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.