Mass and Weight

Mass is a fundamental property of a physical object, a measure of its inertia (according to Newton's second law of motion). In general, mass is a measure of the amount of matter in an object. The mass of an object is independent of the object's location (the mass of an object is the same on the Earth, the moon or in deep space). The SI unit of mass is kgkilograms depicted by letters k g. The force acting on an object due to gravitation FG=mg equal to mass multiplied by gravitational acceleration is called weight, as illustrated in the upper image of the Figure 1. If the gravitational acceleration and the weight are known, the mass of an object can be determined.

A weighing scale does not measure the weight of an object but rather a force with the same magnitude as the normal force which acts on the object and is supplied by the scale. This situation is depicted in the lower image of Figure 1. When the net force on the apple is zero (apple is not accelerating) the normal force (FN) has the same magnitude as the weight (FG) of the apple. In other words: The scale is pushing upwards with a force equal in magnitude to the weight of the apple. This force (indicated by the red arrow in the free body diagram of the scale) is actually measured by the scale and equals the weight of the apple in case of zero net force.

Upper illustration presents an image of a red apple with black vertical arrow coming from its centre downwards, representing its weight, which is equal to its mass multiplied by the gravitational acceleration. The lower set of illustrations, starting from the left presents a red apple on a grey rectangular representing a scale. Middle image shows the same apple with normal force and the weight represented by two vertical arrows. The normal force arrow comes from the centre of the apple upwards, and the weight arrow goes from the centre downwards. The image on the right presents the scale with the normal forces and the weight of the scale. Two vertical arrows point downwards from the scale and represent the weight of the scale and the normal force. The last vertical arrow points upwards and represents the normal force the floor is exerting on the scale.

Figure 1: The weight of an apple of mass m is given by FG=mggravitational force equal to mass multiplied by gravitational acceleration. Apple on a scale (indicated by the gray rectangle) and the two corresponding free body diagrams (right). FG=mg gravitational force equal to mass multiplied by gravitational acceleration is the weight of the apple, FN F N (or N) the normal force, msg m of s times g the weight of the scale, FFS F of F S is the normal force the floor is exerting on the scale.