Momentum

Definition and Properties

Momentum is a measure of an object's inertia in motion. It is a vector quantity, meaning it has both magnitude and direction. The momentum of an object depends on its mass and velocity.

• Formula:

• p: momentum (unit: kg·m/s)

• m: mass (unit: kg)

• v: velocity (unit: m/s)

• Objects at rest have zero momentum.

• Doubling the mass or velocity doubles the momentum.

Example: A 2 kg ball moving at 3 m/s has momentum .

Impulse

Definition and Relationship to Momentum

Impulse is the product of the force applied to an object and the time interval over which it acts. Impulse causes a change in an object's momentum.

• Formula:

• J: impulse (unit: N·s or kg·m/s)

• F: force (unit: N)

• t: time interval (unit: s)

• Impulse-Momentum Theorem:

• Therefore,

• A greater impulse produces a greater change in momentum.

Example: If a 10 N force acts for 2 s, .

Increasing the Time of Impact

Reducing Force in Collisions

For a given change in momentum, increasing the time over which the force acts reduces the average force experienced by the object.

• Key Principle:

• Applications include airbags, seatbelts, catching a ball by moving hands backward, bending knees when landing, and landing on soft surfaces.

• The longer the stopping time, the smaller the average force.

Example: Landing on a haystack takes more time to stop than hitting concrete, so the force is less.

Bouncing

Impulse in Rebound Situations

When an object bounces, the impulse delivered is generally greater than when it simply comes to rest. This is because the object's momentum changes direction, resulting in a larger overall change in momentum.

• Catching an object: momentum goes to zero.

• Catching and throwing back: momentum goes to zero, then to the opposite direction (double impulse).

Example: Catching a ball and throwing it back requires more force than just stopping it.

Conservation of Momentum

Law and Applications

The Law of Conservation of Momentum states that if no external force acts on a system, the total momentum of the system remains constant.

• Formula:

• Total momentum before an event equals total momentum after the event.

• Applies to all types of collisions and explosions in isolated systems.

Example: When a cannon fires a cannonball, the cannon recoils backward with equal and opposite momentum to the cannonball's forward momentum.

Collisions

Types and Characteristics

Collisions are classified based on how objects interact and whether kinetic energy is conserved.

• Elastic Collision:

  • Objects rebound without lasting deformation.

  • No heat is generated.

  • Mechanical energy is conserved.

• Inelastic Collision:

  • Objects deform and/or generate heat.

  • Some mechanical energy is lost.

• Totally Inelastic Collision:

  • Objects stick together after collision.

  • They move with the same velocity afterward.

Example: Two identical freight cars, one moving and one stationary, collide and stick together. The final velocity is half the original velocity of the moving car.

Momentum Vectors

Vector Nature of Momentum

Momentum is a vector quantity, so direction matters. When objects move in different directions, their momenta must be combined using vector addition.

• Draw momentum vectors for each object.

• Use vector addition to find the resultant momentum.

Example: If one car moves right and another moves upward, the combined momentum points diagonally up and right.

Summary Table: Key Concepts in Momentum