Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

# Weight and mass

Figure f shows masses of one and two kilograms hung from a spring scale, which measures force in units of newtons. Explain the readings.

Let's start with the single kilogram. It's not accelerating, so evidently the total force on it is zero: the spring scale's upward force on it is canceling out the earth's downward gravitational force. The spring scale tells us how much force it is being obliged to supply, but since the two forces are equal in strength, the spring scale's reading can also be interpreted as measuring the strength of the gravitational force, i.e., the weight of the one-kilogram mass. The weight of a one-kilogram mass should be

FW = mg
= (1.0 kg)(9.8 m/s2) = 9.8 N ,

and that's indeed the reading on the spring scale.

Similarly for the two-kilogram mass, we have

FW = mg
= (2.0 kg)(9.8 m/s2) = 19.6 N .

Last Update: 2009-06-21