The impulse-momentum theorem sets an impulse equal to a momentum change. The numbers already matched: 8 N·s made 8 kg·m/s.
Can the newton-second and the kilogram-meter per second really be the same unit? The 8s say they must be.
Unpack the newton first.
A newton is the force that gives 1 kg an acceleration of 1 m/s², so 1 N = 1 kg·m/s².
Now build the newton-second.
1 N·s = 1 (kg·m/s²)·s.
The second you multiplied by cancels one of the two seconds under the line.
1 N·s = 1 kg·m/s.
So the newton-second and the kilogram-meter per second are the same unit, exactly as the theorem requires.
One quantity, one unit, two spellings: N·s when you build it from force and time, kg·m/s when you build it from mass and velocity.
Which unit is the same as the newton-second (N·s)?
Which chain of steps shows that the newton-second is the kilogram-meter per second?
Show that the newton-second is the same unit as the kilogram-meter per second.
Write down the newton in base units:
1 N = 1 kg·m/s²
Multiply by one second:
1 N·s = 1 (kg·m/s²)·s
Cancel one second:
1 N·s = 1 (kg·m/s²)·s = 1 kg·m/s
The newton-second and the kilogram-meter per second are the same unit.
A hammer blow delivers an impulse of 9 N·s to a tent stake. State the stake's momentum change, in either spelling of the unit.
The theorem: the impulse equals the momentum change.
The units agree: 1 N·s = 1 kg·m/s.
So the number carries straight over.
The stake's momentum change is 9 kg·m/s, which is the same as 9 N·s.
A dart receives an impulse of 2.2 N·s. Enter its momentum change in kg·m/s.
Which unit can state a momentum change?
Gunnar writes four unit chains. Which one is correct?
Impulse and momentum change share one unit. The newton-second is one spelling of it. Type the other spelling, built from the mass and velocity units.