In a perfectly elastic collision, is all the energy always conserved?

Yes, in a perfectly elastic collision, the total kinetic energy of the system is conserved alongside the total momentum. This is an idealization. In the real world, some kinetic energy is always converted to other forms, making most collisions somewhat inelastic. The simulator allows you to set this ideal case to see the mathematical consequences clearly.

Why does a small object bouncing off a massive, stationary object seem to reverse direction?

This is a classic result of conservation of momentum and energy. For an elastic collision where a light object hits a much heavier stationary object, the heavy object gains very little velocity. To conserve both momentum and kinetic energy, the light object must rebound with a velocity nearly equal in magnitude but opposite in direction to its initial velocity. You can test this in the simulator by setting one mass to be much larger than the other.

What happens to the 'lost' kinetic energy in an inelastic collision?

The kinetic energy that disappears from the motion of the objects is not destroyed; it is transformed into other forms of energy. In a collision where objects stick together (perfectly inelastic), this energy goes into deforming the objects, generating heat, and producing sound. The total energy of the universe is still conserved, but the simulator's energy graph tracks only the kinetic energy of the center-of-mass motion.

Can momentum be conserved even if the objects are accelerating during the collision?

Yes. Momentum conservation applies to the entire isolated system. During the brief collision event, the objects exert large, equal-and-opposite forces on each other (Newton's third law), causing accelerations. However, these are internal forces. Since no net external force acts on the system during the instant of collision, the total momentum of the system remains constant throughout the process.

1D Collisions

One-dimensional collisions provide a foundational framework for understanding how objects interact through forces over very short time intervals. This simulator models the motion of two objects, often idealized as blocks or carts, moving along a single straight line. It demonstrates the core principles of conservation of momentum and, depending on the collision type, conservation of kinetic energy. The total momentum of the system, defined as the sum of the mass times velocity for each object (p = m₁v₁ + m₂v₂), is always conserved in the absence of external forces, a direct consequence of Newton's third law. For perfectly elastic collisions, kinetic energy (KE = ½m₁v₁² + ½m₂v₂²) is also conserved. The resulting post-collision velocities can be calculated using these conservation laws. Inelastic collisions, where objects stick together, conserve momentum but not kinetic energy; some energy is transformed into other forms like heat or sound. The simulator simplifies reality by assuming a frictionless surface, point-like masses, and instantaneous collisions, allowing students to isolate and explore these fundamental concepts. By adjusting masses, initial velocities, and the coefficient of restitution (which controls elasticity), learners can visualize the immediate outcomes, track momentum and energy bar graphs in real-time, and build intuition for how mass and speed dictate the results of an impact.

Who it's for: High school and introductory college physics students studying momentum, energy, and the dynamics of collisions.

Key terms

Conservation of Momentum
Conservation of Energy
Elastic Collision
Inelastic Collision
Coefficient of Restitution
Kinetic Energy
Velocity
Newton's Third Law

How it works

One-dimensional collision with coefficient of restitution e: relative speed after along the line of centers is −e times the relative speed before. e = 1 elastic, e = 0 perfectly inelastic (sticking). Momentum is conserved if no external impulse.

Key equations

v₁′ = v₁ − (1+e)m₂(v₁−v₂)/(m₁+m₂)

v₂′ = v₂ + (1+e)m₁(v₁−v₂)/(m₁+m₂)

Frequently asked questions

In a perfectly elastic collision, is all the energy always conserved?: Yes, in a perfectly elastic collision, the total kinetic energy of the system is conserved alongside the total momentum. This is an idealization. In the real world, some kinetic energy is always converted to other forms, making most collisions somewhat inelastic. The simulator allows you to set this ideal case to see the mathematical consequences clearly.
Why does a small object bouncing off a massive, stationary object seem to reverse direction?: This is a classic result of conservation of momentum and energy. For an elastic collision where a light object hits a much heavier stationary object, the heavy object gains very little velocity. To conserve both momentum and kinetic energy, the light object must rebound with a velocity nearly equal in magnitude but opposite in direction to its initial velocity. You can test this in the simulator by setting one mass to be much larger than the other.
What happens to the 'lost' kinetic energy in an inelastic collision?: The kinetic energy that disappears from the motion of the objects is not destroyed; it is transformed into other forms of energy. In a collision where objects stick together (perfectly inelastic), this energy goes into deforming the objects, generating heat, and producing sound. The total energy of the universe is still conserved, but the simulator's energy graph tracks only the kinetic energy of the center-of-mass motion.
Can momentum be conserved even if the objects are accelerating during the collision?: Yes. Momentum conservation applies to the entire isolated system. During the brief collision event, the objects exert large, equal-and-opposite forces on each other (Newton's third law), causing accelerations. However, these are internal forces. Since no net external force acts on the system during the instant of collision, the total momentum of the system remains constant throughout the process.

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