Thermodynamics and Elastic Collisions: Conservation of Momentum

Thermodynamics and Elastic Collisions: Conservation of Momentum - AP Physics 2 Study Guide

Hello, future physicists and aspiring engineers! Ready to dive into the magical world of thermodynamics and elastic collisions? Well, grab your lab coats and get ready to geek out over some physics fun as we explore how momentum and energy decide to play nice (or not so nice) with each other.✨🔬

Let's start with the basics: collisions. No, we are not talking about awkward run-ins with your high school nemesis. In physics, we’re talking about two objects smacking into each other and then deciding their next move. It's like objects playing a high-stakes game of bumper cars!

If the net external force acting on a system is zero, then the total momentum within that system remains conserved. Think of it like a momentum savings bank: what goes in must come out unless a sneaky external force meddles.

There are mainly two kinds of collisions: elastic and inelastic. Here’s the scoop:

1. Elastic Collisions:

   • Think of it like a perfectly bouncy ball. In these collisions, the total kinetic energy of the objects before and after the collision is the same. They rebound off each other without losing energy to squishing or heating up.
   • In simpler terms: All the kinetic energy they had before the collision stays as kinetic energy afterward. They’re just swapping momentum like it’s a game of hot potato.
   • Example: Imagine two ice skaters who push off each other and glide away at the same speed they had before the collision. They just swap directions.

2. Inelastic Collisions:

   • This is like when two marshmallows smash together and stick. Some or all of the kinetic energy is converted into other forms such as heat, sound, or even deformation energy.
   • In simpler terms: These objects tend to smoosh together and wander off as a single squishy blob post-collision.
   • Example: A car crash where the cars crumple and stick together, absorbing and dissipating energy.

In the realm of elastic collisions, both kinetic energy (KE) and momentum (p) are star players. You can use the Kinetic Energy formula (KE = 1/2 mv^2) to understand and solve problems since energy in this system likes to remain consistent.

However, if dealing with a 2D collision, you’ll need to consider both the x and y directions independently. Use your given angles and break down vectors if no net forces or velocities are provided. Remember to juggle those vectors carefully – it's like balancing a physics circus!

In most thermodynamics problems, especially in AP Physics 2, we assume collisions to be elastic to simplify our calculations and reasoning. However, make sure you understand the distinctions between elastic and inelastic collisions — it's critical for dealing with problems related to conservation laws.

Imagine a 2 kg cart moving to the right at 3 m/s collides with a stationary cart weighing 1 kg. After the collision, the first cart moves at 2 m/s, and the second cart starts zooming to the right at 1 m/s.

Classify the Collision:

To figure out whether the collision is elastic or inelastic, check the kinetic energy before and after the party.

• Before collision: ( KE_i = (1/2) * 2 , \text{kg} * (3 , \text{m/s})^2 + (1/2) * 1 , \text{kg} * (0 , \text{m/s})^2 = 9 , \text{J} )

• After collision: ( KE_f = (1/2) * 2 , \text{kg} * (2 , \text{m/s})^2 + (1/2) * 1 , \text{kg} * (1 , \text{m/s})^2 = 5 , \text{J} )

Since the kinetic energy is not conserved (from 9J to 5J), this collision is inelastic. Yup, our carts lost some bounce in the crash!

Solving for Missing Variables Using Conservation of Momentum:

The initial momentum (p_i) and final momentum (p_f) should balance out if no external forces interfere:

• Before collision: ( p_i = (2 , \text{kg} * 3 , \text{m/s}) + (1 , \text{kg} * 0 , \text{m/s}) = 6 , \text{kg*m/s} )

• After collision: ( p_f = (2 , \text{kg} * 2 , \text{m/s}) + (1 , \text{kg} * 1 , \text{m/s}) = 5 , \text{kgm/s} + 1 , \text{kgm/s} = 6 , \text{kg*m/s} )

So the momentum conserved perfectly. Hooray, physics victory! 🎉

• Conservation of Kinetic Energy: In a closed system with no external work or non-conservative forces, the total kinetic energy remains unchanged. Energy can neither be created nor destroyed (yeah, it’s stubborn like that).

• Conservation of Linear Momentum: In a system free from external forces, the total momentum remains constant. Essentially, the system’s motion keeps on keepin’ on unless something external butts in.

• Elastic Collision: Both kinetic energy and linear momentum are conserved. The objects bounce off each other retaining their initial energy and momentum.

• Inelastic Collision: Kinetic energy is not conserved. Some energy transforms into other forms like heat or deformation, though momentum still remains conserved.

• Kinetic Energy: The energy possessed by an object just because it’s moving. Calculated with ( KE = 1/2 mv^2 ).

• Momentum: A way to measure an object’s motion. Calculated as mass times velocity (( p = mv )).

• Sound Energy: Vibrational energy traveling through matter in longitudinal waves, like those squeaky noises during collisions.

• Thermal Energy: Internal energy due to particle motion, often linked with temperature.

Did you know that when you're ice skating and you push off from your friend, you're experiencing real-life momentum conservation? Next time you glide away, whisper a thank you to Newton! 😜

And there you have it, a crash course (pun intended) on thermodynamics and elastic collisions! Armed with this knowledge, you're ready to tackle momentum and energy problems like a pro. Remember, in the world of physics, it's all about balance and keeping track of where that tricky energy and momentum decide to go. Happy studying, and may the forces be with you! 🌟🔬