In Fig. 13-23, two particles, of masses m and 2m, are fixed in place on an axis,
ID: 2200364 • Letter: I
Question
In Fig. 13-23, two particles, of masses m and 2m, are fixed in place on an axis, Where on the axis can a third particle of mass 3m be placed (other than at infinity) so that the net gravitational force on it from the first two particles is zero: to the left of the first two particles, to their right, between them but closer to the more massive particle, or between them but closer to the less massive particle? Does the answer change if the third particle has, instead, a mass of 16m? Is there a point off the axis (other than infinity) at which the net force on the third particle would be zero?Explanation / Answer
(a) forces can only be balanced at a point between the two masses, since they both pull (attract.) And to balance the two forces, the point would have to be closer to the smaller mass.
So... BETWEEN THEM AND CLOSER TO THE LESS MASSIVE PARTICLE
(b) No, the mass of the third particle does not matter, only the relative masses of the two fixed particles.
(c) NO, there is no off-axis point where the forces can be balanced. This is because both fixed particles atttract the third particle, so they would pull in the same direction perpendicular to the axis (e.g. the "y" direction) and those forces could not balance each other.