Impulse–Momentum Principle

m v_{1} + \int_{t_{1}}^{t_{2}} F d t = m v_{2}

Linear impulse of the resultant force equals the change in linear momentum. For a constant force, ∫F dt = F Δt. If the net impulse is zero, momentum is conserved.

$m$ (kg): Mass
$v_{1}, v_{2}$ (m/s): Velocities at 1 and 2
$\int F d t$ (N·s): Linear impulse
$F$ (N): Resultant force

Step-by-step solved example

A 4 kg mass moving at 3 m/s receives a constant 20 N force in the direction of motion for 2 s. Find v2.

Impulse J = ∫F dt changes the momentum vector.

1. Impulse
J = 20 × 2 = 40 N·s.
$J = 40 N\cdots$
2. Momentum balance
4(3) + 40 = 4 v2 → 52 = 4 v2 → v2 = 13 m/s.
$v_{2} = 13 m/s$

Answer: 13 m/s

10 practice questions

0/10 correct

1.Impulse of 50 N lasting 0.4 s is

2.2 kg with Δv = 8 m/s. Magnitude of impulse =

3.Impulse equals

4.5 kg slows from 10 m/s to 4 m/s. Impulse =

5.If ΣF = 0 over an interval, then

6.Average force for J = 100 N·s in 0.05 s is

7.m = 0.25 kg, v1 = 0, J = 10 N·s. v2 =

8.SI units of impulse are

9.A 1500 kg car, 0 to 20 m/s. Impulse =

10.∫ 10t dt from 0 to 2 s (F in N, t in s) equals