Interactive physics simulator
Collision Mechanics
Collisions are short-duration interactions where bodies exchange momentum. Explore 1D air track gliders, crumpling bumper crash tests, and 2D oblique billiard deflections in our premium interactive physics laboratory.
Collision Mechanics Simulator
Configure velocities, mass values, and stiffness, then hit run to analyze force and momentum transfers.
Live Telemetry
- Glider 1 Mass
- 1.0 kg
- Glider 2 Mass
- 1.5 kg
- Glider 1 Vel
- 8.0 m/s
- Glider 2 Vel
- -5.0 m/s
- Glider 1 Momentum
- 0.0 kg·m/s
- Glider 2 Momentum
- 0.0 kg·m/s
- Total Momentum (P)
- 0.0 kg·m/s
- Total Kinetic Energy
- 0.0 J
What is a Collision in Physics?
A collision is an interaction between two or more bodies that come into contact, exerting relatively strong forces on each other for a short time interval. Because the contact forces during impact are massive compared to any external forces (such as friction or gravity), we can treat the colliding bodies as an isolated system. The total linear momentum of the system is conserved immediately before and after the collision.
The mathematical formulation of momentum conservation in a one-dimensional collision is expressed as:
Perfectly Elastic Collisions
In perfectly elastic collisions, both total momentum and total kinetic energy are conserved:
KE_initial = KE_final
- No kinetic energy is lost to heat, sound, or permanent deformation.
- Objects bounce away with a relative speed of separation equal to the relative speed of approach.
- The coefficient of restitution is exactly e = 1.0. Examples include collisions between gas molecules or steel bearings.
Inelastic & Stuck Collisions
In inelastic collisions, momentum is conserved, but kinetic energy is dissipated:
KE_final < KE_initial
- Completely Inelastic (e = 0.0): The colliding bodies stick together, moving with a single final velocity: vf = (m1·u1 + m2·u2) / (m1 + m2).
- The maximum possible amount of kinetic energy is lost during completely inelastic impacts.
- Real-world crashes are partially inelastic (0 < e < 1).
Impulse and Crumple Zones
Impulse is the measure of momentum change: J = Δp = F_avg · Δt.
- For a car stopping in a crash, its momentum change Δp is fixed.
- By designing a front bumper to buckle and fold (crumple zone), engineers increase the duration of the crash Δt.
- A larger Δt yields a smaller peak force F_avg, preventing severe stress or injuries on passengers inside.
2D Oblique Collisions
Collisions that do not occur head-on scatter in two dimensions:
- Momentum is a vector quantity, meaning X and Y momentum components conserve independently: P_ix = P_fx and P_iy = P_fy.
- For identical masses colliding elastically off-center where one is at rest, they deflect at exactly 90° relative to each other.
- Sliders in Mode 3 demonstrate how target offset drives deflection angles.
Solved Examples
A 2.0 kg glider (Glider 1) moving East on a frictionless air track at +6.0 m/s collides elastically with a 1.0 kg glider (Glider 2) traveling West at -3.0 m/s. Find their final velocities after collision.
- First, state initial conditions: m1 = 2.0 kg, u1 = +6.0 m/s, m2 = 1.0 kg, u2 = -3.0 m/s.
- Since the collision is perfectly elastic (e = 1.0), use the velocity equations:
- v1f = [(m1 - m2) * u1 + 2 * m2 * u2] / (m1 + m2) = [(2.0 - 1.0) * 6.0 + 2 * 1.0 * (-3.0)] / (2.0 + 1.0) = [6.0 - 6.0] / 3.0 = 0.0 m/s.
- v2f = [(m2 - m1) * u2 + 2 * m1 * u1] / (m1 + m2) = [(1.0 - 2.0) * (-3.0) + 2 * 2.0 * 6.0] / (2.0 + 1.0) = [3.0 + 24.0] / 3.0 = +9.0 m/s.
- After collision, Glider 1 stops completely (0.0 m/s) and Glider 2 rebounds East at +9.0 m/s.
Answer: Glider 1: 0.0 m/s | Glider 2: +9.0 m/s
A 1200 kg vehicle moving at +20 m/s crashes into a stationary 800 kg car. They lock bumpers during the collision and stick together. Calculate their combined final velocity and find the kinetic energy lost.
- Initial conditions: m1 = 1200 kg, u1 = +20 m/s, m2 = 800 kg, u2 = 0.
- This is a completely inelastic collision (e = 0), so they stick together. Total momentum is conserved: m1 * u1 + m2 * u2 = (m1 + m2) * vf.
- 1200 * 20 + 0 = (1200 + 800) * vf => 24,000 = 2000 * vf => vf = +12.0 m/s.
- Find initial kinetic energy: KE_initial = 1/2 * m1 * u1^2 = 1/2 * 1200 * (20)^2 = 240,000 Joules.
- Find final kinetic energy: KE_final = 1/2 * (m1 + m2) * vf^2 = 1/2 * 2000 * (12)^2 = 144,000 Joules.
- Calculate energy loss: KE_lost = KE_initial - KE_final = 240,000 - 144,000 = 96,000 Joules.
- The combined velocity is +12.0 m/s, and 96 kJ of kinetic energy is lost to heat and metal deformation.
