Energy in Motion — Crumple Zones and Momentum
Energy in Moving Objects
Whenever an object moves, it stores energy in its kinetic energy store. The equation is:
$$E_k = \frac{1}{2}mv^2$$
where \(E_k\) is kinetic energy in joules (J), \(m\) is mass in kilograms (kg), and \(v\) is speed in m/s. Notice that speed is squared — doubling speed quadruples kinetic energy, which is why fast driving is so much more dangerous than slow driving.
Kinetic energy is proportional to the square of speed. Double the speed → four times the kinetic energy. This means braking distance also increases with the square of speed — twice as fast means four times the distance to stop with the same braking force.
Gravitational Potential Energy
When an object is raised above the ground, work is done against gravity and energy is stored as gravitational potential energy (GPE):
$$E_{gpe} = mgh$$
where \(m\) is mass in kg, \(g\) is gravitational field strength (approximately 10 N/kg near Earth), and \(h\) is height in metres. When the object falls, GPE transfers to kinetic energy (assuming no friction or air resistance).
A 2 kg ball is dropped from a height of 5 m. Calculate its speed just before it hits the ground. (Ignore air resistance.)
GPE at top = \(mgh = 2 \times 10 \times 5 = 100\) J
By conservation of energy: \(E_k = 100\) J
\(\frac{1}{2}mv^2 = 100 \Rightarrow \frac{1}{2} \times 2 \times v^2 = 100 \Rightarrow v^2 = 100 \Rightarrow v = 10\) m/s
Stopping Distances and Road Safety
When a vehicle needs to stop suddenly, the total stopping distance has two components:
Stopping distance = thinking distance + braking distance
Thinking distance increases linearly with speed (higher speed → more distance covered in the same reaction time). Factors that increase thinking distance: tiredness, alcohol or drugs, distractions. Braking distance increases with the square of speed (because kinetic energy ∝ v²). Factors that increase braking distance: worn tyres or brakes, wet or icy roads, greater vehicle mass or speed.
Large decelerations during sudden braking generate very large forces on vehicle occupants (\(F = ma\), large negative \(a\) → large \(F\)). These forces can cause serious injury — which is why reducing deceleration time is the key principle behind vehicle safety features.
Momentum
Every moving object has momentum. The equation is:
$$p = mv$$
where \(p\) is momentum in kg m/s, \(m\) is mass in kg, and \(v\) is velocity in m/s. Momentum is a vector — its direction is the same as the velocity.
In a closed system (no external forces), the total momentum before a collision equals the total momentum after. This is called the conservation of momentum. For two objects colliding: \(m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2\).
When a vehicle collides, its momentum changes from its speed-before value to zero. This change in momentum is called the impulse:
$$\text{impulse} = F \Delta t = \Delta p$$
A crumple zone is the front or rear section of a car designed to deform (crumple) during a collision. By crumpling, the car takes longer to come to rest — the time over which momentum changes (\(\Delta t\)) increases. Since \(F = \Delta p / \Delta t\), a longer time means a smaller force on the passengers for the same momentum change.
This is the precise chain of reasoning you must reproduce in an exam: crumple zone deforms → collision time increases → same momentum change occurs over a longer time → average force on occupants is reduced → injury risk is lower. Saying crumple zones “absorb force” or “act as a barrier” misses the physics and will not earn full marks.
The same principle applies to airbags (increase contact time between driver and steering wheel), seatbelts (stretch slightly to extend stopping time), cycle helmets and padded sports equipment.
Conservation of Momentum: Worked Example
Consider two trolleys: trolley A (2 kg, moving at 3 m/s) collides with stationary trolley B (1 kg) and they stick together. Total momentum before = 2 x 3 = 6 kg m/s. After: (2 + 1) x v = 6, so v = 2 m/s. Kinetic energy before = 9 J; after = 6 J. The 3 J difference converts to thermal energy and sound, making this an inelastic collision. In a perfectly elastic collision both momentum and kinetic energy are conserved. This course does not use the elastic and inelastic labels, but it does expect you to know that momentum is always conserved.