Mass and Weight

In our day to day lives, we treat weight and mass as the same. This is evident to me when I look at my kitchen scale every morning. One of the settings allows you to measure everything in grams. This is funny because the gram is a measure of mass not weight and yet I am weighing not massing my dog’s food in the morning. Even stranger is that if I were to take my scale to the moon with the same amount of food on Earth it would weigh a different amount, but its mass wouldn’t change. So what is mass and how is it different from weight?

Mass Versus Weight

Mass (kg) refers to the amount of matter something contains. My dog’s food contains that same amount of matter on Earth and on the Moon. Basically, if I look at the food here on Earth and on the Moon it would look the same. Even if I managed to pulverize the food and compress it into a block it would still have the same mass. Sure the form is different but the amount of matter present is still the same if I could tally all of the molecules present I would find the same number on Earth as on the moon.

Weight (N) on the other hand refers to the force something with mass exerts as a result of gravity and other competing forces. Therefore food exerts a smaller force on my scale because the gravity of the moon is far less than the gravity of Earth. Not because the mass of the food changed.

Weight=mass\times gravity

This is where the confusion between weight and mass arises because on Earth gravity is consistent and our scales are calibrated to this gravity. When I weigh something on a scale it actually converts the force it receives into a mass using Earth’s gravitational acceleration of 9.8m/s2.

Mass = \frac{Weight}{Gravity}
Mass = \frac{Weight}{9.8\frac{m}{s^2}}

Where our scales go wrong is not calibrating to the difference in gravity between the Earth and the moon. Thus it appears incorrectly as though the mass of our object on the moon is in fact less even though it hasn’t changed.

Changing Weight

Here we have seen one of the factors that can change the weight of an object, the gravity acting on that object. Additionally other forces such as the buoyant force of fluids which counteracts gravity or the additional force of an elevator accelerating upwards. Basically, any force with or against gravity will change the weight of our object.

Ultimately, this point is the most important takeaway from the difference between weight and mass. That the weight of an object is dependent not only on the mass of the object but also the other forces acting on that object. This is one of the few ways the MCAT brings up the distinction between mass and weight. We will continue to explore this phenomenon later when we discuss fluids as well as forces. So you will have more opportunities to see this concept in action in the context of other content material.

Center of Mass

Another more commonly tested concept is the idea of center of mass. Center of mass refers to exactly what it sounds where the mass of an object is centered. Specifically, a single point where we can consider all of the mass to exist. This is all a bit circular though so let’s explore this concept by thinking about a couple of real-world examples. First up we will consider a solid metal ball.

Since this solid metal ball is of uniform shape and uniform density the center of mass will be located at the very center of the ball. If we change the shape of this ball by attaching a metal rod to it. We will shift the center of mass of the new object towards the added mass (i.e the rod).

Now let’s think about how this applies to people. Let’s imagine you are walking calmly and confidently on a tightrope across a gaping chasm. In this case, your center of mass is over the tightrope and thus you are able to walk across it perfectly balanced.

However, if you shift your weight to the right of the tightrope a bit you will lose your balance and fall towards that side. Instinctively we usually thrust out our opposite leg moving more of our weight away from our current center of mass in order to shift it back over the “stable” tightrope.

We don’t need to know how to calculate the center of mass of objects as it is fairly complicated and depends on a great number of factors such as the distance, density, shape, and mass of our object.