In the late 1600s, Sir Isaac Newton published "Principia Mathematica," a book that connected the worlds of math and physics. Among other important ideas, he described the second law of motion – that force is equal to mass times acceleration or f = ma. Although it looks simple at first glance, the law has several important implications, including how objects move on Earth and in space. Fundamental laws such as this have allowed scientists to investigate nature accurately and engineers to build machines that work.

Force is a physical quantity you deal with in everyday life. It takes force to open a door, lift a child, or crack an egg. It is a pull or push exerted by one object on another; the objects can be anything from protons and electrons all the way up to planets and galaxies. The pull or push may come from direct contact or, in the case of gravity, electricity and magnetism, from a distance. Scientists measure force in units called newtons, where one newton is the force needed to accelerate a 1-kilogram mass one meter per second squared.

When a hockey puck slides across the ice, it does so at a fairly constant speed until it hits the goal or a player’s stick. Although it’s moving, it’s not accelerating. Acceleration comes only from a change in speed. When an object gains speed, its acceleration is positive; when speed is lost, acceleration is negative. You measure speed in units of distance divided by time, such as miles per hour or meters per second. Acceleration is the change in speed divided by the time the speed takes to change, so it is meters per second per second, or meters per second squared.

The mass of an object is a measure of how much matter it contains. A rubber ball has less mass than a lead ball of the same size because it has less matter in it, fewer atoms and fewer of the protons, neutrons and electrons that make up the atoms. Mass also resists the effort to push or pull it; a ping-pong ball is easy to pick up and toss; a garbage truck is not. The truck is more massive than the ping-pong ball by many thousands of times. The standard unit for mass is the kilogram, about 2.2 pounds.

Mass is a simple kind of quantity. You can have large masses, tiny masses and in-between masses. That’s about it. Scientists call simple quantities scalars because one number will describe it. Force and acceleration, however, are more complicated. They have both a size and a direction. A TV weather forecaster, for example, talks about a wind coming from the west at 20 miles per hour. This is the velocity (speed) vector of the wind. To fully describe a force or acceleration, you need both the amount and the direction. For example, on a snowy day, you pull a child’s sled in the forward direction with a force of 50 newtons, and it accelerates in the same direction at 0.5 meters per second squared.

Newton’s second law of motion seems simple enough: Push on an object of a certain mass, and it accelerates based on the amount of force and mass. A small force with a large mass results in a slow acceleration, and a large force with a small mass gives a fast acceleration. What happens when there’s no force? A force of zero on any mass gives zero acceleration. If the object is standing still, it remains still; if it’s moving, it continues to move at the same speed and direction. Keep in mind that several forces can be involved at the same time. For example, you tie a rope around a boulder and pull with all your might. There are force and mass, but the boulder doesn’t budge, so acceleration is zero. The force of friction between the boulder and the ground cancels out the force of your pull. You need a much bigger force, such as from a tractor, to move the boulder.