When we think about collisions, we often imagine a chaotic mess where anything can happen. But surprisingly, there’s a magical simplicity hidden beneath this complexity. If you have just two objects colliding in one direction, there’s only one possible outcome!
In a one-dimensional collision, each object could potentially move in any direction after the impact, meaning there are two unknown variables: their velocities. However, two key principles help us solve this mystery: the conservation of momentum and the conservation of energy. These principles provide us with two equations that these variables must satisfy. In our universe, two independent equations for two unknowns will uniquely determine the outcome. So, for any combination of masses and initial velocities, there’s only one possible result of a 1D collision.
For example, if two identical objects collide at the same speed, they simply bounce off each other. If one object is stationary, it stops, and the other starts moving. If one object is much larger and stationary, the smaller one bounces back with 90% of its speed, while the larger one starts moving at 10% of the speed.
Sometimes, not all energy remains as kinetic energy; some might turn into heat, sound, or rotational energy. In such cases, the conservation of energy equation might seem invalid. However, by accounting for the lost energy, the equation becomes valid again. Thus, there are still two equations and two unknowns, leading to a single possible outcome for the velocities of the objects involved.
What about collisions in two or three dimensions? Surprisingly, they often behave like one-dimensional collisions! Most of the time, the net force between colliding objects acts in one direction, typically perpendicular to the collision surface. This means that the motion in directions perpendicular to this force remains unaffected. So, even in 2D or 3D, once you find the right direction, the collision behaves like a 1D collision in that direction, and the objects pass by each other in the other direction, unaffected.
The magic of collisions lies in their simplicity. Despite appearing complicated and random, they are not. The combination of conservation of momentum, conservation of energy, and the fact that most collisions are secretly one-dimensional means that the outcome of almost any collision is completely determined. This is true as long as you know the incoming masses, velocities, the amount of kinetic energy lost, and the secret direction of the collision.
Even large and complex collisions, which are made up of many two-object collisions, are completely determined. This is why computers can easily simulate numerous collisions.
If you’re curious about the physics of collisions, you might also be interested in Brilliant, a fun and interactive science and math learning platform. Brilliant offers courses ranging from logic to computer science fundamentals to quantum mechanics. To explore more, visit Brilliant.org/MinutePhysics. The first 200 people will get 20% off an annual Premium subscription with full access to all courses and puzzles. Thanks to Brilliant for their support!
Use an online physics simulator to explore one-dimensional collisions. Adjust the masses and initial velocities of two objects and observe the outcomes. Take note of how the conservation of momentum and energy principles apply. Reflect on how these principles predict the final velocities.
Conduct a simple experiment using a ball and a ramp. Measure the ball’s speed before and after it collides with a wall. Calculate the kinetic energy before and after the collision to determine how much energy is lost to sound, heat, or deformation. Discuss how this relates to the concept of energy conservation in collisions.
Work in pairs to solve a series of momentum conservation problems. Each problem should involve different masses and initial velocities. Use the conservation of momentum equation to predict the outcomes of these theoretical collisions. Compare your predictions with the actual outcomes from a simulation tool.
Create a simple setup using marbles and a flat surface to explore two-dimensional collisions. Observe how the marbles move after colliding at different angles. Discuss how the net force direction affects the motion and how it relates to the concept of one-dimensional behavior in multi-dimensional collisions.
Research and present a real-world application of collision physics, such as car crash safety features or sports equipment design. Explain how understanding the principles of momentum and energy conservation helps in designing safer and more efficient systems.
Collisions – Collisions refer to events where two or more bodies exert forces on each other for a relatively short time, often resulting in a change of motion. – When studying car crashes, physicists analyze the collisions to understand the forces involved and the resulting damage.
Momentum – Momentum is the quantity of motion an object has, which is dependent on its mass and velocity. – In a closed system, the total momentum before and after a collision remains constant, illustrating the principle of conservation of momentum.
Energy – Energy is the capacity to do work or produce change, existing in various forms such as kinetic, potential, thermal, and more. – The energy released during a chemical reaction can be harnessed to power engines or generate electricity.
Velocities – Velocities are vector quantities that describe the speed and direction of an object’s motion. – The velocities of the planets in our solar system vary as they orbit the sun, influenced by gravitational forces.
Kinetic – Kinetic refers to the energy an object possesses due to its motion. – As a roller coaster descends from the peak, its potential energy is converted into kinetic energy, increasing its speed.
Dimensions – Dimensions are measurable extents of an object or space, such as length, width, height, or time. – In physics, understanding the dimensions of a system is crucial for accurately describing its properties and behavior.
Objects – Objects are entities that have mass and occupy space, which can interact with forces and energy. – In classical mechanics, the motion of objects is analyzed using Newton’s laws of motion.
Direction – Direction is the line or course along which something moves or points, often described in terms of angles or coordinates. – The direction of a magnetic field can be determined using the right-hand rule in electromagnetism.
Conservation – Conservation refers to the principle that certain properties of a closed system remain constant over time. – The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
Outcomes – Outcomes are the results or consequences of a particular process or event, often used in the context of experiments or predictions. – By analyzing the outcomes of a physics experiment, scientists can validate or refine theoretical models.
