What Is a Force? Pushes, Pulls, and Units
A force is a push or a pull that one object exerts on another, a vector quantity measured in newtons (N), which can change the velocity of an object, change its shape, or both. In brief: one newton is the force that gives a mass of 1 kg an acceleration of 1 m/s2 (1 N = 1 kg·m/s2). A force has a magnitude, a direction and a point of application, and forces act between two objects, so they come in pairs.
Pushing a door, stretching a spring and kicking a ball are all forces. They are the cause of changes in motion. This guide defines force and its effects, explains how forces are measured and represented, compares examples in a table, works through calculations with the newton and combined forces, and corrects common mistakes.
What is a force?
A force is an interaction between two objects. It is always exerted by one object on another. A force is a vector: it is described by its magnitude (in newtons) and its direction. It is drawn as an arrow whose length is proportional to the magnitude, starting at the point where the force acts. Several forces acting on one object can be added as vectors to give the net (resultant) force.
What are the effects of a force?
- Start, stop or change the motion: a net force on an object produces an acceleration, which means a change in speed or direction.
- Change the shape or size: stretching, compressing, bending or twisting, as with a spring, a rubber band or clay.
- Cause rotation: a force applied away from the axis of rotation turns an object, as when you push a door at the handle.
- No visible effect if balanced: if the net force is zero, the velocity does not change, and a body at rest stays at rest.
How is force measured?
The SI unit is the newton (N), named after Isaac Newton: 1 N = 1 kg·m/s2. Forces are measured with a spring balance (newton meter), which uses the extension of a spring (Hooke’s law). For scale, the weight of a small apple is about 1 N, a 1 kg mass weighs about 9.8 N on Earth, and a car engine may produce a driving force of a few thousand newtons. Other units include the kilonewton (kN = 1,000 N), and the pound-force (1 lbf ≈ 4.45 N).
Examples of forces
| Force | Exerted by | Typical effect |
|---|---|---|
| Weight | Earth’s gravity | Pulls objects downward |
| Friction | Rubbing surfaces | Opposes sliding |
| Normal force | A supporting surface | Pushes perpendicular to the surface |
| Tension | Rope or string | Pulls along the rope |
| Magnetic force | A magnet | Attracts or repels magnetic objects |
Worked example: forces and the newton
- Force from acceleration. A force gives a 2.0 kg trolley an acceleration of 3.0 m/s2. F = ma = 2.0 × 3.0 = 6.0 N.
- Weight. The weight of a 0.50 kg book is W = mg = 0.50 × 9.8 = 4.9 N downward.
- Forces in the same line. Two students push a box in the same direction with 30 N and 40 N: net force 70 N. If they push in opposite directions: net force 40 − 30 = 10 N in the direction of the larger push.
- Perpendicular forces. Forces of 30 N east and 40 N north give a net force of √(302 + 402) = √2500 = 50 N, at an angle tan−1(40 ÷ 30) = 53° north of east.
How was force understood?
Aristotle taught that a force is needed to keep a body in motion. Galileo showed that force is needed to change motion, not to maintain it. Newton formulated the laws of motion in 1687 and defined force through the change of momentum. The unit was named newton in 1948 by the General Conference on Weights and Measures.
Which mistakes are common?
Mistake 1: Thinking that force is needed to keep an object moving
A net force is needed to change the velocity. An object with zero net force keeps moving at constant velocity.
Mistake 2: Saying that an object “has” a force
A force is an interaction. Objects exert forces on other objects; they do not store them.
Mistake 3: Confusing mass in kilograms with weight in newtons
Mass is the amount of matter. Weight is the force of gravity on it, W = mg.
Mistake 4: Adding forces as plain numbers
Forces are vectors, and the directions must be taken into account.