“Oh crap!!!” is the first thought that runs through your head as you lay on the field/ice/court in excruciating pain immediately following a sports injury.  Whether it is an ankle sprain in soccer, a dislocated shoulder in football, or a broken wrist in basketball, sports-related injuries are painful and frustrating, but unfortunately, inevitable.

The second thought that runs through the injured athlete’s head is, “I wish I could take the last moment back.”  It is an appropriate thought to have, as whenever a collision occurs, the severity of the injury is dependent on just how short the duration of the collision was.  Although impacts in sport between two athletes appear instantaneous, there is actually a small amount of time over which they take place, which we will refer to as dt. 

The extent of the deformation of the athlete’s bone or joint depends on the force imparted during the collision.  If the magnitude of this force is constant throughout the collision, then the total force, F, may be calculated as F = I/dt, where I is the impulse of the collision.  Impulse is the total change in momentum by the bodies involved in the collision.  If a hockey player skates directly into the boards, his change in momentum is his mass multiplied by his speed just before impact.  However, dt depends on the stiffness of the boards.

If the boards were made of concrete, the roster of a hockey team would deplete very quickly, because the dt during impact would be near zero, and the force imparted when crashing into them would be very high.  High-intensity sports lead to high-impulse collisions because the athletes move at high speeds.  Since high-impulse collisions are unavoidable, it is essential that the duration of these collisions be maximized.  The actual hockey boards have ‘give’, and the collision lasts for say one hundredth of a second instead of one thousandth of a second.  The force at the point of collision is then ten times less, and the deformation of the player is as well.

Another example of minimizing the force of impact is when a skier lands a jump.  If the skier does not bend her knees, the impulse will be transferred all at once, and the imparted force through the knee joint will be a maximum value.  By bending her knees, dt is larger, the impulse is ‘absorbed’ gradually, and the lower magnitude force does no harm.  Injury averted.

Once the force applied to an athlete is minimized, it is hopefully distributed over a large area on the athlete.  This is the function of padding.  The extent of the injury is dependent on the pressure transmitted, and p = F/A, where p is pressure and A is area.  The reason a knife is so dangerous is because it cuts even when the force is small, as the area is so tiny.

Most sports injuries occur at joints.  There are two kinds of loads that pass through a joint: forces, which are linear in nature, and torques, which are angular in nature.  It is in fact the torque that is usually responsible for causing damage to a joint.  The torque in the joint is the result of some force being applied some distance away from it.  When an ankle twists the wrong way under an athlete’s own weight, the bending torque is the product of the upwards (reaction) force of the surface and the small distance from the sole of the foot to the joint itself.  A large torque occurs when a large angular impulse is transmitted swiftly.  Again, whether the cause of injury is linear (force) or angular (torque), the level of devastation of the injury is dependent on how quickly it occurs.

I suppose the key to averting sports injuries is to not compete.  I sprained my ankle last week playing soccer, and, I won’t lie: the thought of hanging up my cleats for good did cross my mind as I repeatedly rested, iced, compressed and elevated my injured joint.  Some years ago, a doctor suggested to me that I take up swimming instead of soccer because it is safer.  That may be true, but swimming is also as boring as sin.

I am not willing to give up high-intensity sports, as the benefits outweigh the potential consequences.  If you use the right padding, you minimize the likelihood of injuries occurring.  Still, there are additional measures that can and should be taken for an injury-prone athlete such as myself.  Sports braces for ankles and knees reduce the likelihood of sustaining an injury, and as an engineer, I can appreciate why that is.

When designing a structure, some analysis for an anticipated worst-case environment allows the designer to predict what the maximum force and torque across a given section of the design will be.  If the anticipated load is greater than what a given joint is able to sustain, then the joint must be reinforced to avoid a failure.  A smart way to reinforce a given joint is to give the load a stiffer path to follow.  Stiff braces do this very thing when the joints they are protecting begin to deform.

When I do return to soccer, some weeks from now, I will be sporting an ankle brace.  As a result, the allowable loads for my ankle joint will be higher, and, hopefully, it will not sustain a failure in the near future.  While injuries leave me with much time to write, I much prefer playing sports to writing about them.

Here is a prayer for all athletes out there: “May all of your loads be distributed over a large area, and may your high-impulse collisions be gradual.”

The 2005 film, Crash, won the “Best Picture” award at the Oscars, and is one of the best dramas I have ever seen.  The movie follows several characters that are involved in negative interactions fuelled by racial differences and hate.

