Answer to Question #88886 in Mechanics | Relativity for Taylor

Question

Three balls (mA=15kg, mB=12kg, mC=35kg) are places at the corners of a right angle triangle as shown. Ball A is directly north of ball B and ball C is directly east of ball B. Calculate the net force on ball B due to the presence of the other two balls. Write out all formulas, free body diagrams and calculations to get full marks

Answer 1

The force on ball B because of ball A is

$$F_{BA}=G\frac{M_AM_B}{R_{AB}^2}=\frac{1.2\cdot10^{-8}}{R_{AB}^2}\text{ N}.$$

The force on ball B because of ball C is

$$F_{BA}=G\frac{M_CM_B}{R_{CB}^2}=\frac{2.8\cdot10^{-8}}{R_{BC}^2}\text{ N}.$$

The net force produced by these two forces:

$$F_N=\sqrt{F_{BA}^2+F_{BC}^2}=10^{-8}\sqrt{\frac{1.44}{R_{AB}^4}+\frac{7.84}{R_{BC}^4}}\text{ N}.$$