Question #01ea1

Sep 27, 2015

Because it's practical to ignore the gravitational acceleration in everyday activities.

Explanation:

The weight of an object is simply a measure of the force the object has as a result of gravity.

The mass of an object can be though of as the amount of matter that respective object has.

The weight of an object is actually a vector quantity. The magnitude of that vector is the product between the mass of the object and the gravitational acceleration, $g$

$W = m \cdot g$

As you can see, the only difference between the mass of an object and the magnitude of its weight is the gravitational acceleration, $g$.

This means that for most everyday activities and situations, the difference between the weights of two objects will actually be equivalent to the difference between their two masses.

Let's say that you put an object on a scale and read its weight to be $\text{9.81 kg}$. Here is where it can get a little confusing.

In this case, the word "weight" is used correctly, but the value that's being read is actually interpreted as mass, that's why it uses kilograms instead of Newtons.

If the scale were to give you the weight in Newtons, then you would have to get the mass of the object by dividing that weight by the value of $g$.

$m = \frac{W}{g} = \text{9.81 N"/(9.81"m"/"s"^2) = "1 kg}$

Now, although this is the correct approach, it is not very practical for everyday situations because the value of $g$ is constant.

Moreover, your body is so accustomed to the value of $g$ that it makes more sense to "classify" the object as having a "mass" of $\text{9.81 kg}$, than to introduce the difference between weight and mass and be forced to constantly divide by the same value of $g$.

So, as a conclusion, everyday activities do not require a distinction between weight and mass, which is why our scales measure weight but use the units of mass to express it.

If $g$ does not change, then it's practical to use mass and weight interchangeably.