Define resultant force as the change in momentum per unit time; recall and use the equation F = Δp / Δt

1.6 Momentum – Resultant Force

Resultant force is the net push or pull that changes an object's momentum.

It is defined mathematically as the change in momentum per unit time:

\$F = \frac{\Delta p}{\Delta t}\$

where \$p = mv\$ is momentum, \$m\$ is mass, and \$v\$ is velocity.

Why Momentum Matters

• Momentum tells us how “heavy” a moving object feels.
• It helps predict the outcome of collisions.
• It’s the bridge between force and motion.

Analogy: The Shopping Cart 🚗

Imagine pushing a shopping cart.

- The heavier the cart (larger \$m\$), the more force you need to change its speed.

- If you push harder (larger \$F\$), the cart’s speed changes faster (larger \$\Delta v\$).

- The time you spend pushing (\$\Delta t\$) determines how quickly the cart accelerates.

Key Equation in Detail

Step‑by‑Step Example

1. Car mass \$m = 1500\,\text{kg}\$, initial speed \$v_i = 20\,\text{m/s}\$.
2. After braking, final speed \$v_f = 10\,\text{m/s}\$.
3. Change in momentum:

   \$\Delta p = m(vf - vi) = 1500(10-20) = -15000\,\text{kg·m/s}\$

4. Braking lasts \$\Delta t = 5\,\text{s}\$.
5. Resultant force:

   \$F = \frac{\Delta p}{\Delta t} = \frac{-15000}{5} = -3000\,\text{N}\$

   (negative sign shows force opposes motion).

Exam Tip Box 📌

- Always check units: \$F\$ in newtons, \$p\$ in kg·m/s, \$t\$ in seconds.

- Remember \$\Delta p = m(vf - vi)\$; if \$vf < vi\$, \$\Delta p\$ is negative.

- For quick calculations, use the average force if the change is linear.

- In multiple‑choice, look for the correct sign of the force (positive vs. negative).

- Practice converting between \$F\$, \$\Delta p\$, and \$\Delta t\$ to build confidence.