Impulse (AQA AS Physics)

• Force can also defined as the rate of change of momentum on a body
• The change in momentum is the final momentum minus the initial momentum
• These can be expressed as follows:

Direction of Forces

• Force and momentum are vector quantities with both magnitude and direction 
• The force that is equal to the rate of change of momentum is still the resultant force
• The positive direction is taken to be the direction of the initial motion; therefore:
  • a force on an object will be negative if the force opposes its initial velocity
  • the opposing force is exerted by the object it has collided with 
  • the forces will be of equal magnitude and opposite in direction, in accordance with Newton's Third Law

The car exerts a force on the wall of  300 N, and due to Newton's third law, the wall exerts a force of -300N on the car 

• When an external resultant force acts on an object for a very short time and changes the object's motion, we call this impulse
  • For example:
    • Kicking a ball
    • Catching a ball
    • A collision between two objects
• Impulse is the product of the force applied and the time for which it acts

• Where:
  • Impulse is measured in newton seconds (N s)
  • = resultant external force applied, measured in newtons (N)
  • = change in time over which the force acts, measured in seconds (s)

• Because the force is acting for only a short time, it is very difficult to directly measure the magnitude of the force or the time for which it acts
• Instead, it can be measured indirectly

• Newtons' second law can be stated in terms of momentum

The resultant force on an object is equal to its rate of change of momentum

• Therefore:

• Where:
  • = resultant force, measured in newtons (N)
  • = change in momentum, measured in kilogram metres per second (kg m s⁻¹) 
  • = change in time over which the force acts, measured in seconds (s)
• Change in momentum is equal to impulse
• Therefore, change in momentum can be used to measure impulse indirectly

• Where:
  • Impulse is measured in newton seconds (N s)
  • = change in momentum, measured in kilogram metres per second (kg m s⁻¹) 
  • = mass, measured in kilograms (kg)
  • = final velocity, measured in meters per second (m s⁻¹) 
  • = initial velocity, measured in meters per second (m s⁻¹) 

• These equations are only used when the force F is constant
• Impulse, like force and momentum, is a vector quantity with both a magnitude and direction
• The impulse is always in the direction of the resultant force

• A small force acting over a long time has the same effect as a large force acting over a short time

Examples of Impulse

• When rain and hail (frozen water droplets) hit an umbrella they feel very different. This is an example of impulse.
  
  • Water droplets tend to splatter and roll off the umbrella because there is only a very small change in momentum
  • Hailstones have a larger mass and tend to bounce back off the umbrella, because there is a greater change in momentum
  • 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 applied by the umbrella to the hail stones is greater than the impulse applied to the rain drops

• The concept of impulse is used to prevent injury
  • Increasing the time over which the change in momentum occurs, reduces the force experienced by the person
• For example, in cricket:
  • A cricket ball travels at very high speeds and therefore has a high momentum
  • When a fielder catches the ball, the ball exerts a force on their hands
  • Stopping a ball with high momentum abruptly will exert a large force on their hands
  • This is because the change in momentum (impulse) acts over a short period of time which creates a large force on the fielder's hands and could cause serious injury
  • A fielder moves their hands back when they catch the ball, which increases the time for the change in momentum to occur
  • This means there will be less force exerted on the fielder's hands and therefore, less chance of injury

A cricket fielder moves their hands backwards when catching a cricket ball to reduce the force it will exert on their hands