Impulse (Cambridge (CIE) IGCSE Physics): Revision Note

Impulse

Extended tier only

• The impulse of a force is the product of the force applied and the time for which it acts

$\mathrm{impulse}=F∆t$

• Where:

  • $F$ = resultant force, measured in newtons (N)

  • $∆t$ = the time for which the force acts, measured in seconds (s)

• Therefore, the units of impulse are newton seconds (N s)

• The impulse of a force acting on an object can change the object's motion

  • For example:

    • Kicking a ball

    • Catching a ball

    • A collision between two objects

• The impulse of the resultant force is equal to the change in momentum of the object

$\mathrm{impulse}=F∆t=∆p$

• Change in momentum (opens in a new tab) can also be described as:

$∆p=∆\left(mv\right)$

$∆p=mv-mu$

• Where:

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

  • $m$ = mass, measured in kilograms (kg)

  • $v$ = final velocity, measured in metres per second (m/s)

  • $u$ = initial velocity, measured in metres per second (m/s)

• Therefore:

$\mathrm{impulse}=F∆t=∆p=mv-mu$

• Since impulse is equal to the change in momentum, kilogram metres per second (kg m/s) is also accepted as the units of impulse

Examples of impulse

• When rain and hail (frozen water droplets) hit an umbrella, they feel very different due to the impulse of the force

• Water droplets tend to splatter and roll off the umbrella, so their velocity is reduced to near zero — a relatively small change in momentum

• Hailstones have a larger mass and tend to bounce back off the umbrella, so their velocity reverses — a greater change in momentum than simply stopping

• Therefore, the impulse that the umbrella applies on the hail stones is greater than the impulse the umbrella applies on the raindrops

• This means that more force is required to hold an umbrella upright in hail compared to rain

The impulse exerted by the umbrella on the hailstones is greater than the impulse exerted on the raindrops

Force & momentum

Extended tier only

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

$F=ma$

• Momentum is given by the equation:

$p=mv$

• Since $a=\frac{∆v}{∆t}$, this can be substituted into Newton's second law:

$F=\frac{m∆v}{∆t}$

• Since $∆p=m∆v$, combining these equations gives Newton's second law in terms of momentum:

$F=\frac{∆p}{∆t}$

• Therefore, the resultant force on an object is defined as the change in momentum per unit time

  • This is also described as the rate of change of momentum

Impulse and safety features

• This result has important implications when it comes to safety

• A large force acting for a short time can have the same impulse and same change in momentum as a smaller force acting for a longer time

• Safety features such as air bags and crumple zones increase the time taken for a driver to stop

  • This would reduce the force on the driver in a collision and the risk of injury, since the change in momentum is fixed