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

`F_1=196\ N`

Step-by-step 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* 9.8=F_2`

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

Take moment about the extreme right:

`F_2* 0.5=m.g* 1`

`F_2=392\ N`

Now, put this value in eq. (1)

`F_1=392-196`

`F_1=196\ N`