Momentum Edexcel IGCSE Physics Vocabulary Flashcards

Momentum Edexcel IGCSE Physics

Momentum

  • Momentum is a property of all moving objects.
  • An object with mass m moving at a velocity v has a momentum p.

Momentum Equation

  • Momentum is the product of an object's mass and velocity.
  • p = mv
    • p = momentum in kilogram meter per second (kg m/s)
    • m = mass in kilograms (kg)
    • v = velocity in meters per second (m/s)
  • An object at rest (v = 0) has no momentum.
  • Momentum keeps an object moving in the same direction.
  • It is difficult to change the direction of an object with large momentum.
  • Velocity is a vector with both magnitude and direction.
  • Momentum depends on the direction of travel and can be positive or negative.
  • Positive direction is usually to the right, and negative to the left.

Change in Momentum

  • The momentum of an object will change if:
    • Its velocity increases or decreases (acceleration).
    • Its direction changes (acceleration).
    • Its mass changes.

Example

  • A tennis ball and a brick can have the same momentum if the ball is traveling much faster than the brick, even if the brick has much higher mass.

Conservation of Momentum

Principle

  • The total momentum before an interaction is equal to the total momentum after an interaction if no external forces are acting on the objects.
  • Interaction can be:
    • A collision (two objects collide).
    • An explosion (a stationary object explodes into two or more parts).

Collisions

  • For a collision between two objects:
    • Total momentum before a collision = total momentum after a collision
  • If the right is taken as the positive direction, the total momentum of the system is m \times u
  • After the collision, mass M also has momentum. The velocity of m is now -v (since it's traveling to the left), and the velocity of M is V.
  • The total momentum is now the momentum of M + the momentum of m:
    • (M \times V) + (m \times -v) or (M \times V) – (m \times v)
  • Momentum is always conserved over time.
  • A system of objects moving in opposite directions at the same speed will have an overall momentum of 0 since they will cancel out.

Example (Car and Van Collision)

  • Car mass = 990 kg, initial velocity = 10 m/s, final velocity = 2 m/s
  • Van mass = 4200 kg, initial velocity = 0 m/s
  • Initial momentum of car: p_{car} = 990 \times 10 = 9900 kg m/s
  • Initial momentum of van: p_{van} = 0
  • Total momentum before collision: p_{before} = 9900 + 0 = 9900 kg m/s
  • Final momentum of car: p_{car} = 990 \times 2 = 1980 kg m/s
  • Final momentum of van: p_{van} = 4200 \times v
  • Total momentum after collision: p_{after} = 1980 + 4200v
  • Conservation of momentum equation: 9900 = 1980 + 4200v
  • v = \frac{9900 - 1980}{4200} = 1.9 m/s

Forces & Momentum

Rate of Change in Momentum

  • When a force acts on an object that is moving, the object will accelerate (or decelerate).
  • This causes a change in momentum.
  • F = ma
  • p = mv
  • \Delta p = mv - mu
  • force = \frac{change \ in \ momentum}{time}
  • F = \frac{(mv - mu)}{t}
    • F = resultant force, measured in newtons (N)
    • a = acceleration, measured in meters per second squared (m/s²)
    • m = mass, measured in kilograms (kg)
    • \Delta p = change in momentum, measured in kilogram meters per second (kg m/s)
    • v = final velocity, measured in meters per second (m/s)
    • u = initial velocity, measured in meters per second (m/s)
    • t = time, measured in seconds (s)

Direction

  • Consider the direction of the object's motion.
  • If the initial direction is positive, the reverse direction is negative.
  • Force can also be described as the rate of change of momentum on a body.
  • The shorter the time over which momentum changes, the bigger the force.
  • Force and time are inversely proportional to each other.

Example (Tennis Ball)

  • Change in momentum each time, \Delta p = 0.5 kg m/s
  • Contact time of first hit, t_1 = 2.0 s
  • Contact time of second hit, t_2 = 0.1 s
  • F1 = \frac{\Delta p}{t1} = \frac{0.5}{2} = 0.25 N
  • F2 = \frac{\Delta p}{t2} = \frac{0.5}{0.1} = 5.0 N
  • The tennis racket experiences the greatest force from the ball during the second hit.