Answer: Combined Velocity: +12.0 m/s | KE Lost: 96 kJ
A 0.20 kg cue ball moving at +5.0 m/s strikes an identical 0.20 kg target ball elastically off-center. After impact, the cue ball deflects at +30.0° to the original line of motion. Assuming equal masses, find the speed of both balls and target ball deflection angle.
- For two identical masses colliding elastically where one ball is initially at rest, the velocity vectors after collision are perpendicular: theta1 + theta2 = 90°.
- Target ball angle: theta2 = 90° - 30° = -60.0° (measured relative to the X-axis).
- Using trigonometry: v1f = u1 * cos(theta1) = 5.0 * cos(30°) ≈ 4.33 m/s.
- For Ball 2: v2f = u1 * sin(theta1) = 5.0 * sin(30°) = 2.50 m/s.
- The cue ball moves at 4.33 m/s at +30.0°, and the target ball moves at 2.50 m/s at -60.0°.
Answer: Cue Ball: 4.33 m/s (+30.0°) | Target Ball: 2.50 m/s (-60.0°)
Common Misconceptions
- "Momentum is lost in inelastic collisions": False. Momentum is always conserved in any closed, isolated system. It is only kinetic energy that is lost and converted to internal thermal energy.
- "Perfect elastic collisions are common in everyday life": False. Macro-scale objects always lose a small fraction of energy to sound, heat, and internal vibration. Elastic collisions are mostly limited to atomic particles.
- "Heavier cars always feel less impact force": False. If a heavy vehicle has a rigid frame with no crumple zone, the impact time is tiny, resulting in extremely high deceleration forces. Crumpling is key.
Quick Summary
- Momentum is conserved in all isolated collisions: P_initial = P_final.
- Kinetic energy is conserved ONLY in elastic collisions (e = 1.0).
- In completely inelastic collisions (e = 0.0), colliding bodies stick together.
- Crumple zones decrease impact forces by expanding contact duration (t).
- Oblique 2D collisions conserve momentum component vectors independently.
Practice Questions
1. What is a collision, and why can we ignore external forces during a collision event?
A collision is a short-duration interaction between two or more bodies. Because the contact forces (normal impact force) are extremely large and act over a very brief time interval, their impulse is much larger than the impulse of external forces like friction or gravity. Consequently, external forces can be ignored during the actual impact interval.
2. Compare elastic, inelastic, and completely inelastic collisions.
In all three collision types, momentum is conserved. In an elastic collision, kinetic energy is also conserved. In an inelastic collision, some kinetic energy is lost (converted to thermal energy, sound, or work done during deformation). In a completely inelastic collision, the maximum possible kinetic energy is lost and the colliding bodies stick together.
3. Explain how crumple zones in cars utilize impulse physics to protect passengers.
During a crash, the change in momentum (impulse) of the car is determined by its mass and speed. By design, crumple zones deform plastically, which increases the time duration of the collision (t). Since Impulse = Force * time, increasing the contact duration decreases the average impact force acting on the vehicle and its passengers.
4. How is momentum conservation represented mathematically in 2D oblique collisions?
Momentum is a vector quantity, so it must be conserved independently along perpendicular axes. In a 2D collision, the total momentum in the x-direction is conserved: m1*u1x + m2*u2x = m1*v1x + m2*v2x, and the total momentum in the y-direction is conserved: m1*u1y + m2*u2y = m1*v1y + m2*v2y.
FAQ
Frequently Asked Questions
What is a collision in physics?
A collision is an event where two or more bodies exert forces on each other in a relatively short time, resulting in a sudden exchange of momentum and energy.
Is momentum always conserved in every collision?
Yes, in any closed and isolated system, the total momentum remains constant during a collision. External forces like friction are negligible during the brief impact.
Why is kinetic energy lost in inelastic collisions?
The lost kinetic energy is converted into other forms of energy, such as thermal energy (heat), sound energy, and mechanical work done to deform the colliding objects.
What is a perfectly elastic collision?
It is a collision in which there is no net loss of total kinetic energy. The colliding objects bounce off each other with the same total kinetic energy they started with.
What is a completely inelastic collision?
It is a collision in which the colliding objects stick together after impact. This results in the maximum possible loss of total system kinetic energy.
What does the coefficient of restitution (e) represent?
The coefficient of restitution (e) is a number between 0 and 1 that measures elasticity. e = 1.0 is perfectly elastic, e = 0.0 is completely inelastic, and values in between represent realistic partially elastic bounces.
How do crumple zones reduce impact forces?
By buckling during a crash, crumple zones increase the duration of the impact. According to the impulse-momentum theorem, a longer collision time reduces the average force.
Why do identical billiard balls scatter at 90 degrees in elastic collisions?
When a moving ball elastically strikes a stationary ball of the same mass off-center, conservation of momentum and kinetic energy mathematically forces their post-collision velocity vectors to be perpendicular.
Can collisions occur without physical contact?
Yes. In physics, a collision includes electromagnetic or gravitational deflections (like alpha particles scattering off a nucleus, or gravity assists in spaceflight) where objects deflect without physical touch.
How does the simulator show kinetic energy loss?
In the Gliding Air Track mode, a live graph plots the kinetic energy of each cart and the total system. When e < 1.0, the total KE line drops at impact, showing the exact energy lost.
What is an oblique collision?
An oblique collision is one where the collision force does not act along the initial line of motion, causing the colliding objects to deflect at angles in two dimensions (2D).