from Insultingly Stupid Movie Physics
The following is a segment from one of my favorite web sites: Insultingly Stupid Movie Physics.
The Attractive Force of Glass
Our hero stands innocently on the sidewalk as a sinister car approaches with a shotgun protruding from the window. Suddenly he sees it, but—blam— it's too late. He's blown violently off his feet and flies several feet backward through the nearest display window. Fortunately, he's wearing his bulletproof vest and survives.
If he were not on the sidewalk by a display window, then invariably he'd be blown into a rack of whisky bottles, a giant mirror, or some other large glass object. This happens so often that if we didn't know better we'd think Hollywood had discovered a new principle of physics: the attractive force of glass for shooting victims.
Hollywood apologists would explain that the hero was blown backwards by the force of the shotgun blast, and glass objects are in the way 98% of the time due entirely to random chance. Unfortunately the current laws of physics don't agree.
A load of buckshot hitting a vest can be considered an inelastic collision. This means that the kinetic energy of the victim with the buckshot stuck on his vest is less than the original kinetic energy of the buckshot before the collision. The "lost" kinetic energy is not really lost, it has just changed forms. Some of it becomes a shock wave in the victim that creates bruises and possibly cracked ribs. Some is converted to heat.
Even though kinetic energy is "lost" during the collision, momentum is not. The momentum of the victim is the same as the original momentum of the buckshot. So, the collision can be analyzed using conservation of momentum. This will let us estimate the backwards velocity of the shooting victim and judge whether he would indeed be thrown violently backwards.
To make the analysis we have to decide on some simplifying assumptions. As a rule of thumb, physicists and engineers (who should be considered applied physicists) generally start with the simplest reasonable calculation or model when analyzing whether an event will occur. They will also attempt to make assumptions which favor the event's occurrence. The reasoning is that if a simple model with favorable assumptions shows there could be no effect then there's no point in making a more rigorous model.
We'll make a simplifying assumption that there is no friction to impede the backward motion of the victim. This would favor the event's occurrence.
To calculate the momentum of an object we use the following equation:
p = mv
Where p is momentum, m is mass, and v is velocity.
Before the buckshot collides with the victim, the victim's momentum is zero, since he is not moving. This means that we only have to consider the momentum of the buckshot. For simplicity we will treat the buckshot as though it is a single object rather than calculating individual momentums for each pellet and adding them together. Both of these methods give the same result.
After the collision the victim and buckshot stick together and so, again, we only have to calculate the momentum of their combined mass. We'll use a subscript of 1 to indicate conditions before the collision and a subscript of 2 to indicate conditions after the collision. Hence:
p2 = p1
By substitution:
m2v2 = m1v1
Solving for the velocity of the victim after the collision gives:
v2 = (m1/m2)v1
Note that the velocity of the victim is proportional to the buckshot's mass to victim's mass ratio. This ratio is going to be tiny. Using the following values: the mass of the man with buckshot stuck to his vest equals 80 kg and the mass of the buckshot alone equals 0.0318 kg with a velocity of 486 m/s, we obtain:
v2 = (0.0318 kg)/(80 kg)(486 m/s)
= 0.193 m/s
This is about 0.4 miles per hour. Keep in mind that humans can walk about 4 miles per hour. Since our model was set up with favorable assumptions, we have to conclude that shooting victims aren't going to be blown backwards through display windows by the force of a shotgun blast.
There's yet another way to view the problem. Conservation of momentum works for shooters as well as victims. In other words, recoil from firing a weapon will give a shooter backward momentum equal to the forward momentum of the bullet and hot gasses from burning gun powder exiting the gun barrel. (Note: buckshot will also include a light weight, fibrous wad placed between the powder and buckshot.) When the bullet strikes the victim he'll end up with only the momentum the bullet had immediately before striking. The magnitude of the victim's backwards momentum will be less than the magnitude of the shooter's backward momentum because the victim will not be hit by the firearm's hot gasses. Also, thanks to air resistance, the bullet will be moving more slowly and have less momentum than when it first exited the gun barrel. If the recoil from discharging a firearm is insufficient to throw the shooter backwards through the nearest window then the bullet also will not throw the victim backwards through the nearest window.
There is one other possible mechanism for being blown through a window: involuntary muscle contraction. The victim could be so stunned by being shot that he involuntarily jumps backwards. Since we haven't run this experiment, and have no desire to do so, we can't totally rule it out, but it does seem unlikely.