ag = acceleration of gravity on earth (9.81 m/s2, 32.17405 ft/s2)
The acceleration of gravity on the moon is approximately 1/6 of the acceleration of gravity on the earth. The weight of a body with mass 1 kg on the earth can be calculated as
Fg_earth = (1 kg) (9.81 m/s2)
= 9.81 N
The weight of the same body on the moon can be calculated as
Fg_moon = (1 kg) ((9.81 m/s2) / 6)
= 1.64 N
The handling of mass and weight depends on the systems of units used. The most common unit systems are
One newton is
In the SI system the mass unit is the kg and since the weight is a force - the weight unit is the Newton (N). Equation (2) for a body with 1 kg mass can be expressed as:
Fg = (1 kg) (9.807 m/s2)
= 9.807 (N)
9.807 m/s2 = standard gravity close to earth in the SI system
As a result:
The British Gravitational System (Imperial System) of units is used by engineers in the English-speaking world with the same relation to the foot - pound - second system as the meter - kilogram - force second system (SI) has to the meter - kilogram - second system. For engineers who deals with forces, instead of masses, it's convenient to use a system that has as its base units length, time, and force, instead of length, time and mass.
The three base units in the Imperial system are foot, second and pound-force.
In the BG system the mass unit is the slug and is defined from the Newton's Second Law (1). The unit of mass, the slug, is derived from the pound-force by defining it as the mass that will accelerate with 1 foot per second per second when a 1 pound-force acts upon it:
1 lbf = (1 slug) (1 ft/s2)
In other words, 1 lbf (pound-force) acting on 1 slug of mass will give the mass an acceleration of 1 ft/s2.
The weight (force) of the mass can be calculated from equation (2) in BG units as
Fg (lbf) = m (slugs) ag (ft/s2)
With standard gravity - ag = 32.17405 ft/s2 - the weight (force) of 1 slug mass can be calculated as
Fg = (1 slug) (32.17405 ft/s2)
= 32.17405 lbf
In the English Engineering system of units the primary dimensions are are force, mass, length, time and temperature. The units for force and mass are defined independently
In the EE system 1 lbf of force will give a mass of 1 lbm a standard acceleration of 32.17405 ft/s2.
Since the EE system operates with these units of force and mass, the Newton's Second Law can be modified to
F = m a / gc (3)
gc = a proportionality constant
or transformed to weight (force)
Fg = m ag / gc (4)
The proportionality constant gc makes it possible to define suitable units for force and mass. We can transform (4) to
1 lbf = (1 lbm) (32.174 ft/s2) / gc
gc = (1 lbm) (32.174 ft/s2) / (1 lbf)
Since 1 lbf gives a mass of 1 lbm an acceleration of 32.17405 ft/s2 and a mass of 1 slug an acceleration of 1 ft/s2, then
1 slug = 32.17405 lbm
The mass of a car is 1644 kg. The weight can be calculated:
Fg = (1644 kg) (9.807 m/s2)
= 16122.7 N
= 16.1 kN
- there is a force (weight) of 16.1 kN between the car and the earth.
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