In the forces topic you used w = mg again and again. This lesson says what that g really was all along — and what weight really is.
You now know g as a field strength. Near Earth's surface, the field exerts a force of 9.8 newtons on each kilogram: g = 9.8 N/kg. Read w = mg again with that meaning.
The equation comes straight from the field strength. g = F/m is the force on each kilogram. Rearrange it: F = mg — the force the field exerts on a mass m is m times g. That force is the object's weight.
Run it once on Earth. The field (g = 9.8 N/kg) exerts 2 kg × 9.8 N/kg = 19.6 N on a 2 kg bag. The bag's weight is 19.6 N.
A sack of rice hangs from a hook. What is the sack's weight?
The same equation works at any place — with that place's own g.
Where g = 3.7 N/kg — the surface of Mars — what is the weight of a 10 kg toolbox?
Write down the values in the question:
m = 10 kg
g = 3.7 N/kg
w = ?
Write down the equation:
w = mg
Substitute in the values:
w = (10)(3.7)
Simplify:
w = 37 N
The same 10 kg toolbox comes home to Earth, where g = 9.8 N/kg. What is its weight now?
Write down the values in the question:
m = 10 kg
g = 9.8 N/kg
w = ?
Write down the equation:
w = mg
Substitute in the values:
w = (10)(9.8)
Simplify:
w = 98 N — the same toolbox, a different field, a different weight.
Weight belongs to the field as much as to the object: where g differs, the same object's weight differs. Mass, meanwhile, never changes with location. The kilograms travel unchanged; the newtons do not.
A student says a rover's weight on Mars differs from its weight on Earth. Is the student correct?
Diego lifts a 3 kg sack and says its weight is 3 kg. Is Diego correct?
On Titan, g = 1.4 N/kg. Enter the weight, in newtons, of a 6.0 kg instrument case there.
Near Earth's surface (g = 9.8 N/kg), enter the weight of a 15 kg crate, in newtons.
An astronaut flies from Earth to the Moon. Compared with her values on Earth, which row describes her on the Moon?