Subject: Gravity

Is any way that you could be so kind as sending me information about a lab that would be easy to show a class how gravity works?

    Gravity as the attraction of mass for other mass. And the attraction decreases as the square of the distance between the masses: F =GmM/R^2 where F is the force of attraction of gravity in Newtons (N), G is the universal gravity constant = 6.67x10^-11 N m^2/kg^2, M and m are the masses in kg, and R is the distance between them in meters. This is the same as "weight". The ACCELERATION of gravity at the surface of the earth is how fast the mass of the earth pulls us towards it. Since F=ma where a is acceleration, g=Gm/R^2, where g is the acceleration of gravity. The force of gravity is very small, a mosquito slamming into a wall at full speed generates a force of about 1 dyne=10^-5 N, and the force between a 100 kg bus driver and his 10,000 kg bus when they are separated by 3 meters is LESS than one dyne.

Interesting facts:

  1. If you are outside a sphere, the acceleration of gravity caused by the mass of the sphere is the same as if the mass were all concentrated at the center of the sphere.
  2. If you are INSIDE a hollow sphere, the force of gravity is zero, no matter how much mass the sphere has.
  3. If you approach a flat plate infinite in extent, the attraction depends only on its thickness, not how far away from it you are.
Here's a lab for you:

    Problem: given that the earth has a radius of about R= 6370 km, and given the formula for g above, and fact #1, find the mass of the earth. Since you are given big-G, and R, all you need to know is little-g, the acceleration of gravity at the surface of the earth to solve for m. So the trick is to measure g. If you drop a ball from some height, neglecting drag, the height of the ball is given by:
    y=0.5 g t^2 + vt + y0, where y is the height, v is the velocity at the start, and y0 is the height at the start. So, if you drop a ball from a known height (y0=0) with no velocity (v=0), and you measure how long it takes (t) to fall some distance y, then you can solve for g: g=y/(0.5 t^2).
    Use a heavy ball - like a steel ball bearing, or a croquet ball - heavier the better because of drag slowing it down. The farther you can drop it, the better you can measure the time, but the faster it goes, the more drag there is, and the ball will not be traveling as fast as it should be. So maybe drop it down an inside flight of stairs, measuring at each landing, if possible, then graphing the time vs the distance the ball falls, which should be t=sqrt(2 y /g). To check, g should be 9.8 m/sec^2.
    Watch your students! The ball can get moving very fast and possiblly hurt somebody. Good idea is to have it land in a bucket of sand at the bottom so it doesn't bounce. Measuring time is not easy, but you don't have to be too accurate to get a reasonable number.
    Once you have g, you can solve for the mass of the earth, which should be about 4x10^24 kg.

Dr. Fred Duennebier, Professor
Department of Geology and Geophysics
University of Hawaii, Honolulu, HI 96822

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