Force

What it is

A force is an interaction between two bodies: one pulls or pushes on the other. It can change the second body’s motion (speed or direction) or its shape. Because direction matters, force is a vector; see vectors. The unit is the newton (N): 1 N is the force that gives a mass of 1 kg an acceleration of 1 m/s², so 1 N = 1 kg · m/s².

Examples:

• Gravity. Earth pulls on a book of mass 2 kg with a force of 2 · 9.8 = 19.6 N, downward; see weight.
• Friction. The surface slows a sliding crate with a force pointing against the motion; see friction force.
• Normal force. The table pushes up on the book. With the book at rest it is as large as the weight: 19.6 N up against 19.6 N down.
• Driving force. A 1 000 kg car that must accelerate at 2 m/s² needs a net force of 1 000 · 2 = 2 000 N; see Newton’s second law.

What is not a force:

• Mass. 2 kg is how much matter the book has, not how hard something pulls on it.
• Speed. 20 m/s says how fast, not how hard something pushes.
• Energy. The joule and the newton are different quantities. A force over a distance gives work: 10 N along 3 m is 30 J.

Forces add as vectors. Forces of 3 N and 4 N give a net force of 7 N if they point the same way, 1 N if they point in opposite ways and 5 N if they are at right angles (√(3² + 4²) = 5).

Why it matters

The idea of force is what ties motion to its cause. Newton’s three laws say what forces do:

• With no net force the motion does not change; see Newton’s first law.
• The net force is mass times acceleration; see Newton’s second law.
• Forces come in pairs between two bodies; see Newton’s third law.

Equilibrium is the case where the forces sum to zero; see balance of forces. Gravity between two bodies is a force with its own law; see the law of gravitation. And when a force acts along a distance the result is work, and with it energy; see energy.

Common misconceptions

• “It takes a force to keep something moving.” It takes a net force to change the motion. A body moving with no net force keeps the same speed in the same direction. A sled stops because friction is a force.
• “Weight and mass are the same.” The mass is 2 kg everywhere; the weight is a force, 19.6 N on Earth, and is different on the Moon.
• “A force and its reaction cancel.” They act on different bodies, so they cannot cancel each other. The book on the table: the weight on the book and the normal force on the book cancel, but they are not a pair in the third-law sense. The partner of the weight on the book is the book pulling on Earth.
• “A bigger body exerts a bigger force.” In a pair the forces are equal. It is the accelerations that differ, because a = F/m.

Common questions