Why did this not work?
Classical mechanics dictates:
- Force = Mass x Acceleration
- Maximum Force of static friction = “static friction constant” x Support Force (in this case, weight)
- Maximum Force of kinetic friction = “kinetic friction constant” x Support Force (in this case, weight)
Since support force in this case is equal to weight, this means that Gobber will have a significantly larger force of friction available compared to Hiccup, assuming they’re standing on the same surfaces with similar shoe. (They’re each missing one leg, too!)
The force of tension (marked F-t, which is caused by the tension on the rope) acts the same way to both of them but in opposite directions as shown in the picture, so that the only way they can move is towards each other. However, because of the unequal force of friction:
- The force of static friction on Gobber is large enough that it negates the force of tension on him, making the net horizontal force on him pretty much zero. He doesn’t even budge.
- On the other hand, the force of static friction on Hiccup couldn’t get large enough to cancel out the force of tension, so Hiccup accelerates toward Gobber. This is the same case when the static friction changes to kinetic friction, since kinetic friction is always smaller than static friction.
What would happen if this case was in outer space, with no gravity or friction? [They would die, but that’s besides the point] Well, the friction is gone, so we only have force of tension, so they would both accelerate towards each other. But since Force = Mass x Acceleration, bigger mass with same force means smaller acceleration, while smaller mass with same force means bigger acceleration. Therefore, Hiccup would accelerate towards Gobber at a much higher rate than Gobber would accelerate towards Hiccup.
Bottom line: Use your physics, Hiccup.