Question

A 60 kg mass and a 20 kg mass are separated by 10 m. At what point on a line joining these charges will another mass experience zero resultant force?

Answer 1

A 60 kg mass and a 20 kg mass are separated by 10 m. At what point on a line joining these charges will another mass experience zero resultant force?

Solution

$$m _ {1} = 6 0 \mathrm {k g}, m _ {2} = 2 0 \mathrm {k g}$$ $$F _ {2 0} = F _ {6 0} \rightarrow \frac {m m _ {1}}{x ^ {2}} = \frac {m m _ {2}}{(1 0 - x) ^ {2}} \rightarrow x ^ {2} m _ {2} = m _ {1} (1 0 - x) ^ {2} \rightarrow x = \sqrt {\frac {6 0}{2 0}} (1 0 - x)$$ $$x = 1. 7 3 2 (1 0 - x) \rightarrow x = 1 7. 3 2 - 1. 7 3 2 x \rightarrow x = \frac {1 7 . 3 2}{2 . 7 3 2} = 6. 3 4$$

Answer: $x = 6.34\mathrm{m}$ from the 60-kg mass.