What is the equation to find the mass of an object in kilograms?

Question

Im in physics and i was wondering how to find the mass of an object knowing only the objects height in meters and the gravitational potential energy?

Answer 1

In your case, potential energy is due to weight and height above ground level; so that PE = mgh; where m is mass, g is distance per sec^2, and h is height above ground h = 0, where PE = 0 exists.

Thus, m = PE/gh and everything on the RHS of the = is a known factor if you assume g = 9.81 m/sec^2, which is average acceleration due to gravity at Earth's surface. If you keep the units straight, m will be in kg because PE units are kg-m^2/sec^2; where kg-m/sec^2 has the arcane definition Newton.

PS: Point of clarification g is not "always" 9.81 m/sec^2 on Earth. In fact g = GM/R^2; so that it varies inversely with the square of the distance (R) from the center of Earth's mass M. In fact, as the surface of Earth is not a perfect sphere and as its center of mass is not exactly in the center of the planet, g varies from point to point on the surface.

We take g = 9.81 m/sec^2 on Earth's surface because the variances are slight and this value is an average around those variances. On the other hand, if we set r = 2R, like we have a satellite orbiting Earth at twice the radius of Earth, that would reduce g to 1/4 its 9.81 value.

That results because g varies as the inverse of the SQUARE of the distance. Assume g = GM/R^2 = 9.81 on average on the surface R, and g' = GM/(2R)^2 at twice the distance 2R; so that g/g' = 1/R^2//1/(2R)^2 = 4/1; so that g' = (1/4)g because the separation distance is 2R instead of on the surface at R.

Answer 2

GPE = mass x gravity x height.

On Earth, the gravity's always 9.81 m/s². If you know the height in meters and the GPE in Joules, just plug 'n' chug, my friend.

Good luck!

EDIT: Okay, excuse me. The average gravity on Earth's surface is 9.81 m/s². I doubt your physics teacher is going to be anal enough to worry about the minor variations caused by small differences in altitudes or subsurface density. If so, hopefully he or she will let you know before you start working your problem set.