Safe policing

Grabbit and Grubbit (Solicitors to the Common Man) Ltd are proposing to take a case to the European Court claiming that the use of rubber bullets is a violation of Human Rights. Their grounds are that, for the same mass and speed, the momentum in a rubber bullet is the same as that in a lead one. Thus they do the same damage on impact and are therefore equally likely to be lethal.

How will you prepare a case for the Government’s defence?

Hide

Hint

The relevant physics is in S4.6
 

Solution

Reveal
Hide

Solution

Assume that both bullets are stopped inside the body. If they have the same initial momentum, the change $\Delta \vec{p}$ will be the same for both and so is the impulse

$$\vec{J} = \Delta \vec{p} = \vec{F}_{ave} \Delta t$$
Clearly Fave is the force exerted on the bullet by the body, but by Newton’s Third Law it is also the force the bullet exerts on the body as it penetrates it. To determine whether the rubber bullet is as lethal as a lead one, you should determine the force exerted by each. What makes the difference during the collision is the fact that a rubber bullet will be deformed much more than a lead bullet, hence the "collision time" Δt is longer for the rubber bullet than it is for the lead bullet. As a consequence, the force exerted by the rubber bullet is less than that exerted by the lead one, implying that the former will be less penetrating, i.e. less lethal.

If this still does not convince you, consider the impact of a car:

  • [a)] on a concrete wall, and
  • [b)] on a stack of tyres.

Experience tells you that the first case is more likely to be fatal for the driver than the second. What matters here is the degree of "inelasticity" of the collision and not whether the car hits the wall or "the wall hits the car". After all the force exerted by the wall on the car is the same as the force exerted by the car on the wall changed in sign.