What is the difference
between weight and mass?

From a physicist's point of view, it is difficult to teach the difference between weight and mass without first helping a student to discover and understand the natural laws of force and motion first made famous by Isaac Newton:

  1. An object at rest tends to remain at rest, and an object in motion tends to remain in motion (in a straight line). This is also known as the law of inertia.

  2. A change in state (rest, or motion) is called acceleration a, which is proportional to the net force Fnet applied to the object from outside:

    Fnet = m a.

    The proportionality "constant" m is what physicists call mass.

  3. For every action (a force applied to an object from the outside) there is always an equal-and-opposite reaction (the object pushes back on whatever pushed on it).

Newton's Second Law essentially defines mass: it is the numerical size of an object's inertia; that intrinsic property of matter which makes it resist being accelerated. The more mass an object has, the less acceleration it will have when pushed or pulled by a given size of force. The amount of mass is a measure also of the quantity of matter that makes up an object. The more mass (more matter) in an object, the harder it is to get it moving and the harder it is to stop it once it is moving. All matter has mass, down to the subatomic level; energy (light, for example) is not matter and so has no mass.

Weight is one type of force that can be exerted on an object from the outside. Other forces besides weight are: push, pull, and normal (support from beneath). Weight (a.k.a. gravity) is the force of attraction between two masses when they occupy the same region of space (Sun and Earth, Earth and your body). It is an observed fact that the attractive force of gravity between the Earth and an object is proportional to the object's mass:

weight = m g

where the proportionality constant g is called the acceleration of gravity, and is found to depend on location (distance between the object and the Earth's center). The weight of an object can be varied (move to a higher altitude or move to a different planet) but the mass of an object is fixed.

To experiment with the difference between mass and weight, try this:

  1. Support a ball from underneath, holding it above the floor at rest. You are supplying a force (called normal force) equal and opposite to the weight force (gravity) pulling down on the ball.
  2. Throw the same ball sideways (parallel to the floor) at various speeds, and notice that there is pressure (force) between your hand and the ball in proportion to the acceleration that you give to it. You are now sensing the ball's mass, its quantity of inertia. The inertia would still be there even if gravity were to somehow switch off; force would be required to move an object with mass.

Unfortunately for us teachers, there is a tendency for non-scientists to use the terms weight and mass interchangeably. The unit of mass is the gram or kilogram; scales that provide readings in those units when an object is layed on them are not really measuring mass: they are measuring force needed to support against an object's weight. But because mass and weight are proportional, the readout has been "fudged" to calculate the mass from the weight. It is incorrect for a person to say that he/she "weighs 50 kilo's" (kilograms). The unit of weight is the Dyne or Newton (in the British system: mass is in slugs and weight is in pounds).

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