2.4 Momentum & Vehicle Safety
Momentum is a measure of how difficult it is to stop a moving object. It is a vector quantity.
Momentum = Mass × Velocity
p = m × v
Where:
- p is momentum in kilogram-metres per second (kg m/s)
- m is mass in kilograms (kg)
- v is velocity in metres per second (m/s)
A heavy truck and a light car travelling at the same speed have very different momentums. The truck has much more momentum and is harder to stop.
Conservation of Momentum
In a closed system (where no external forces act), the total momentum before a collision or explosion is equal to the total momentum after.
This is why when a cannon fires a cannonball, the cannon recoils backwards. The forward momentum of the cannonball is equal and opposite to the backward momentum of the cannon, so the total momentum remains zero.
Force and Momentum
Force is also the rate of change of momentum.
Force = (Change in Momentum) / Time
F = (mv - mu) / t
v = final velocity (m/s)
u = initial velocity (m/s)
This equation is the key to all vehicle safety.
Crash Safety Features
In a car crash, your momentum must change from very large to zero in a very short time.
From the equation F = (mv - mu) / t, we know that a large change in momentum (mv-mu) in a small time (t) will create a huge, dangerous force (F) on the passenger.
The goal of all safety features is to increase the time (t) of the impact. By increasing the time, we decrease the force (F), which reduces injury.
- Crumple Zones: The front and back of the car are designed to crumple, increasing the time it takes for the car to stop.
- Seatbelts: They stretch slightly, increasing the time it takes for your body to stop.
- Airbags: They provide a soft cushion and increase the time over which your head slows down.
Stopping Distances
The total distance it takes for a car to stop is made of two parts:
Stopping Distance = Thinking Distance + Braking Distance
- Thinking Distance: The distance the car travels in the time it takes for the driver to react (their "reaction time").
- Braking Distance: The distance the car travels after the brakes have been applied.
Source: Wikimedia Commons
Factors affecting Thinking Distance:
- Vehicle Speed: The faster you go, the further you travel before reacting.
- Driver's Reaction Time: This is slowed down by tiredness, alcohol, drugs, or distractions (like using a phone).
Factors affecting Braking Distance:
- Vehicle Speed: The faster you go, the more kinetic energy you have, which takes more work (and distance) to get rid of.
- Road Conditions: Wet or icy roads reduce friction and increase braking distance.
- Vehicle Condition: Worn-out brakes or tires will not work as well.