If you should buy a quantity of gold in Mexico and weigh it carefully on a spring scale would the same quantity of gold weigh more less or the same if weighed on the same spring scale in Alaska?

Answer 1

All things being equal and the accuracy of the scale sufficient to detect it, the gold will weigh more in Alaska than it did in Mexico. The question is designed to push the investigator in the direction of the effects of latitude as regards the way the force of earth's gravity will work. Why? Glad you asked. Let's look. A scale (regardless of the type) measures the pull of gravity (a force) on an object. We call that pulling by gravity the weight of the object. The more mass it has, the more gravity will pull on it - the more the object will weigh. Very simple, yes? Yes. But two things will determine the amount of gravitational attraction, the amount of force due to gravity, that is acting between two objects. One is the mass of the objects, and the other is the distance that separates them. Let's look at how that applies here. In this case, the mass of the gold remains the same. But in Alaska, the distance between the gold and the earth's center, which is the "center point" of earth's gravity, is less. The gold is "closer" to the earth. If two masses are attracted to each other, the closer they are, the more the force of attraction. But how does that work as regards Mexico and Alaska? Jump with me and we'll see. The earth is not a ball, but is an "oblate spheroid" as far as its shape. Take a balloon and pretend it's the earth. Give it a north and south pole, and an equator. Now put the palms of your hands on the poles and give just a tiny squeeze to the balloon. It will "puff out" a tiny bit at the equator. That's the shape of the earth. Because the earth spins, it "puffs out" around the equator. That means points farther from the equator, farther north or south, will be "closer to the center of the earth" and experience just a tiny bit more gravimetric attraction. Even though the mass of the gold stays the same, it weighs more in Alaska than it did in Mexico. Problem solved. Note: the "closer to the center" thing will break down at some point. If you think it through, that is, if you take a journey to the center of the earth, gravity won't be the same throughout your trip. And you'll be surprised when you get to the middle of the planet! Can you guess why?