Answer to Question #188098 in Classical Mechanics for Heide

Question

We have a Cavendish balance set up with two spheres (one small and one large) that are five centimeters apart of masses m = 1 g and m0 = 500 m, respectively. Suppose these design is placed at a point in space far removed from all other bodies. ,→ What is the acceleration a of the body m, and the acceleration a' of the body m' ? [15] ,→ Is this a constant acceleration problem? Explain why or why not!

Answer 1

Given,

$m_1=1g$

$m_2=500g$

$d=5cm=0.05m$

Force between the masses $(F)=\frac{Gm_1 m_2}{r^2}$

$=\frac{6.67\times 10^{-11}\times 10^{-3}\times 0.5}{25\times 10^{-4}}N$

$=0.1334\times 10^{-10}N$

Hence, acceleration of the masses will be $0.1334\times 10^{-7}m/s^2$ and $0.2668\times 10^{-10} m/s$

Both of the masses will apply the equal amount of force on each other. But only smaller block will move towards the larger block because as comparison the the larger block, the mass of the smaller block is negligible.