Unfortunately it’s rarely on TV more than once every four years, but I have to say I’ve really gotten to curling. Not only is it interesting to watch, it looks like it’s actually a sport that could be played for fun at the beginning level. Unfortunately there doesn’t seem to be a whole lot of curling in Texas for some reason, so I have to content myself with watching. And thinking about the physics.
The goal in curling is to end each round with your stones closest to the center of the ring. From the release point to the center of the ring is about 97 feet or so. Friction with the ice brings the stone to a stop in that period. Why not estimate the amount of friction of the ice against the stone?
Friction is intrinsically a very complicated phenomenon, but it’s frequently a good approximation to say that it’s a force in the opposite direction of the motion, with a magnitude proportional to the force holding the moving object against the surface – gravity, in this case. We generally call this latter force the “normal” force, because normal in this context means “perpendicular”, and the force is perpendicular to the surface. The ratio of those two forces (frictional force and the normal force) is the coefficient of friction.
So we can write the equation describing the frictional force:
Where Greek mu is the coefficient of friction, and the mass m of the stone times the gravitational acceleration g is the normal force. We also know, because we’ve used them so many times, that an object in 1d accelerated motion obeys the standard equations of accelerated motion:
Here d is the distance the stone travels, t is the time it takes for to stone to complete its travel, a is the acceleration due to friction, v0 is the initial velocity. When the stone completes its travel the velocity will be 0, hence the 0 for the final velocity in the last equation. We know that force is equal to mass times acceleration, so the accleration due to friction will be the frictional force divided by mass: a = -μ*g.
But we don’t know the initial velocity. We have no way of measuring it. But we do have the total time of travel. If I understand the announcers, 24 seconds or so is a typical “hog line to tee line” time. From that, we can algebraically manipulate the equations to eliminate the initial velocity and solve for the coefficient of friction:
As expected, the longer a stone takes to travel a given distance, the lower the friction. Curling tends to use English units, so with g = 32 feet/s^2, d = 97 feet, and t = 24 seconds, plugging in I get μ = 0.011. This is a terribly tiny amount of friction, smaller than teflon on teflon. It could be that the particular approximation we’re using for friction isn’t so great here, or it could be that granite on vigorously swept ice simply has a very tiny coefficient of friction.
Either way, best of luck to the Olympians as the curl their hearts out. Team USA needs all the luck they can get!