Momentum

Momentum is mass times velocity:

$$p = m\,v$$

It is measured in kilogram metres per second, the same as newton seconds (N s). Momentum is conserved: in a collision, what one body loses the other gains. A force $F$ acting for a time $\Delta t$ changes momentum by the impulse $F\,\Delta t$ (see newton).

Punching

A punch passes momentum from the fist, arm and the body behind them into the target. A heavy bag that starts at rest and moves at speed $v$ just after the hit has received $p = m_{\text{bag}}\,v$. The more of the body’s mass that is moving with the fist at contact, the more it can pass on. That is why coaches care about the hips and the step, not only the arm speed (the kinetic chain).

The time window matters. A slow shove can move a bag a long way with little speed at contact. A punch transfers its momentum in a few hundredths of a second.

In this project

On the heavy targets, the punch’s impact is the bag’s momentum in the first 0.06 s after the fist reaches it: the 35 kg bag’s mass times its top speed in that window. A punch counts as a hit at about 21 N s on the bag (the bag moving at 0.6 m/s), and about 17 N s on the 25 kg ball. The final model’s jab gives the bag 29–33 N s and its cross 20–29 N s. The hooks give 11–15 N s: they connect, but light.