Weight

1. Definition

Weight is the gravitational force exerted on an object by a massive body such as Earth.

Weight is a force, so it is a vector quantity.

2. Equation for Weight

Near Earth’s surface:

where:

• W = weight
• m = mass of the object
• g = gravitational acceleration

Magnitude of gravitational acceleration near Earth:

\(g\approx9.8m/s^2\)

Direction:

• always toward the center of Earth

3. different between Weight and Mass

These concepts are different.

Mass remains constant, but weight depends on gravitational field strength.

4. Vector Form

Weight can be written as:

\(\vec{W}=m\vec{g}\)​

If upward is positive:

\(\vec{W}=-m\vec{g}\)​​

because gravity points downward.

5. Weight in Free-Body Diagrams

In mechanics problems, weight is represented as:

• a force vector pointing downward
• acting through the object’s center of mass

Weight is almost always included in free-body diagrams near Earth’s surface.

6. Apparent Weight

The force a scale measures is called apparent weight.

This is usually the normal force exerted by the scale.

Example:

• elevator accelerating upward → apparent weight increases
• elevator accelerating downward → apparent weight decreases

7. Weight and Newton’s Second Law

If vertical acceleration exists:

\(\Sigma{F_y}=ma_y\)​

Example for an elevator:

\(N-mg=ma\)

where:

• N = normal force
• mg = weight

8. Weightlessness

Astronauts in orbit appear weightless because:

• they are in continuous free fall
• support forces become nearly zero

Gravity still acts on them.

Thus “weightless” does not mean “gravity-free.”

9. Universal Gravitation Connection

The expression

\(W=mg\)

is a near-Earth approximation of Newton’s universal gravitation law:

\(F_g=G\frac{Mm}{r^2}\)​

where Earth’s gravity produces the local value of $g$.

10. Physical Meaning

Weight represents how strongly gravity pulls on an object.

Larger mass:

• greater gravitational force
• larger weight

Different planets produce different weights because $g$ changes.

Summary

Weight is the gravitational force acting on an object.

Near Earth:

Key ideas:

• weight is a force
• points downward
• depends on gravitational field strength
• differs from mass