Inelastic Collision#
Welcome to the Inelastic Collision Simulator#
Imagine two balls rolling around and then smashing into each other, but instead of bouncing apart, they stick together like glue and keep moving as one big lump. That’s what an “inelastic” collision is all about! This simulator lets you watch that happen in a fun, interactive way. It’s called “perfectly inelastic” because the balls merge completely, and some energy gets “lost” (turned into heat or sound, but not motion).
This app is perfect for beginners—no physics background needed. We’ll explain everything simply, including the basic math. You’ll see a screen with balls moving, walls they can bounce off, and when they hit each other, they combine into one. There’s also a graph showing live data, like a chart that updates as things happen. You can change settings to try different setups and see what changes.
By playing with this, you’ll learn how the balls’ speeds and masses affect what happens when they stick together. The key rule is that “momentum” (a combo of mass and speed) stays the same before and after, but “kinetic energy” (motion energy) decreases. We’ll show the math step by step with just algebra—no complicated stuff.
Getting Started: How to Use the Simulator#
New to the app? No problem! It’s straightforward. When you open it, here’s what you’ll find:
The Main Screen (Simulation Area)
This is the play area where the action happens. You’ll see two balls—one red, one blue—moving around on a flat space with walls, a ceiling, and a ground. They can bounce off these boundaries like in a pinball game. But when the two balls touch each other, they merge into a single purple ball that keeps going.
Controls for the Balls
On the side or bottom, there are inputs to customize the balls:
Mass (m): How heavy each ball is. Try making one super heavy (like 10) and the other light (like 1) to see the difference!
Radius: The size of the ball. It mostly affects looks, not the physics much.
Initial Velocity (\(v_x\) and \(v_y\)): Speed and direction. v_x is left-right (positive right, negative left), v_y is up-down (positive up, negative down). Start simple, like one ball moving right and the other still.
Buttons to Control the Action
Start: Gets the balls rolling.Pause: Freezes everything to check or adjust.Reset: Starts over from scratch, clearing everything.
The Graph for Seeing Data
There’s a line graph that updates live. Use dropdowns to choose what to show:
X-axis (bottom): Often time, but pick what you want.
Y-axis (side): Things like kinetic energy, momentum, or collision count.
For example, plot “Time” vs. “Total Kinetic Energy” to watch the energy drop when they collide.
Hint
Make one ball much heavier than the other and give the heavy one some speed. After they stick, the combined ball moves almost like the heavy one did—showing how mass influences momentum!
The Physics Behind the Sticking#
Let’s dive into the science with easy explanations. We’ll use simple math to show how it works. This is for 2D (like on a table), so speeds have directions (vectors), but we’ll break it down.
What is Momentum?
Momentum is the “push” from something moving. Formula: \(p = m \times v\) (mass times velocity). For two balls, total momentum is their p’s added up. In any collision (even inelastic), total momentum before equals after. That’s conservation of momentum.
What is Kinetic Energy?
Kinetic energy (KE) is energy from motion: \(KE = \frac{1}{2} \times m \times v^2\) (half mass times speed squared). In inelastic collisions, total KE decreases because some turns into heat or deformation—not conserved.
Now, let’s figure out the speed after they stick. We have Ball 1 (mass \(m_1\), initial velocity \(\vec{v}_{1i}\)) and Ball 2 (\(m_2\), \(\vec{v}_{2i}\)). After merging, they have one velocity \(\vec{v}_f\) and mass \((m_1 + m_2)\).
Step 1: Write the Momentum Equation
Total momentum before = total after:
This is for vectors, so it works in 2D. To solve for \(\vec{v}_f\), rearrange by dividing both sides by total mass:
That’s it! No more steps needed because they stick together—the final velocity is just the weighted average of the initials.
Step 2: Breaking It Down for 2D
Since it’s 2D, we do this separately for x and y directions (components):
The full \(\vec{v}_f\) combines these.
Step 3: Calculating Kinetic Energy Loss
Initial KE (before):
(Note: \(v_{1i}^2\) means the square of the speed, like \((v_{1ix}^2 + v_{1iy}^2)\) for 2D.)
Final KE (after):
Where \(v_f^2 = v_{fx}^2 + v_{fy}^2\).
The loss is \(\Delta K = K_i - K_f\), which is always positive (energy decreases) if they were moving relative to each other.
Note
In the graph, look for a sudden drop in kinetic energy right when they collide—that’s the “lost” energy turning into something else, like heat.
What You Can Learn from This Simulator#
This app makes physics hands-on and fun:
Momentum Stays the Same: See how the total “push” doesn’t change, even when balls merge.
Energy Changes Form: Watch KE drop on the graph, showing it’s not lost but transformed.
Test Different Setups: Change masses or speeds to predict and verify outcomes, like how a heavy ball dominates the motion.
Wrapping Up#
The Inelastic Collision Simulator is an awesome tool to explore sticky crashes in physics. Whether you’re a total newbie or just experimenting, adjust the controls, press Start, and observe the results on the graph. It’s a great way to see math and science in action. Have fun simulating!