Answer to Question #107622 in Mechanics | Relativity for Daniel Felipe

Question

You and your little brother are shifting a large 58 kg rock by carrying it together on a 3.0 m long litter.
Your little brother is capable of exerting an upwards force of 100 N on one end of the litter.

How far should the rock be placed from you in order for you and your brother to carry the litter without it tipping? (in m to 2 s.f)

Answer 1

On this picture $F_1$ is the force you provide, $100 N$ is the force of your brouther and $mg = 58*10 = 580N$ is the weight of the stone. $h_1$ and $h_2$ are corresponding shoulders.

In order to prevent  litter move up or down, all three forces must be balanced:

$F_1 + 100 = 580 \Rightarrow F_1 = 480N$

In order to prevent the litter to tip the angular momentum with respect to the left point of revolution should be balanced:

$580\cdot h_1 = 100\cdot 3 \Rightarrow h_1 \approx0.52$

Answer. The rock should be placed at the distance 0.52 m from you.