Science Buddies: "Ask an Expert"

My 9 year old is doing the Archimedes squeeze project. Am I correct that the MASS of the aluminum spheres which weigh 5 grams would be .005/9.8 or 5.1 grams? But how does that compare to the lifting force expressed as the WEIGHT of the water displaced? Am I getting too complicated?

Mom of - This experiment is pretty straight forward. The mass of the aluminum foil (5 grams) takes on several physical forms, assuming various volumes. On the largest physical example of the crushed ball, the mass vs volume is lowest and the ball will float on the water. As the volume is reduced (5 gram mass remains the same) the ball will sink lower into the water. At precisely the point of compression when the density of the ball exactly equals the density of water, the ball is equilibriate, and it just submerges below the surface and seems to be held in suspension. Any further compression and the ball will sink. I'm not sure what your calculation means, but the mass vs weight should be considered to be the same for this experiment,

Rick Marz

Hi momofcoolscientist,

To answer your question about mass and weight, the metric unit for force is newtons. The equation to convert mass to weight (which is a force) is:

Weight [newtons] = mass [kilograms] x gravity [meters/second squared]

So to convert 5 grams to weight in newtons, you MULTIPLY

weight = 0.005 grams x 9.81 m/s^2 = 0.04905 newtons

What Rick meant by "mass vs weight should be considered the same for this experiment" is that you're doing the entire experiment in Earth gravity (at least, I assume your son isn't launching his experiment into space or doing this on the moon). So, that "9.81" to convert between mass and weight always remains the same. So, if you wanted to, you could just leave everything in grams. However, since the metric unit for force is technically newtons, and buoyant force and weight are both forces, I'd recommend using newtons just to be rigorous about it.

Hope that helps - if it's been a while since you took high school or college physics, it can take a minute to catch on to the difference between mass and weight.

Here's another way to think of mass and weight.

Mass is a part of you, as much as your height, age or hair color. It is the same no matter where in the universe you happen to be. Weight, by contrast, will change depending on whether or not an object exerting gravitational force is nearby.

Weight is the force of gravity on you. In outer space, your "weight" is zero, but your mass is still the same. On earth, your "weight" is whatever your scale measures (you stand on it, the earth pulls on you with gravity and (in a non-electronic scale) it pushes a spring - how far it pushes the spring is how the scale knows your weight. On the moon, your weight is 1/6 of what you would measure on Earth, because the moon's gravity is weaker than that of the earth.

The strength of gravity depends both on Mass and distance. The reason you don't fly off the Earth toward the Sun at Dawn is that the Sun is very far away, which is more important to its gravitational force than the fact that it is much more massive than the Earth.

So your Weight depends on what massive objects you might be near, but your Mass does not care if you are in outer space or next to a black hole.

For most people, the two terms are identical because they never leave the planet Earth. There are some very slight differences in the gravitational pull of Earth if you are in, say, an airplane vs standing at sea-level but they're small enough that we normally can't measure them without sophisticated tools.