← Newton's second law in momentum form, and collision safety

The momentum form is the more general law

A rocket climbs, burning fuel. Every second it throws exhaust out of its nozzle, so every second it has less mass than before.

Which form of Newton's second law can handle an object whose mass keeps changing?

F = ma needs one value for m.

The rocket has no single m to offer: the mass it had at launch is partly gone a minute later.

F = Δp/Δt asks for something different: the momentum change, and the time it took.

Momentum can change because the velocity changes, because the mass changes, or both.

The rate Δp/Δt covers every one of those cases.

So F = Δp/Δt still applies when the mass changes. F = ma does not.

Which form appliesobjectmassF = ma?F = Δp/Δt?delivery vanconstantappliesappliesclimbing rocketchangingdoes not applyapplies
Both forms work for the van. Only the momentum form works for the rocket.

A law that applies in more situations is called more general. F = Δp/Δt is the more general form of Newton's second law.

When the mass is constant, the two forms agree, as you saw in the last lesson.

This course keeps changing-mass cases qualitative: you name the form that applies, and leave the arithmetic alone.

A firefighting helicopter releases its water on a fire, losing mass as it flies. Which form of Newton's second law still applies to the helicopter?

F = Δp/Δt is called the more general form of the second law. Why?

F = Δp/Δt is the more general form of Newton's second law: it still applies when the mass changes.

A rocket burns fuel as it climbs, losing mass. Which form of Newton's second law applies to it?

The rocket's mass, read off the fuel gaugetimemass0 s500 kg30 s476 kg60 s452 kg
No single m to put into F = ma: the mass is a moving target.

The rocket's mass is changing, so F = ma has no single m to use.

F = Δp/Δt needs only the momentum change and the time.

A changing mass still produces a momentum change.

Only F = Δp/Δt applies to the rocket.

rocket's mass (kg)500 kgat launch452 kg60 s later
The same rocket, two masses. F = ma cannot choose; F = Δp/Δt never has to.

A delivery van drives with constant mass. Which forms of the second law apply to it?

The van's mass is constant.

With mass constant, Δp/Δt equals ma.

So both forms apply, and they agree.

Both forms apply to the van, and they make the same prediction.

Wilma says: 'A cart leaks sand as it rolls, so its mass is falling. F = Δp/Δt still applies to it.' Is Wilma correct?

Your turn

For which object does only the momentum form of the second law apply?

Which statement about the two forms of Newton's second law is correct?

A rolling snowball picks up snow, so its mass grows as it moves. For the snowball, only F = Δp/Δt applies. What is the reason?