How do you calculate impulse in a collision?

Impulse in a collision is calculated by multiplying the force by the time over which it acts.

Impulse is a key concept in physics, particularly when analysing collisions. It is defined as the change in momentum of an object when a force is applied over a period of time. Mathematically, impulse (J) can be expressed as the product of the average force (F) and the time duration (Δt) during which the force acts: \( J = F \times \Delta t \).

To understand this better, let's break it down. Momentum (p) is the product of an object's mass (m) and its velocity (v): \( p = m \times v \). When a collision occurs, the velocity of the object changes, leading to a change in momentum. This change in momentum is what we call impulse. According to Newton's second law, the force applied to an object is equal to the rate of change of its momentum. Therefore, the impulse experienced by an object is also equal to the change in its momentum: \( J = \Delta p \).

For example, if a car of mass 1000 kg is initially moving at 10 m/s and comes to a stop in 5 seconds due to a collision, the change in velocity (Δv) is -10 m/s (since it stops). The change in momentum (Δp) is \( 1000 \, \text{kg} \times (-10 \, \text{m/s}) = -10000 \, \text{kg m/s} \). The impulse, therefore, is -10000 kg m/s. If we know the time duration of the collision, we can also find the average force: \( F = \frac{J}{\Delta t} = \frac{-10000 \, \text{kg m/s}}{5 \, \text{s}} = -2000 \, \text{N} \).

In summary, impulse provides a useful way to quantify the effect of a force acting over time, helping us to understand and predict the outcomes of collisions in terms of changes in momentum.