Here is a great \"mind puzzle\". For many years I used one of those flat scales

Question

Here is a great "mind puzzle". For many years I used one of those flat scales with an internal spring but finally decided I couldn't trust the damn thing: if it looked like I'd gained a couple of pounds, maybe the spring had gone soft!

So finally I got a scale that uses counter-balance weights that you slide along an arm to get really precise measurements. Just this morning it occurred to me: what if I was on Mars, where the gravity is much weaker than here on Earth?

Obviously with weaker gravity scales with an internal spring would give grossly inaccurate results, since they measure only the pressure of your body pressing against the spring.

But here's the amazing fact: on Mars the counter-balance scale would still work perfectly, since the weakened gravity would pull with equal force against you and the counter-balancing weights. Of course you would "weigh" less, but since your mass remained the same, you would get accurate readings for what you would weigh on Earth!

Explanation / Answer

I've never been there either and I love John that you've got two different types of scale in your bathroom. That's fantastic! I avoid both of them. You've hit on the difference between weight and mass. So, a traditional scale in your bathroom uses a spring. That is measuring a force which is mass times acceleration which is the mass times the acceleration which on Earth is gravity. So, that measurement would be different on Mars because gravity is less, and even more different on the moon because again, gravity is less. If you look at one of the counterbalance ones though, that does measure mass. So, you have you on one side and your masses on the other, so your kilos or your pounds if you're American on the other side. That should work equally well both on Earth and on Mars because gravity is affecting both sides of that balance equally.

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