Physics in Action: Impulse Revision Notes for Grade 12 NSC Matric Physical Sciences

Physics in Action: Impulse

Understanding impulse in real-world applications

Impulse has many important practical applications, particularly in improving safety and reducing injuries. The key principle is that when an object needs to be brought to rest from a certain initial velocity, there is a specific change in momentum that must occur. If we can increase the time during which this momentum change happens, the force that must be applied will be smaller, causing less damage.

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This principle forms the foundation for many safety devices and techniques we encounter in everyday life: extending the collision time reduces the force experienced.

Safety applications of impulse

Air-bags in motor vehicles

Air-bags work by reducing the effect of force experienced by a person during an accident. They extend the time required to stop the momentum of the driver and passenger during a collision.

When a collision occurs, the motion of the driver and passenger carries them towards the windshield. If they were stopped by hitting the windshield directly, this would result in a large force being exerted over a very short time. Instead, when they hit an air-bag, the time of impact is increased, which decreases the force.

The relationship between force, momentum change and time is given by:

$F = \frac{\Delta p}{\Delta t}$

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Therefore, if time (t) is increased for a constant change in momentum, the force on the body is reduced. This is the fundamental physics principle behind most safety applications.

Padding as protection during sports

The same principle explains why wicket keepers in cricket use padded gloves, and why there are padded mats in gymnastics.

In cricket, when the wicket keeper catches the ball, the padding is slightly compressible. This reduces the effect of the force on the wicket keeper's hands. Similarly, if a gymnast falls, the padding compresses and reduces the effect of the force on the gymnast's body.

Arrestor beds for trucks

An arrestor bed is a patch of ground that is softer than the road. Trucks use these when they need to make an emergency stop.

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When a truck reaches an arrestor bed, the time interval over which the momentum changes is increased. This decreases the force and causes the truck to slow down safely.

Follow-through in sports

In sports where rackets and bats are used (tennis, cricket, squash, badminton, baseball), players are often encouraged to follow through when striking the ball.

High-speed films of collisions between bats/rackets and balls have shown that following through increases the time over which the collision between the racket/bat and ball occurs. This increase in collision time causes an increase in the velocity change of the ball. This means that a player can cause the ball to leave the racket/bat faster by following through, which often increases the chances of success.

Crumple zones in cars

Crumple zones represent another safety application that reduces the force experienced during collisions. When two cars collide, two outcomes are possible:

The cars bounce off each other
The cars crumple together

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Which situation is more dangerous? When cars bounce off each other (rebound), there is a larger change in momentum and therefore a larger impulse. A larger impulse means a greater force is experienced by the occupants.

When cars crumple together, there is a smaller change in momentum and therefore a smaller impulse. This smaller impulse means the occupants experience a smaller force.

Car manufacturers design crumple zones so that cars have a greater chance of crumpling than rebounding in a collision. Additionally, when the car crumples, the change in momentum happens over a longer time, resulting in an even smaller force on the occupants and increasing their chances of survival.

Worked examples

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Worked Example 1: Bullet through target

A bullet of mass 20 g strikes a target at 300 m·s $^{-1}$ and exits at 200 m·s $^{-1}$ . The tip of the bullet takes 0.0001 s to pass through the target.

Calculate the change in momentum:

Initial momentum = $mv_1 = 0.02 \,\mathrm{kg} \times 300 \,\mathrm{m\,s^{-1}} = 6.0 \,\mathrm{kg\,m\,s^{-1}}$
Final momentum = $mv_2 = 0.02 \,\mathrm{kg} \times 200 \,\mathrm{m\,s^{-1}} = 4.0 \,\mathrm{kg\,m\,s^{-1}}$
Change in momentum = $\Delta p = 4.0 - 6.0 = -2.0 \,\mathrm{kg\,m\,s^{-1}}$

Calculate the impulse:
Impulse = $\Delta p = -2.0 \,\mathrm{kg\,m\,s^{-1}}$

Calculate the force:

F = \frac{\Delta p}{\Delta t} = \frac{-2.0 \,\mathrm{kg\,m\,s^{-1}}}{0.0001 \,\mathrm{s}} = -20{,}000 \,\mathrm{N}

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Worked Example 2: Ball striking wall

A ball with mass 200 g strikes a wall at right angles at 12 m·s $^{-1}$ and rebounds at 9 m·s $^{-1}$ .

Calculate the change in momentum:
Taking the initial direction as positive:

Initial momentum = $0.2 \,\mathrm{kg} \times 12 \,\mathrm{m\,s^{-1}} = 2.4 \,\mathrm{kg\,m\,s^{-1}}$
Final momentum = $0.2 \,\mathrm{kg} \times (-9) \,\mathrm{m\,s^{-1}} = -1.8 \,\mathrm{kg\,m\,s^{-1}}$
Change in momentum = $-1.8 - 2.4 = -4.2 \,\mathrm{kg\,m\,s^{-1}}$

Calculate impulse of wall on ball:
Impulse = $\Delta p = -4.2 \,\mathrm{kg\,m\,s^{-1}}$

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Worked Example 3: Collision duration

If the collision in Example 2 takes 0.02 s, calculate the magnitude of force exerted by the wall on the ball:

F = \left|\frac{\Delta p}{\Delta t}\right| = \left|\frac{-4.2 \,\mathrm{kg\,m\,s^{-1}}}{0.02 \,\mathrm{s}}\right| = 210 \,\mathrm{N}

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Key Points to Remember:

Impulse applications work by extending collision time - the longer the collision takes, the smaller the force for the same momentum change
$F = \frac{\Delta p}{\Delta t}$ - this relationship shows that increasing time decreases force
Safety devices like air-bags, padding, and crumple zones all increase collision time to reduce the forces experienced
Follow-through in sports increases collision time to give the ball higher velocity
Crumpling is safer than bouncing in car collisions because it produces smaller momentum changes and longer collision times

Physics in Action: Impulse (Grade 12 NSC Matric Physical Sciences): Revision Notes