Question

A person carries a plank of wood 1.6 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at 43 cm from the end of the plank with force F2. If the plank has a mass of 13.7 kg and its center of gravity is at the middle of the plank, what is the force F1

Answer 1

Answer: $115.52\ N$

Explanation:

Given

Length of plank is 1.6 m

Force $F_1$ is applied on the left side of plank

Force $F_2$ is applied 43 cm from the left end O.

Mass of the plank is $m=13.7\ kg$

for equilibrium

Net torque must be zero. Taking torque about left side of the plank

$\Rightarrow mg\times 0.8-F_2\times 0.43=0\\\\\Rightarrow F_2=\dfrac{13.7\times 9.8\times 0.8}{0.43}\\\\\Rightarrow F_2=249.78\ N$

Net vertical force must be zero on the plank

$\Rightarrow F_1+W-F_2=0\\\Rightarrow F_1=F_2-W\\\Rightarrow F_1=249.78-13.7\times 9.8\\\Rightarrow F_1=115.52\ N$