NovaSolver›1D Collision Simulator (Elastic & Inelastic) Back
Collision Simulator
1D Collision Simulator (Elastic & Inelastic)
Set mass, velocity, and coefficient of restitution of two objects to calculate pre- and post-collision velocity, momentum, and energy. Visualize the collision process with animation.
Parameters
Presets
Object 1 (blue)
Mass m₁
kg
Initial velocity v₁
m/s
Positive: rightward / Negative: leftward
Object 2 (orange)
Mass m₂
kg
Initial velocity v₂
m/s
Coefficient of restitution e
0: Perfectly inelastic1: Perfectly elastic
Playback Controls
Result comparison
Drag controls:Drag objects on canvas to change initial position; drag velocity arrows to set initial velocity.
Results
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v₁' after [m/s]
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v₂' after [m/s]
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Δp₁ [N·s]
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Energyloss [J]
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KE retained [%]
CollisionAnimation
Physical Quantity
Before collision
After collision
v₁ [m/s]
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v₂ [m/s]
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Total momentum p [kg·m/s]
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Total kinetic energy KE [J]
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Energyloss ΔKE [J]
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CAE Applications
Directly related to coefficient of restitution (contact restitution) settings in LS-DYNA / Abaqus Explicit. Used for initial condition settings in barrier collision tests, pedestrian protection analysis, and SPH-based fragmentation simulations.
What exactly is the "coefficient of restitution" (e) in this simulator? I see it's a slider from 0 to 1.
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Basically, it's a number that tells you how "bouncy" a collision is. In practice, e=1 means a perfectly elastic collision where kinetic energy is conserved, like two superballs colliding. e=0 means a perfectly inelastic collision where the objects stick together, like two lumps of clay. Try moving the slider above and watch how the final velocities and the energy loss change.
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Wait, really? So if I set one mass much larger than the other, the small one just bounces off, right? How does the math handle that?
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That's a great observation! For instance, if a ping-pong ball (m₁) hits a stationary bowling ball (m₂), it will bounce back with a speed close to its original. The simulator's equations account for this mass ratio. Try setting m₁=1, v₁=5, m₂=100, v₂=0, and e=1. You'll see v₁' is nearly -5 (it rebounds), while the heavy m₂ barely moves.
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Okay, I see the final velocities. But the "Kinetic Energy" chart shows a big loss when e is less than 1. Where does that energy go?
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In real-world collisions, that "lost" kinetic energy is transformed into other forms. A common case is in car crash tests: the energy deforms the metal, creates sound, and generates heat. That's an inelastic process. In the simulator, when you drag the restitution slider below 1, the energy bar turns red to visualize this loss, which is crucial for accurate engineering simulations.
Physical Model & Key Equations
The core physics is governed by two principles: Conservation of Momentum (always true for the collision) and the definition of the Coefficient of Restitution, which relates the relative speed before and after impact.
$$m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'$$
Conservation of Momentum: The total momentum before collision (left side) equals the total momentum after (right side). This holds true for both elastic and inelastic collisions.
The Coefficient of Restitution (e) is defined as the ratio of the relative speed of separation to the relative speed of approach. Combining this with momentum conservation gives the general formulas used by the simulator.
Variables: $m_1, m_2$ are masses (kg), $v_1, v_2$ are initial velocities (m/s), $v_1', v_2'$ are final velocities (m/s). The parameter $e$ is the coefficient of restitution you control with the slider.
Frequently Asked Questions
Yes, it is possible. The sign of velocity indicates direction, with positive values treated as rightward and negative values as leftward. Inputting a negative value for mass is physically meaningless, but the calculation itself will still be performed. We recommend using positive mass for realistic simulations.
When the coefficient of restitution is 0.5, some kinetic energy is lost after the collision. Compared to a perfectly elastic collision (e=1), the lost energy is primarily converted into heat or deformation. You can check the numerical changes before and after the collision in the energy display at the top of the screen.
Please drag the simulation speed adjustment slider (usually at the bottom of the screen) toward the 'slow' side. Additionally, instead of pressing the 'Reset' button after the collision, you can change the velocity or mass and click 'Run' again to replay the simulation under the same conditions.
When e=0, the two objects move at the same velocity after the collision. This common velocity is calculated from the law of conservation of momentum, using the formula v' = (m1*v1 + m2*v2) / (m1+m2). In the simulator, the combined object is displayed as a single block in the animation.
Real-World Applications
Automotive Crash Testing: Engineers use coefficients of restitution (often called "contact restitution" in software) to simulate vehicle collisions. In LS-DYNA or Abaqus Explicit, setting accurate 'e' values for different materials is critical for predicting crumple zones and passenger safety in barrier tests.
Sports Equipment Design: The bounce of a basketball, the "ping" of a golf club, or the rebound of a hockey puck are all analyzed using collision physics. Designers tweak materials to achieve an optimal restitution that balances performance and control.
Particle & Granular Flow Simulations: In chemical engineering or astrophysics, simulating millions of particle collisions (like grains in a hopper or dust in a protoplanetary disk) relies on efficient 1D collision models with a defined 'e' to model energy dissipation.
Animation & Game Physics: To make virtual collisions look realistic, game engines implement simplified versions of these equations. The mass and restitution values you set in this simulator are directly analogous to parameters a game developer would adjust for a physics object.
Common Misconceptions and Points to Note
First, the misconception that "the coefficient of restitution e is a material-specific constant." In reality, it can also change depending on impact velocity, object shape, and temperature. For example, even the same rubber ball will have a lower e if it hits a wall at an extremely high speed (high-velocity impact) due to significant internal heat generation. While the simulator uses a fixed value, in practice, you often use it conditionally, like "use this e for this velocity range."
Next, complacency because "it's one-dimensional, so it's simple." This tool deals strictly with the collision of "point masses." Real components have size and shape, which can cause rotation upon impact or change the contact point. For instance, when a long rod collides end-on, translational and rotational motion couple, resulting in behavior unpredictable by 1D equations alone. The key to leveling up is to first grasp the concept with the point mass model while also understanding its limitations.
Finally, pitfalls in CAE settings. When setting e for contact conditions in software like LS-DYNA, be careful not to mistake "which pair to set it for." You need to assign an appropriate e to every contact pair: contact between part A and B, part B and C, and so on. Applying a default value (e.g., 0.1) to everything can lead to unrealistic bouncing behavior, so be cautious. Experiencing the effect of e "between two objects" in this simulator will make it easier to visualize the CAE setup.