Momentum and Collisions

Momentum is the quantity that explains why things are hard to stop, and it is the one conservation law in this subtest besides energy.

Momentum

Momentum = mass x velocity.

It has a direction, because velocity does. Two objects of equal mass moving toward each other at the same speed have equal and opposite momentum, which sums to zero.

A 2,000 kg vehicle at 15 meters per second.

2,000 times 15 is 30,000 kg m/s.

Both factors count equally. A 4,000 kg truck at 10 m/s and a 2,000 kg car at 20 m/s have the same momentum, 40,000 kg m/s, and are equally hard to stop.

A heavier object at the same speed has more momentum, which is the everyday statement and the one questions usually ask: a loaded truck takes longer to stop than an empty one at the same speed.

Conservation

In any collision, the total momentum before equals the total momentum after.

That holds whether the objects bounce apart, stick together, or shatter. It is the most reliable thing in the topic, and a question about what happens after a collision is nearly always answered by applying it.

A 4 kg cart moving at 3 m/s strikes a stationary 2 kg cart and they couple together. How fast do they move afterward?

Momentum before: 4 times 3 is 12, plus 2 times 0 is 0, giving 12.

Momentum after: the combined mass is 6 kg, so 12 divided by 6 is 2 m/s.

They move slower than the first cart did, because the same momentum is now carried by more mass. That is the general result for this kind of collision and it is a useful check.

A collision between objects moving toward each other subtracts, because the momenta oppose. A 5 kg object at 4 m/s meeting a 3 kg object at 4 m/s the other way gives 20 minus 12, which is 8 in the first object's direction.

Impulse: force over time

Changing momentum takes a force applied for a time, and the product of those two is the change.

So the same momentum change can come from a large force briefly or a small force for longer.

The same principle is behind:

• Crumple zones, which extend the stopping time of a crash so the peak force on the occupants is lower.
• Airbags, for the same reason.
• Helmet padding, boxing gloves, landing mats, and packaging.
• Bending your knees when landing, which lengthens the stop.

None of these reduce the momentum that has to be removed. They spread the removal over more time, which reduces the force.

A question asking how a safety feature works wants "increases the time, reducing the force", and it is asked often.

Collision types

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Real collisions between vehicles are inelastic, which is why they crumple and why the energy goes into the wreckage. Momentum is still conserved, which is what lets it be calculated.

What you can skip

Across the 15 questions on this topic in our bank:

• Collision type labels. Elastic and inelastic are not asked by name here; the questions ask what happens to momentum.
• Impulse arithmetic comes up twice, in pound-seconds. Impulse is force times time, and that is the calculation.

Where people lose points

Ignoring direction. Opposing momenta subtract.

Saying momentum is not conserved when objects stick together. It is; kinetic energy is not.

Thinking a safety device reduces the momentum. It extends the time.

Confusing momentum with kinetic energy. Different formulas, different behavior.

Forgetting that a light fast object can match a heavy slow one.

Work one in under a minute

Why does a crumple zone reduce injury in a crash?

The vehicle's momentum has to be removed either way, and removing it takes force applied over time.

A crumple zone extends the time the stop takes, by collapsing progressively rather than stopping dead.

Spreading the same momentum change over more time means less force, and it is force that injures.

The momentum removed is identical in both cases. Only the time changed, and therefore the peak force.

Where this leads

Momentum is the second conserved quantity in the subtest, alongside energy, and the impulse idea is behind every piece of safety equipment.