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This is one of my jobs. When there is something that happens, I have to do an analysis---the internet needs me. In this case, it's a hit between Draymond Green and LeBron James. Was it a hit, or did LeBron flop? I'm not the judge, I'm just going to present evidence.
When an object interacts with another object (with zero external forces), this is called a collision. Here are some important physics ideas about collisions.
- When two objects collide, there is a force. Object 1 pushes on Object 2 with an equal magnitude force (but in an opposite direction). This is just part of the nature of forces.
- A net force changes the momentum of an object. The change in momentum depends on both the net force and the time interval that it is applied.
- Since the two objects have the same magnitude force for the same time interval, they have the same magnitude of change in momentum. This is also called conservation of momentum.
- If there are external forces on the system of two objects, then momentum is not conserved. However, if the external forces are small in comparison to the interaction forces---they can mostly be ignored and momentum is mostly conserved.
That's just about all the physics you need for collisions. Yes, if you want more details, check out these older posts and have fun.
But why should anyone look at momentum? Well, it's one way that you can detect a fake flop (which I've covered before). Basically, you can look at LeBron's momentum change. If his change in momentum can not be accounted for by Draymond's change in momentum then LeBron might have pushed off the floor for a fake flop. Of course this means I need to find the momentums for both players.
Finding positions and velocities from videos just happens to be one of my things. I like to think that I am reasonably experienced in this area---I even published a book on this topic. The basic idea is to use some software (I like Tracker Video Analysis) to look at the positions of objects in each frame of the video. For a real video (I assume this is real), there are just two things I need. First, I need the frame rate. I will just assume the actual frame rate is the same as the playback frame rate (playing in real time). Second, I need something to scale the length of the video. For this, I will use the dimensions of an NBA court---in particular the size of that circle in the middle.
I will call the direction towards the goal, the x-direction (this is mostly the direction of travel for both players). With that, I get the following data for their positions.
By looking at the slopes of these lines, I can get the velocities for both players before and after the "collision." But I really want the momentum of the two players. Since momentum is the product of mass and velocity, I need the masses. LeBron is 113 kg and Draymond is 104 kg. This gives the following values for momentum (well, the x-component of momentum).
- LeBron before the collision = 548 kg*m/s
- LeBron after the collision = 264 kg*m/s
- Draymond before the collision = 362 kg*m/s
- Draymond after the collision = 290 kg*m/s
Notice that all of the momentum values are in the positive x-direction. Draymond collided with LeBron by moving slower than him (but in the same direction). But was momentum conserved? Before the collision, the total momentum for the two players was 910 kg*m/s and after the collision it was 554 kg*m/s. The total momentum decreased. Does this mean there was a flop on the part of LeBron? Not necessarily. It does mean that there must at least be an external force during this collision. It's possible (and even likely) that Draymond was pushing significantly on the floor in the negative x-direction and this would change the total momentum of the system (Draymond plus LeBron).
What kind of force would it take to result in this change in momentum? To find this, I will need the time interval for the collision. It's tough to know exactly when the collision started and ended, but to a rough approximation I get an interval of 0.23 seconds. Now I can use this with the momentum principle.
Using my value for the change in momentum, I get a net force of 1548 Newtons (348 pounds). That seems like a plausible force.
OK, so here's what I think. Yes, Draymond hit LeBron (that seems clear). Draymond used his foot to exert a force on the system of both players and this changed their momentums. Did LeBron throw up his hands to emphasize the hit? Maybe, but it doesn't matter---he was still hit. The end.
