Rate of Change of Momentum (Oxford AQA IGCSE Physics)

Rate of Change of Momentum

• Newton's second law is defined by the equation:

• Momentum is calculated using the equation:

• Combining these equations gives Newton's second law in terms of momentum:

• Where:

  • F = resultant force measured in newtons (N)

  • ∆p = change in momentum measured in kilogram metres per second (kg m/s)

  • t = time measured in seconds (s)

• Remember to consider the direction of object's motion

  • If you take the initial direction as positive then the reverse direction is negative

• Force is the rate of change of momentum on a body

  • Where the rate of change describes how a variable changes with respect to time

• The shorter the time over which momentum changes then the bigger the force applied

• So, force and time are inversely proportional to each other

Momentum and safety

• 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

  • Contact time is the period of time between the colliding objects first touching and the moment they lose contact or come to rest

Vehicles

• 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, in turn, 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 to a passenger

• The usefulness of safety equipment depends on two main factors: mass and velocity

• If the impact is from a large mass, for example, a truck travelling very fast and colliding with a wall, the momentum will be very large

  • The change in momentum (ie. from a high speed to rest) will also be very large

  • This means that a very long contact time is needed to reduce the force of impact

Safety features on a car

• Seat belts

  • These are designed to stop a passenger from colliding with the interior of a vehicle by keeping them fixed to their seat in an abrupt stop

  • They are 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

  • These are deployed at the front on the dashboard and steering wheel when a collision occurs

  • They act as a soft cushion to prevent injury on the passenger when they are thrown forward upon impact, increasing contact time

• Crumple zones

  • These are designed into the exterior of vehicles

  • They are at the front and back and are designed to crush or crumple in a controlled way in a collision

  • This is why vehicles after a collision look more heavily damaged than expected, even for relatively small collisions

  • The crumple zones increase the time over which the vehicle comes to rest, lowering the impact force on the passengers

Crash mats

• Crash mats used in gymnasiums help reduce the risk of injury for falls in gymnastics and climbing

  • They are thick and soft to offer shock absorption of the force created by the person landing on the mat

• When a person lands on a crash mat with a large force, for example after jumping, the soft landing means their body is in contact with the mat for a longer period of time than if it was otherwise not there

• This increases the contact time over which their momentum is reduced creating a smaller impact force and a lower chance of injury

Climber using a crash mat

• In a similar way, playgrounds utilise cushioned surfaces as children will often fall onto these with a large momentum

  • The cushioned surface reduces the risk of a severe injury by increasing their contact time with the ground

• Meanwhile, a child in a gymnasium can use a thinner crash mat than an adult due to having a lower mass and therefore lower momentum for a given speed

• This is the same for activities where a person/adult will fall with a low velocity such as falling from lower heights

  • Therefore, thin crash mats are suitable for low-impact activities

• Safety features are intended to reduce the chance of serious injury but do not completely prevent it in all cases