Newtonian mechanics

Gravity and weight

Measure the attraction between two masses as m₁, m₂, and distance r vary. Verify the law of gravitation $F=G\,m_1m_2/r^2$ and follow its effect on the orbit.

Middle school

Equipment

3D model of two attracting bodies and their orbit
Mass 1, Mass 2, and Distance sliders
Virtual force readout and Pause button

Procedure

Test the inverse-square law
Hold m₁ = 12, m₂ = 5 and sweep «Distance» through 2, 4, 8. Read the force each time: doubling r quarters F. Quickly plot F against $1/r^2$ — the points fall on a straight line, evidence for $F\propto 1/r^2$ .
Test linearity in each mass
Hold r = 5, vary «Mass 1» from 1 to 20, then «Mass 2» similarly; record F each step. F is proportional to each mass, giving $F=G\,m_1m_2/r^2$ — estimate G from the slope of F versus $m_1m_2/r^2$ .
Watch the orbit as masses change
Toggle «Pause» to follow mass 2 orbiting mass 1. Raising m₂ or shrinking r strengthens the pull and curves the path more; note both bodies move about the common center of mass — the point closer to the heavier body.
Relate to weight at Earth's surface
Predict the free-fall acceleration of a small body near a heavy one: $g=GM/R^2$ with R the distance to the center. Check: double the distance and g quarters — which is why weight measured atop a mountain is less than at its base (though the effect is tiny).

Simulation

Experiment history

Newton published the law of universal gravitation in the Principia (1687): every pair of particles attracts with

F=Gm_1m_2/r^2

. The falling-apple legend marks the insight that one force both holds the Moon in orbit and pulls objects down — Newton verified it by comparing the Moon's acceleration with g at Earth's surface. G was too small to measure in a laboratory until 1798, when Henry Cavendish used a torsion balance to «weigh the Earth»: he measured the attraction between lead spheres and inferred Earth's density within about 1% of the modern value. Newton's law predicted planetary orbits superbly; the small precession of Mercury's perihelion was only explained by Einstein's general relativity in 1915.

Related physicists

Isaac Newton Galileo Galilei

Equipment

Procedure

Simulation

Experiment history

Related physicists

Related library topics