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A.2.3 Collisions and explosions

Types of Collisions: Elastic, Inelastic, and Perfectly Inelastic

Definition

Collisions

Collisions are interactions where two or more objects exert forces on each other for a short time.

Hint

Momentum is always conserved in collisions, but kinetic energy may or may not be conserved.

Elastic Collisions

Definition

Elastic collision

In an elastic collision, both momentum and kinetic energy are conserved.

Example

Imagine two billiard balls colliding. After the collision, they move apart with the same total kinetic energy they had before.

Mathematically, for two objects with masses m1 and m2 and initial velocities u1 and u2:

  • Momentum conservation: m1u1+m2u2=m1v1+m2v2
  • Kinetic energy conservation: 12m1u12+12m2u22=12m1v12+12m2v22

Inelastic Collisions

Definition

Inelastic collision

In an inelastic collision, momentum is conserved, but kinetic energy is not.

Some kinetic energy is transformed into other forms, such as heat or sound.

Example

When a car crashes into a barrier, the car deforms, and energy is lost as heat and sound.

Perfectly Inelastic Collisions

Definition

Perfectly inelastic collision

In a perfectly inelastic collision, the colliding objects stick together and move as one mass after the collision.

This type of collision results in the maximum possible loss of kinetic energy.

Example

Two clay balls collide and merge into a single mass, moving together with a common velocity.

Dissipation of Energy in Collisions:

Kinetic Energy Dissipation

In inelastic and perfectly inelastic collisions, some kinetic energy is transformed into other forms, such as:

  • Thermal energy: Heat generated by friction or deformation.
  • Sound energy: Noise produced during the collision.
  • Deformation energy: Energy used to permanently deform the objects.

Note

The law of conservation of energy still holds, but kinetic energy is not conserved because it is converted into other forms.

Explosion Dynamics: The Reverse of Inelastic Collisions

  1. An explosion is the opposite of a perfectly inelastic collision.
  2. Instead of objects sticking together, a single object breaks apart into multiple fragments.

Momentum Conservation in Explosions

  1. Just like in collisions, momentum is conserved in explosions.
  2. If the initial momentum of the system is zero (e.g., a stationary object), the total momentum of the fragments after the explosion is also zero.

Example

A firework explodes in mid-air. Before the explosion, its momentum is zero. Afterward, the fragments move in different directions, but their total momentum still sums to zero.

Illustration of the explosion: momentum is conserved.
Illustration of the explosion: momentum is conserved.

Energy in Explosions

  1. In explosions, kinetic energy increases.
  2. This energy comes from stored potential energy (such as chemical energy) that is released during the explosion.

Example

  1. A rocket engine expels gas backward, propelling the rocket forward.
  2. The chemical energy in the fuel is converted into kinetic energy of the rocket and the expelled gas.

Multi-Body Systems: Applying Momentum Conservation

Momentum Conservation in Multi-Body Systems

Definition

The law of conservation of momentum

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.

This principle applies to systems with multiple bodies, such as colliding particles or exploding fragments.

Solving Multi-Body Problems

To solve problems involving multi-body systems, follow these steps:

  1. Identify the system: Determine which objects are part of the system and ensure no external forces act on it.
  2. Calculate initial momentum: Find the total momentum of the system before the interaction.
  3. Apply momentum conservation: Set the initial momentum equal to the total momentum after the interaction.
  4. Solve for unknowns: Use the conservation equation to find unknown velocities or masses.
Example question

Two ice skaters, one with mass 50 kg and the other with mass 70 kg, push off each other. If the 50 kg skater moves at 2 m/s, what is the velocity of the 70 kg skater?

Solution

  1. Initial momentum: 0 (both skaters are initially at rest).
  2. Final momentum: (50,kg×2m/s)+(70kg×v)=0
  3. Solve for v: v=−10070m/s≈−1.43m/s

The negative sign indicates the 70 kg skater moves in the opposite direction.

Tip

Always pay attention to the direction of velocities when applying momentum conservation. Momentum is a vector, so direction matters.

Reflection and Broader Connections

Theory of Knowledge

  • How do the principles of momentum conservation apply to large-scale systems, such as galaxies or ecosystems?
  • Can you think of examples where these concepts intersect with other disciplines, such as biology or economics?

Collisions and explosions are fundamental in physics, illustrating the interplay between momentum and energy.

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Questions

Recap questions

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Question 1

Consider a collision between two objects where they stick together after the collision. Which of the following statements is true about this type of collision?

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Note

Collisions and Explosions

A collision

is an event where two or more objects come into contact and exert forces on each other for a short period of time. During collisions, two fundamental physical quantities are at play:

  • Momentum
    : The product of an object's mass and velocity
  • Kinetic energy
    : The energy an object possesses due to its motion

Definition

Collision

An interaction where two or more objects exert forces on each other for a brief period.

Analogy

Think of a collision like a handshake - a brief interaction where both parties feel a force.

Note

While momentum is always conserved in collisions, kinetic energy may not be.

Example

When a basketball bounces off the floor, both momentum and kinetic energy are involved in the collision.