Watching these intense situations play out from a distance is thought-provoking and highly entertaining.  However, experiencing such conflicts first-hand is often very stressful.  One-on-one confrontations between strangers, colleagues, friends, and, worst of all, family members, can be extremely detrimental to one’s personal equilibrium. 

A person is like a particle moving along through space – if left to one’s own devices, one will continue along pleasantly, unaffected.  This is predicted by Newton’s first law of motion, which says that an object in motion will only change velocity if a non-zero net external force acts on it.  One way to think of Newton’s first law is that life would be dull if we just kept to ourselves.  Going through life with constant velocity is no fun; human contact makes for a far more interesting journey.

One of the characters in Crash goes so far as to suggest that people seek out conflicts because they are bored or lonely – as though colliding into one another is a mechanism that people use to confirm they are still alive.

A life that is completely devoid of conflict is boring.  On the other hand, a life that is filled with destructive interactions is too stressful.

Like particles floating in the air, or cars driving on the road, people moving through life will inevitably collide with one another.  Usually, these collisions are positive, like a friendly hello from a neighbour.  Sometimes, however, people collide in an explosive manner, like when colleagues disrespect one another.

Newton’s third law predicts that two particles in contact with one another will exert equal and opposite forces on one another.  An extension of this law is known as the conservation of linear momentum, which may be used to predict the final state of colliding bodies given their initial states.  I see an elegant parallel between colliding particles and clashing personalities.  Can we learn from these mechanics principles in order to resolve our interpersonal conflicts more harmoniously?  Let us see.

First of all, what is momentum?  It is defined as the product of mass and velocity.  Heavier, faster-moving objects have more momentum than lighter, slower-moving ones.  For this reason, if two football players collide at equal speeds, the heavier one will “win” the collision.

I was once sitting at the back of a city bus that was stopped at a red light, when I felt a slight vibration and a loud BANG.  It turned out that a car had slid into the rear of the bus.  The bus, having a much larger mass than the car, sustained barely a scratch.  The poor Toyota Yaris had transformed into an accordion.

In an interpersonal conflict, each person has an analogous velocity and mass.  Each “body” has a velocity they bring to the collision – it is their point of view.  The mass of each body is then how strongly they feel about the issue at hand.  If two people have colliding views and feel very strongly about them, you can expect to see real fireworks.  Conversely, when people ‘agree to disagree’, their masses, and corresponding momentum vectors are small.  In such cases, the resulting collisions are negligible; those involved in the confrontation deem the argument to be not worth the trouble.  As they say, one should pick one’s battles.

Does this mean that voicing strong contradictory opinions must result in a destructive impact?  Actually, there is one more important aspect about collisions to consider: when two particles with high momentum collide, they need not sustain damage as a result of the collision.

There are two kinds of collisions.  The kinds of collisions that we see most typically in life are inelastic in nature.  Here, the total kinetic energy of the bodies involved is not conserved.  Much of the energy goes into deforming the bodies, like the aforementioned Yaris.  When two people confront one another in a disrespectful manner, it is simply an inelastic collision of personalities.  Rather than resolving the conflict, the energy deforms one or both spirits involved.  Usually, the person with less momentum going into the confrontation gets flattened by the other.  If both people have significant momentum, and are disrespectful to one another, both will sustain damage.  It turns out that ‘heated’ debates are appropriately named, as heat loss signifies a loss in energy.

The other kind of collision is elastic.  Think of two balls in billiards that smash into one another.  They are certainly affected by the collision, yet they sustain no damage.  The bodies learn from one another, and waste no energy hurting the other’s feelings.  We can learn much from these colliding objects.  If we keep our discourse respectful, we come out of it ahead.  Our total momentum is conserved, and our energy is too.

There are so many things that can fuel a confrontation.  Much of the time, they are a direct result of miscommunication or a false assumption by one or both parties involved.  Sometimes they are the result of a toxic situation, like the racism present in Crash.  Legitimate arguments can be political in nature – the result of different beliefs or perspectives.  They can be socio-economic as well, stemming from an imbalance of wealth or natural resources.

Many collisions in life are unavoidable.  If you find yourself involved in a high momentum collision, remember that the nature of the collision is not predetermined.   Unlike inanimate objects that collide, people get to choose how these intense moments will play out.  Let us collide elastically, with mutual respect.  We will conserve our energy for more important things, like enjoying life. 

Newtonian mechanics teaches us how bodies move and interact with one another.  Social situations are less predictable and actually more complex than problems involving physics.  Yet, within the simplicity of two colliding bodies, there exists a lesson that will help us resolve our real life differences respectfully.