Momentum in one direction
Impulse
- If a constant force \(F\) acts for time \(t\) then we define the impulse of the force to be \(Ft\)
Derivation of the Impulse Momentum Principle
-
\[a=\frac{v-u}{t}\]
- Substitute into \(F=ma\): \(\(F=m\left( \frac{v-u}{t} \right)\)\)
- Change to impulse: \(\(Ft=m(v-u)\)\)
- Therefore: \(\(Ft=mv-mu\)\)
- Or Impulse = final momentum - initial momentum
- Impulse = change in momentum
Momentum Questions
- Ball: \(0.5kg\)
Impulse: \(15Ns\)
Impulse = \(mv-mu\)
\(15=0.5v-0\)
\(v=30\)
- Ball: \(0.3kg\)
Speed: \(3.5ms^{-1}\)
Ball rebounds at right angles
Impulse exerted on the ball is \(1.8Ns\)
Find the speed of the ball after it rebounds
\(1.8=(0.3\times v)-(0.3\times3.5)\)
\(0.75=0.3\times v\)
\(v=2.5\)
- Toy car at rest: \(0.2kg\)
Pushed with \(0.4N\) for \(1.5s\)
Find the speed at the end of the \(1.5s\)
\(0.6=0.2v-0\)
\(v=3\)