## Mass and Weight

Mass is simply the total amount of material in an object. It can be thought of as a tally of all the subatomic particles - electrons, protons, and neutrons - in a body. With this in mind, it is easy to see that mass remains constant everywhere in the universe. Mass is expressed in kilograms or slugs.

t0.1 Weight is the force between a mass and an accelerating surface or gravitating t02 body. It depends on three things: an object's mass, the strength of the local accelera-t04 tion field, and the state of motion of the object relative to the field. The weight of t0.5 an object is just its mass times the acceleration of gravity acting on that object. It is t0.6 expressed in newtons or pounds.

t0.7 Example 1: Find the universal mass of Astrid the Swedish astronaut, in slugs, who t0 8 weighs 21 lbs at a Moonbase, before she dons her spacesuit. The acceleration of gravity on Earth is 32.17 ft/s2 and the acceleration of Lunar gravity is 1/6 that on Earth.

Solution: Using Newton's second law, we know that weight equals mass times acceleration of gravity:

Plugging in numbers:

m = (21 1b x 6) / (32.17 ft/s2) m = 126 1b/ (32.17 ft/s2) m = 3.9 slugs

Examining the problem, we see Astrid's 126-Ib Earth weight appear in the numerator. The astronaut has a universal mass of 3.9 slugs, an Earth weight of 126 lb, and a Lunar weight of 21 lb.

Example 2: If 1 kg weighs 2.2 lb on Earth, what is the Astrid's mass in kilograms and weight in newtons on Moon and Earth? The acceleration of gravity on Earth is 9.807 m/s2.

Solution:

(126 1b) / (2.2 1b/kg) = 57kg WE = mg = (57kg)(9.807m/s2 ) = 560N WM = (57kg)(1/6)(9.807m/s2) = 93N

The astronaut has a universal mass of 57 kg, an Earth weight of 560 N, and a Lunar weight of 93 N.