Weight

Mass and weight are often misused terms. One often refers the body mass as the body weight. Scientifically, mass and weight is defined differently. Mass refers only to the number of atoms or particles present in a body or object. Weight is the measure of the force exerted by the gravity on an object.

When one says I weigh $$50 \;kg$$, he/she is really pertaining to his/her mass which is measured by a scale. Weight from its definition is measured by the mass of the object multiplied by the pull of gravity, $$W=mg$$. The unit for weight is Newton, $$N$$.

Example 1.

A loaded box has a mass of $$100\;kg$$. What is the weight of the box?

Given:

$$m=100\;kg\\ g=9.8\;m/s^2$$

Solution:

$$W=mg=(100\;kg)(9.8\;m/s^2)=980\;N$$.

The weight of the box is $$980\;N$$.

Example 2.

A book on the table is supported by a force of $$50\;N$$. What is its mass?

Given:

$$F_N=50\;N$$

Solution:

From the concept of force, forces acting on an object at rest are equal, resulting to a zero net force. Thus, $$F_N=F_g=50\;N$$.

Now, using the formula for weight, derive the equation for the mass.

$$W=mg \implies m=\frac Wg$$

$$m=\frac{50\;N}{9.8\;m/s^2}=5.1\;kg$$

Example 3.

An astronaut weighs of $$735-N$$ on Earth. What is his weight on the moon? The pull of gravity on the mooon is $$1.622\;m/s^2$$

Given:

$$W_{Earth}=735\;N\\ g_{moon}=1.622\;m/s^2$$

Solution 1:

Solve first for the mass of the astronaut on Earth.

$$W=mg \implies m=\frac Wg$$

$$m=\frac{735\;kg}{9.8\;m/s^2}=75\;kg$$

Solution 2:

Use the mass of the astronaut to solve for the astronaut's weight on the moon.

$$W_{moon}=mg_{moon}=(75\;kg)(1.622\;m/s^2)=121.65\;N$$

The astronaut weighs $$121.65\;N$$ on the moon.