Mass and Gravitational Weight

What you’ll learn

Calculate gravitational force without confusing it with mass.

គណនាកម្លាំងទំនាញដោយមិនច្រឡំទម្ងន់និងម៉ាស។

Meaning and use

Weight is the gravitational force on an object. Mass measures the amount of matter or inertia and is not the same quantity. Near Earth’s surface, weight is approximately mass times local gravitational field strength. State the value of g used; 10 N/kg is a convenient classroom approximation.

ទម្ងន់ជាកម្លាំងទំនាញលើវត្ថុ ខុសពីម៉ាស។ ជិតផ្ទៃផែនដី ប្រើ W=mg ដោយបញ្ជាក់ g។ មេរៀននេះប្រើ g=10 N/kg ជាការប្រហែលសម្រាប់គណនាសាមញ្ញ។

Formulas

Gravitational weight

\[F_g=mg\]

Rearrangement

\[m=\frac{F_g}{g}\]

Symbols and units

Symbol	Meaning	Unit or restriction
Fg	Magnitude of gravitational weight	newton (N)
m	Mass	kilogram (kg)
g	Local gravitational field strength	N/kg, equivalent to m/s²

Conditions and limits

• Use the local g value supplied by the question.
• Examples here use g = 10 N/kg unless another value is given.
• ទម្ងន់មានឯកតា N ហើយម៉ាសមានឯកតា kg។

Worked examples

Weight on Earth, approximately

Mass 3 kg; use g = 10 N/kg.

1. Use \(F_g=mg\).
2. Calculate \(3\times10=30\) N.

30 N

ម៉ាសនៅជា kg ប៉ុន្តែលទ្ធផលកម្លាំងជា N។

Recovering mass

Weight 80 N in a field of 10 N/kg.

1. Use \(m=F_g/g\).
2. Calculate \(80/10=8\) kg.

8 kg

រកម៉ាសដោយចែកកម្លាំងនឹងកម្លាំងទំនាញក្នុងមួយ kg។

Common mistakes

Instead of	Use	Why
A 3 kg object has weight 3 kg.	Its mass is 3 kg; its approximate Earth weight is 30 N when g = 10 N/kg.	Mass and force have different units.
Weight is identical everywhere for the same mass.	Weight changes with g.	Mass can stay the same while gravitational field strength differs.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find weight for 5 kg with g = 10 N/kg.
2. Find mass for 120 N with g = 10 N/kg.
3. Mass 2 kg, g = 1.6 N/kg: find weight.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 50 N

   5 × 10 = 50.

2. 12 kg

   120/10 = 12.

3. 3.2 N

   2 × 1.6 = 3.2.

Quick recap

• Weight is a force.
• State the g value used.
• Use kilograms for mass and newtons for weight.