Thermodynamics and Inelastic Collisions: Conservation of Momentum
Mia Gonzalez
7 min read
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Study Guide Overview
This study guide covers inelastic collisions, where kinetic energy is not conserved, unlike elastic collisions. It explains the difference between elastic and inelastic collisions, including completely inelastic collisions. The guide emphasizes the conservation of momentum in all collisions. It provides example problems involving colliding carts and bowling balls, focusing on calculating final velocities and changes in kinetic energy. Finally, it offers practice questions and exam tips for identifying and solving collision problems.
#Inelastic Collisions: When Kinetic Energy Isn't Conserved 💥
In our previous discussion, we explored momentum and elastic collisions, where kinetic energy (KE) is conserved. Now, let's dive into inelastic collisions, where things get a bit more interesting because KE is not conserved.
#What are Inelastic Collisions?
- In an elastic collision, both momentum and kinetic energy are conserved. Think of billiard balls bouncing off each other perfectly. 🎱
- In an inelastic collision, momentum is still conserved, but some kinetic energy is converted into other forms of energy, such as heat, sound, or deformation. Imagine two cars colliding and crumpling. 🚗💥
- A completely inelastic collision is a special case where the colliding objects stick together after the collision.
Key Concept: Momentum is ALWAYS conserved in collisions (both elastic and inelastic), but kinetic energy is only conserved in elastic collisions.
#Understanding the Differences
| Feature | Elastic Collision | Inelastic Collision |
|---|---|---|
| Kinetic Energy | Conserved (KE_initial = KE_final) | Not Conserved (KE_initial ≠KE_final) |
| Momentum | Conserved (p_initial = p_final) | Conserved (p_initial = p_final) |
| Object Behavior | Objects bounce off each other | Objects may stick together, deform, or generate heat/sound |
#Example: Two Carts Colliding
Let's illustrate with an example:
Two carts of the same mass (m) are on a table. Cart 1 is moving with velocity v, and cart 2 is at rest. They collide and stick together. What's their final velocity (vf)?
- Initial Momentum:
- **Final Mo...
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