Impulse
Impulse is the product of a force and the time interval over which it acts, and it equals the change in momentum of the object. It is a vector quantity that describes the total effect of a force applied over time rather than instantaneously. Impulse is widely used in collision analysis, sports biomechanics, and safety engineering to understand how forces affect motion.
Key Formula
J = F × Δt = Δp = m × Δv
LaTeX: J = F \cdot \Delta t = \Delta p = m \Delta v
| Symbol | Meaning | Unit |
|---|---|---|
| J | Impulse | Newton-second (N·s) |
| F | Average force | Newton (N) |
| Δt | Time interval | Second (s) |
| Δp | Change in momentum | kg·m/s |
| m | Mass of object | Kilogram (kg) |
| Δv | Change in velocity | Metre per second (m/s) |
Worked Example
Problem
A cricket ball of mass 0.16 kg is bowled at 30 m/s and the batsman hits it back at 40 m/s in the opposite direction. The bat is in contact for 0.002 s. Find the impulse and the average force exerted by the bat.
Solution
Step 1: Define positive direction as the return direction (towards the bowler). Initial velocity u = -30 m/s, Final velocity v = +40 m/s Step 2: Calculate impulse = change in momentum. J = m(v - u) = 0.16 × (40 - (-30)) = 0.16 × 70 = 11.2 N·s Step 3: Calculate average force. F = J / Δt = 11.2 / 0.002 = 5,600 N
Answer
Impulse J = 11.2 N·s; Average force F = 5,600 N
Impulse in Everyday Sporting Contexts
| Sport / Event | Approximate Force (N) | Contact Time (ms) | Impulse (N·s) |
|---|---|---|---|
| Cricket bat on ball | 5,000–6,000 | 1–2 | ~10–12 |
| Football kick | 1,200–2,000 | 8–10 | ~10–16 |
| Tennis serve | 2,500–4,000 | 4–6 | ~10–24 |
| Boxing punch | 1,000–5,000 | 10–50 | ~10–250 |
| Golf driver | 4,000–9,000 | 0.5–1 | ~2–9 |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Momentum
Momentum is the product of an object's mass and its velocity, representing the quantity of motion possessed by the object. It is a vector quantity, meaning it has both magnitude and direction aligned with the velocity. Momentum is fundamental to Newton's second and third laws and is the conserved quantity in isolated systems during collisions and interactions.
Conservation of Momentum
The law of conservation of momentum states that the total momentum of a closed, isolated system remains constant if no external net force acts on it. This means the sum of momenta of all objects before an interaction equals the sum after the interaction. It is one of the most fundamental conservation laws in physics and applies equally to collisions, explosions, and all mechanical interactions.
Elastic Collision
An elastic collision is one in which both the total kinetic energy and the total momentum of the system are conserved before and after the collision. No energy is lost to deformation, heat, or sound, making it an idealized model most closely approximated by atomic and subatomic particle interactions. Billiard ball collisions and gas molecule interactions are common approximations of elastic collisions.
From Latin "impulsus", past participle of "impellere" meaning "to push against" or "to drive forward". The term entered physics in the 17th century through Newtonian mechanics.