Physics 2.16 - 2.18 - Mass, weight and field strength

Physics 2.16 - 2.18 - Mass, weight and field strength

Explain why mass stays the same when gravitational field strength changes but weight does not. Calculate weight and measure it with a calibrated force meter.

Mass, weight and field strength

Mass measures the amount of matter in a body and is measured in kilograms. Weight is
the force on that body due to a gravitational field, so it is measured in newtons. Near a
planet, weight acts towards the planet's centre. Everyday speech often uses "weight" when it
means mass, but kilograms are not a unit of force.

Gravitational field strength

Gravitational field strength, gg, is the gravitational force per kilogram placed in a
field. Its unit is newtons per kilogram (N kg−1\mathrm{N\,kg^{-1}}).

Weight

W=mgW = m g
  • WW is weight in newtons (N).
  • mm is mass in kilograms (kg).
  • gg is gravitational field strength in newtons per kilogram (N kg−1\mathrm{N\,kg^{-1}}).

Useful rearrangements are m=W/gm=W/g and g=W/mg=W/m.

For a fixed mass, WW is directly proportional to gg. Doubling the field strength
doubles the weight. Moving the same sealed object to a weaker gravitational field does not
remove matter, so its mass stays the same while its weight decreases.

Worked example: the same mass in two fields

A 6.0 kg6.0\,\mathrm{kg} instrument is placed first where g=9.8 N kg−1g=9.8\,\mathrm{N\,kg^{-1}}, then where
g=3.7 N kg−1g=3.7\,\mathrm{N\,kg^{-1}}.

W1=mg=6.0 kg×9.8 N kg−1=58.8 NW_1=mg=6.0\,\mathrm{kg}\times9.8\,\mathrm{N\,kg^{-1}}=58.8\,\mathrm{N} W2=mg=6.0 kg×3.7 N kg−1=22.2 NW_2=mg=6.0\,\mathrm{kg}\times3.7\,\mathrm{N\,kg^{-1}}=22.2\,\mathrm{N}

The 6.0 kg6.0\,\mathrm{kg} mass is unchanged. The second weight is smaller because the gravitational field is
weaker. The units also check: kg multiplied by N kg−1\mathrm{N\,kg^{-1}} leaves N.

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