Question

A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at .500 m from the end of the plank with force F2 . If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what is the magnitude of the force F1?

Answer 1

Answer:

$F_1=196\ N$

Explanation:

Given:

• mass of plank, $m=20\ kg$

• force down the end of plank, $F_1$

• force up at 0.5m from the end of plank, $F_2$

For the plank to be in equilibrium the total sum of total forces & moments (about any point) must be zero:

$\Sigma F=0$

&

$\Sigma M=0$

We take the sum of forces:

$F_1+m.g=F_2$

$F_1+20\times 9.8=F_2$

$F_1+196=F_2$ .............................................(1)

Take moment about the extreme right:

$F_2\times 0.5=m.g\times 1$

$F_2=392\ N$

Now, put this value in eq. (1)

$F_1=392-196$

$F_1=196\ N$