The force acting on an object can be defined as the object's mass—the amount of matter in it—times its acceleration.
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United Launch Alliance / NASA
From Grolier's New Book of Knowledge
A torsion balance can be used to measure the tiny gravitational force between small objects.
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When two balloons are given the same electrical charge, they will push one another apart.
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A force is a push or a pull. Forces make things move, stop, and change direction. They also can make objects accelerate. In fact, the force acting on an object can be defined as the object's mass—the amount of matter in it—times its acceleration. This is expressed mathematically as F = m × a.

One force we experience every moment of our lives is gravity. Like any force, gravity can make an object accelerate. You could prove this by dropping a ball from different heights and measuring how long it takes the ball to reach the ground. For example, you could drop a ball from a height of 4 feet (1.2 meters). And then you could do it again from 8 feet (2.4 meters). You might think that the ball would take twice as long to reach the ground the second time. But you would be wrong. When dropped from 8 feet (2.4 meters), the ball would actually take less than twice as long to reach the ground. This proves that the ball has accelerated under the force of gravity.


Since force may be defined as mass times acceleration, you can find the force acting on an object if you know its mass and acceleration. However, more than one force acts on an object at a time. One of the most common forces besides gravity is friction. Friction is due to electrical forces. It opposes the motion of an object being pushed or pulled. Part of the force applied to an object to make it move must be used to overcome friction. As a result, the force that makes the mass accelerate is less than the force applied.

The unit used to measure force is called the newton (N). The unit's name honors Isaac Newton, an English scientist. He was the first person to explain motion satisfactorily. A newton is the force needed to make a 1 kilogram (2.2 pound) mass accelerate at a rate of 1 meter (3.3 feet) per second per second. This means that the speed increases by 1 meter (3.3 feet) per second for every second the force is applied.

One way to measure forces is with a spring balance. In this device, the spring's stretch is proportional to the force acting on it. If the force doubles, the stretch also doubles. With a spring balance, it is easy to measure the friction opposing an object's motion. Simply pull the object so that it moves at a constant speed. Since the object is not accelerating, the net force (the sum of all the forces acting on the body) is zero. The applied force is just enough to overcome friction.

Forces can also be measured with balances. These devices consist of pans suspended from opposite ends of a bar with a fulcrum (pivot point) at the center. With these devices, an unknown force acting on one pan can be balanced by a known force applied to the opposite pan. Very small forces can be measured with a type of balance known as a torsion balance. This device is a long beam that is suspended from a fine wire. The angle through which the beam turns and the time period of its swing depend on the force. In 1798, British physicist Henry Cavendish used a torsion balance to measure the gravitational force between known masses. Two small lead balls at each end of the balance were attracted to larger ones placed near the smaller balls. With this balance, Cavendish measured forces as small as one-billionth of a newton.

Another way to measure forces is with crystals known as piezoelectric crystals. When a force is applied to such a crystal, a small measurable voltage develops across the crystal.


If you hang a 1 kilogram (2.2 pound) mass from a calibrated spring balance, the balance reads 9.8 N. This reading indicates that the Earth pulls on a 1-kilogram mass with a force of 9.8 N. If we release the mass, it will accelerate toward the Earth at a rate of 9.8 meters (32.2 feet) per second per second. But when an object hangs from a spring balance, it is motionless. Does this mean that there is no force acting on it? No, it simply means that there is no unbalanced, or unopposed, force. As the object hangs from the spring balance, there is gravitational force pulling the object downward. But this force is balanced by the opposing upward pull of the spring. These two opposing forces add up to zero. Thus there is no net force on the object.


Things that can be added or subtracted using ordinary arithmetic are said to be scalar quantities. If you walk 2 miles (3.2 kilometers) and then walk another 2 miles, the total distance you have walked is 4 miles (6.4 kilometers). Distance is a scalar quantity.

However, suppose you walk 2 miles east and then walk 2 miles north. How far are you from your starting point? The answer is not 4 miles. To find your position, you must take into account direction as well as distance. In this case your final position is 2.8 miles (4.5 kilometers) northeast of where you started. The drawingshows how you can use scaled arrows that give both direction and distance to find what is called your displacement. A quantity, such as displacement, that involves both a magnitude (size) and a direction is called a vector quantity.

A force is a vector quantity. It can be represented by an arrow (vector). The arrow's length is scaled to represent the strength of the force. And the head of the arrow gives its direction. If a weight is suspended from a spring, the forces can be represented by arrows of equal length. One arrow points up, and one points down. Vector quantities are added by placing the head of one arrow on the tail of the other. In the case of two equal vectors that point in opposite directions, the sum is zero.

If many forces act on an object, you can find the sum of the forces. You do so by adding all the arrows that represent these forces. If an object is not moving, the sum of the forces (and the arrows used to represent them) must be zero.


There appear to be four basic forces in the universe. The one most people are familiar with is the force of gravity. The three other basic forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force.

The force of gravity pulls objects toward the Earth. It also pulls all the planets toward the sun. But it is the weakest of the four basic forces. When Isaac Newton first proposed his Law of Universal Gravitation, many scientists were deeply troubled.

According to Newton's view, the force of gravity acts across empty space. There is no need for contact between bodies that attract one another. How does the sun pull on the Earth? Newton never answered that question. He assumed that gravitational forces can act at a distance.

Eventually German physicist Albert Einstein developed his General Theory of Relativity. Einstein eliminated the need for gravitational force as an explanation for why the planets circle the sun. Instead, he proposed that their motion arises from the natural geometrical properties of space.

The electromagnetic force is more than 4 million, quintillion, quintillion times stronger than the force of gravity. It is the force that holds together the atoms and molecules that make up matter. It is also the force that resists attempts to push atoms and molecules closer together or pull them apart. That is, it resists compression and extension. Consequently, it is the force that explains most of the muscular pushes and pulls that we exert on objects in our daily lives.

You can see the effects of electrical and magnetic forces quite easily. Use thread to suspend two balloons side by side. Give both balloons like charges by rubbing them with a paper towel or cloth. Because both balloons carry like charges, they will push each other apart. If they were oppositely charged, they would attract one another. Magnets behave in a similar way. The north pole of one magnet will pull on the south pole of another magnet and vice versa. However, like poles—two north or two south poles—will push one another apart.

At one time scientists thought that electrical and magnetic forces were different and unrelated. Now we know that magnetic forces exist because of the motion of electric charges, or currents. In a bar magnet, for example, the flow of charges in the atoms that make up the magnet are aligned. Because of this alignment, a strong magnetic field is produced.

The strong nuclear force is 137 times stronger than the electromagnetic force. Normally, the electrical repulsion between the positive charges that make up the nucleus would cause them to fly apart. But the strong force holds nuclei together. Although it is powerful, it acts only over very short distances. These distances are comparable to the size of nuclear particles.

The fourth force is the weak nuclear force. It was discovered during studies of beta radiation, which is the emission of electrons from some atomic nuclei. Like the strong force, it acts over a very short range. But it is only about one-thousandth as strong.

According to the quantum theory, what we refer to as forces are caused by the emission (giving off) and absorption of particles called field quanta. The electron in the hydrogen atom is attracted to the proton by an exchange of photons. Photons are the field quanta for what we call the electromagnetic force.

Similarly, the other three forces are the result of the interaction of their field quanta. Gravitons account for gravity. Gluons account for the strong nuclear force. And bosons account for the weak nuclear force. Physicists familiar with quantum theory prefer to speak of interactions rather than forces. But most people will continue to refer to the pushes and pulls in their lives as forces.

By Robert Gardner