# Soccer physics

Physics is the branch of science that deals with (surprise!) the physical world and its properties. It attempts to explain in mathematical terms the behaviour of matter as we observe it.

To understand why soccer balls curve, how high they bounce, how the pressure in the ball affects the bounce and even what sort of boots to wear, we need to use things like Newton’s laws of motion, Bernoulli’s discoveries about fluid flow, Maxwell’s equations of electromagnetics, Einstein’s theories of gravitation and relativistic motion, and a lot of other complicated-but-cool stuff.

Why can’t I kick the ball HARD?

You might be taking a long, slow strike at the ball rather than a shorter, sharp strike. This is because a big windup doesn’t necessarily impart sufficient kinetic energy (mass x velocity squared divided by 2). This explains why short, stocky players can generate power on the ball–a short, fast strike contributes to kinetic energy as a square versus the linear increase of weight alone.

Also your head might be coming up on the strike – if you look up as the ball leaves your foot, you impart less mass and velocity, ergo less kinetic energy.

Forces acting on a curving soccer ball This is a bird’s-eye view of a football spinning about an axis perpendicular to the flow of air across it. The air travels faster relative to the centre of the ball where the periphery of the ball is moving in the same direction as the airflow (left). This reduces the pressure, according to Bernoulli’s principle. The pressure increases on the other side of the ball, where the air travels slower relative to the centre of the ball (right). There is therefore an imbalance in the forces, and the ball deflects in the same sense as the spin – from bottom right to top left. This lift force is also known as the “Magnus force”, after the 19th-century German physicist Gustav Magnus.

Assuming that the velocity of the ball is 25-30 ms-1 (about 70 mph) and that the spin is about 8-10 revolutions per second, then the lift force turns out to be about 3.5 N. The regulations state that a professional football must have a mass of 410-450 g, which means that it accelerates by about 8 ms-2. And since the ball would be in flight for 1 s over its 30 m trajectory, the lift force could make the ball deviate by as much as 4 m from its normal straight-line course. Enough to trouble any goalkeeper!

Playing soccer on the Moon During an Apollo 17 Lunar landing mission, the astronauts took time out to play a game of soccer on the surface of the Moon with a 200 lb. moon rock.

How?

The “weight” of an object on the Moon is 1/6th that on Earth. (its mass, of course, remains the same)

THAT’S THE WAY THE BALL BOUNCES! Suppose a soccer ball is dropped from rest at a height of 10 feet. And assume, on each successive bounce, the ball reaches half the previous height attained. How long will it take for the ball to finally come to rest?

Surprisingly, most people immediately and incorrectly guess that the time involved would be infinite. But, the time of each bounce shortens quickly, and using the simple expression d=½ × g × t² for the distance (d) travelled from rest during the time (t) under gravity (g=32 feet/sec/sec), an infinite series leads to a finite time of 4.61 seconds for the ball to come to rest.