative forces, we have to think about conservation laws:

• Momentum in Closed Parts: Even if total momentum changes, in parts where there are no outside forces, momentum stays the same.

• Energy Counts: While mechanical energy may not be conserved due to non-conservative forces, total energy (kinetic, potential, and thermal) still remains constant overall.

Summary

Outside forces are key in changing momentum in physical systems, especially when they lead to non-conservative changes. Examples like collisions with friction, air resistance when falling, explosions, rocket launches, and forces pushing carts show how these factors can affect an object's momentum.

By understanding how these forces work together, we can better comprehend complex physical events and predict what happens when things interact in different systems. The basic concepts of physics help us see the connections that drive motion and energy changes all around us.