Example (Car hitting a wall)

  • Mass of car, m = 1500 kg
  • Initial velocity before collision, u = 15 m/s
  • Final velocity after collision, v = -5 m/s
  • Time of impact, t = 3 s
  • F = \frac{(1500 \times -5) - (1500 \times 15)}{3} = \frac{-7500 - 22500}{3} = \frac{-30000}{3} = -10000 N
  • The direction of the force is to the left (opposite to the car's initial motion).

Newton's Third Law

Definition

  • Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

Examples

  • Walking: The foot pushes the ground backward, and the ground pushes the foot forward.
  • Recognizing Newton's third law:
    • The two forces act on different objects.
    • The two forces are equal in size but act in opposite directions.
    • The two forces are always the same type (weight, reaction force, etc.).

Example (Textbook on a table)

  • The gravitational pull of the Earth acts downwards on the book (weight), and the push force of the table acts upwards on the book (normal contact force).
  • These forces are NOT a Newton's third law pair because both forces are acting on the same object.
  • A correct example:
    • The gravitational pull of the Earth on the book (weight) and the gravitational pull of the book on the Earth (weight).

Collisions

  • When two objects collide, both objects will react, generally causing one object to speed up (gain momentum) and the other object to slow down (lose momentum).
  • Consider the collision between two trolleys, A and B:
    • When trolley A exerts a force on trolley B, trolley B will exert an equal force on trolley A in the opposite direction.
    • F{B-A} = -F{A-B}
    • While the forces are equal in magnitude and opposite in direction, the accelerations of the objects are not necessarily equal in magnitude.
    • From F = ma, acceleration depends upon both force and mass.
    • For objects of equal mass, they will have equal accelerations.
    • For objects of unequal mass, they will have unequal accelerations.

Momentum & Safety Features

Impact Force Reduction

  • Since force is equal to the rate of change in momentum, the force of an impact in a vehicle collision can be decreased by increasing the contact time over which the collision occurs.
  • Safety features are created to reduce the impact of a force, such as in:
    • Vehicles
    • Playgrounds
    • Bicycle helmets
    • Gymnasium crash mats

Vehicle Safety Features

  • Vehicle safety features are designed to absorb energy upon an impact by changing shape.
  • The main vehicle safety features are crumple zones, seat belts, and airbags.
  • For a given force upon impact, these absorb the energy from the impact and increase the time over which the force takes place.
  • This increases the time taken for the change in momentum of the passenger and the vehicle to come to rest.
  • The increased time reduces the force and risk of injury on a passenger.
  • The usefulness of safety features depends on two main factors: mass and velocity.
  • If the impact is from a large mass, the change in momentum will be very large, meaning a very long contact time is needed to reduce the force of impact.

Specific Safety Features

  • Seat belts:
    • Designed to stop a passenger from colliding with the interior of a vehicle by keeping them fixed to their seat in an abrupt stop.
    • Designed to stretch slightly to increase the time for the passenger’s momentum to reach zero and reduce the force on them in a collision.
  • Airbags:
    • Deployed at the front on the dashboard and steering wheel when a collision occurs.
    • Act as a soft cushion to prevent injury on the passenger when they are thrown forward upon impact.
  • Crumple zones:
    • Designed into the exterior of vehicles (front and back).
    • Designed to crush or crumple in a controlled way in a collision.
    • Increase the time over which the vehicle comes to rest, lowering the impact force on the passengers.

Other Safety Features

  • Crash mats (gymnasiums):
    • Help reduce the risk of injury for falls in gymnastics and climbing.
    • Thick and soft to offer shock absorption of the force created by the person landing on the mat.
    • Increase the contact time over which their momentum is reduced, creating a smaller impact force and a lower chance of injury.
  • Playgrounds:
    • Utilize cushioned surfaces as children will often fall onto these with a large force.
    • The cushioned surface reduces the risk of a severe injury by increasing their contact time with the ground.
  • Thin crash mats are suitable for low-impact activities (low velocity falls).
  • Safety features are intended to reduce the chance of serious injury but do not completely prevent it in all cases.