Unit 2 · Topic 04

Mass and weight

Mass and weight describe different ideas: mass measures inertia, while weight is the gravitational force on that mass.

Unit 2Mass and weightOpen navigation

Concept 01

Inertial mass

Essential The minimum you should retain

Mass measures inertia in Newtonian mechanics: under the same net force, a larger mass has a smaller acceleration.

UnderstandInterpret and connect

Mass is a scalar measured in kilograms and has no direction. Defining it only as an amount of matter is insufficient.

DeepenFormulation and conditions

Operationally, the ratio F_net/a compares masses when constant mass and net force are well established.

ExploreConnections for further study

The equality of inertial and gravitational mass is a deep experimentally supported connection, although both are used here within the Newtonian model.

Concept 02

Weight

Essential The minimum you should retain

Weight is the gravitational force exerted by an astronomical body on an object. It is measured in newtons, not kilograms.

UnderstandInterpret and connect

Near Earth's surface, weight can be modeled as W=mg W=mg toward Earth's centre. Mass m and field g play different roles.

DeepenFormulation and conditions

The weight vector can be written W→=mg→ \vec W=m\vec g . The scalar mg is its magnitude when g denotes the local field magnitude.

ExploreConnections for further study

Outside the uniform-field approximation, g changes with position and the gravitational interaction needs a more detailed model.

Mathematical relation

Weight near a planetary surface

W→=mg→ \vec W=m\vec g
Represents

The gravitational force on a mass in a region where g can be treated as uniform.

Physical interpretation

Mass remains; weight changes when g changes.

DeepenVariables, conditions, and checks

Variables

W⃗
weight; usual unit: N
g⃗
local gravitational field; usual unit: ms² m/s^2 or Nkg N/kg

Conditions of application

  • Spatial variation of g is negligible in the region.

Dimensional check

kg· ms² m/s^2 = N.

Errors it helps prevent

  • Confusing mass and weight.
  • Using kg as a weight unit.
  • Treating 9.8 as an exact universal value.
Two identical ten-kilogram bodies show different weight arrows for two gravitational-field values.10 kg10 kgW = 98 NW = 16 Ng = 9.8 m/s²g = 1.6 m/s²

The 10 kg mass is the same in both places. With g = 9.8ms² 9.8\,m/s^2 weight is 98 N; with g = 1.6ms² 1.6\,m/s^2 it is 16 N.

Concept 03

Constant mass and variable weight

Essential The minimum you should retain

Changing gravitational environment changes weight but does not change mass for that reason alone.

UnderstandInterpret and connect

The same body weighs less where g is smaller. The value of g must be stated; 9.8ms² 9.8\,m/s^2 is a local approximation, not an exact universal constant.

DeepenFormulation and conditions

The units Nkg N/kg and ms² m/s^2 are equivalent because 1 N=1 kg·ms² 1\,N=1\,kg\,m/s^2 .

ExploreConnections for further study

Comparing weights in different fields can reveal g when mass is known, or mass when g is established.

Two identical ten-kilogram bodies show different weight arrows for two gravitational-field values.10 kg10 kgW = 98 NW = 16 Ng = 9.8 m/s²g = 1.6 m/s²

The 10 kg mass is the same in both places. With g = 9.8ms² 9.8\,m/s^2 weight is 98 N; with g = 1.6ms² 1.6\,m/s^2 it is 16 N.

Concept review

Common errors

Each warning includes a concrete way to review the reasoning, not only an incorrect-answer marker.

Using mass and weight as synonyms.

Mass measures inertia in kg; weight is a gravitational force in N.

Expressing weight in kilograms.

The kilogram measures mass. Calculate or measure weight and report it in newtons.

Treating g = 9.8ms² 9.8\,m/s^2 as an exact universal value.

Use the stated field for the location and recognize 9.8ms² 9.8\,m/s^2 as a local Earth approximation.