3.4.1.5
Newton's second law in terms of momentum: $F = rate of change of momentum$
Newton's Laws & Momentum — AQA A-Level Physics
- Momentum $p = mv. Rate$ of change of $momentum = m(\Delta v / \Delta t) = ma = F$.
- Newton's second lawThe resultant force on an object is equal to its rate of change of momentum. For constant mass, F = ma. can be stated as: the resultant force equals the rate of change of momentum.
- This form is more general because it also handles cases where mass changes (e.g. rockets).
$$F = \frac{\Delta p}{\Delta t}$$
- $F$: resultant force (N)
- $Δp$: change in momentum (kg m s⁻¹)
- $Δt$: time interval (s)
Worked Example
A girl on a skateboard increases speed from 1 m s^-1 to 4 m s^-1 in 2.5 s. The driving force is 72 N. Find the combined mass.
Show Solution
1
Write Newton's second law in momentum form
$$F = \frac{\Delta p}{\Delta t} = \frac{m(v - u)}{\Delta t}$$
2
Substitute and solve for m
$$72 = \frac{m(4 - 1)}{2.5}$$
$$m = \frac{72 \times 2.5}{3} = 60 \text{ kg}$$Answer
Combined $mass = 60 kg$