Anti-Gravity Carpenter's Square
Newton’s law of universal gravitation is sometimes expressed by the equation F = GMm/r2, where r is the distance between two centers of mass. Consider a carpenter’s square with its center of mass at the point C in the space between its two arms. A small spherical body placed at C should produce an infinite attraction because the distance between the centers of mass is zero! Also, one may even place the small sphere closer to the inside corner of the square at A to produce a movement that looks like a repulsion! How does one resolve this dilemma?
Newton’s law of universal gravitation is sometimes expressed by the equation F = GMm/r2, where r is the distance between two centers of mass. Consider a carpenter’s square with its center of mass at the point C in the space between its two arms. A small spherical body placed at C should produce an infinite attraction because the distance between the centers of mass is zero! Also, one may even place the small sphere closer to the inside corner of the square at A to produce a movement that looks like a repulsion! How does one resolve this dilemma?
A) There is no dilemma. This really happens.
A) There is no dilemma. This really happens.
B) Use F = mg since you’re on the earth.
B) Use F = mg since you’re on the earth.
C) Integrate.
C) Integrate.
D) Newton’s laws are false. Einstein proved this so we shouldn’t use them.
D) Newton’s laws are false. Einstein proved this so we shouldn’t use them.
Solution: C. The formula above only works for spheres or objects separated by distances much bigger than their individual sizes. For shapes other than spheres where the distances are not much larger than the individual sizes, you must integrate.
Solution: C. The formula above only works for spheres or objects separated by distances much bigger than their individual sizes. For shapes other than spheres where the distances are not much larger than the individual sizes, you must integrate.
