# 4.5.5 Collisions

### Elastic & Inelastic Collisions

• In both collisions and explosions, momentum is always conserved
• However, kinetic energy might not always be
• A collision (or explosion) is either:
• Elastic – if the kinetic energy is conserved
• Inelastic – if the kinetic energy is not conserved
• Collisions are when objects striking against each other
• Elastic collisions are commonly those where objects colliding do not stick together and then move in opposite directions
• Inelastic collision are commonly those where objects collide and stick together after the collision

Elastic collisions are where two objects move in opposite directions. Inelastic collisions are where two objects stick together

• An explosion is commonly to do with recoil
• For example, a gun recoiling after shooting a bullet or an unstable nucleus emitting an alpha particle and a daughter nucleus
• To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
• The equation for kinetic energy is:

#### Worked Example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B at speed 3.0 m s–1. Trolley B has twice the mass of trolley A.

The trolleys stick together and travel at a velocity of 1.0 m s–1. Determine whether this is an elastic or inelastic collision.

#### Exam Tip

If an object is stationary or at rest, it’s velocity equals 0, therefore, the momentum and kinetic energy are also equal to 0.

When a collision occurs in which two objects are stuck together, treat the final object as a single object with a mass equal to the sum of the two individual objects.

### Momentum Conservation Issues

• The force of an impact in a vehicle collision can be decreased by increasing the contact time over which the collision occurs
• The contact time is the time in which the vehicle or the passenger is in contact with what it has collided with
• Vehicles have safety features such as crumple zones, seat belts and airbags to account for this
• 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 on a passenger

The seat belt, airbag and crumple zones help reduce the risk of injury on a passenger

#### Designing Safety Features

• Vehicle safety features are designed to absorb energy upon an impact by changing shape
• 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
• 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

• The effect of the increase in time and force can be shown on a force-time graph
• For the same change in momentum, which depends on the mass and speed of a vehicle, the increase in contact time will result in a decrease in the maximum force exerted on the vehicle and passenger
• This is demonstrated by a lower peak and wider base on a force-time graph

The increase in contact time Δt decreases the force for the same impulse

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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