# A)Detemine the horizontal force (F) required to move the plate across the factory floor.? b) Determine the mass of the plate?

## Mar 21, 2018

See below.

#### Explanation:

Assuming

1) A coordinate system with origin at the force $\vec{F}$ application point
2) Brass plate with unknown mass distribution.

Calling

${\vec{F}}_{A} = 3.5 \left(\cos {40}^{\circ} , \sin {40}^{\circ}\right)$
${\vec{F}}_{B} = 2.8 \left(- \cos {50}^{\circ} , \sin {50}^{\circ}\right)$
${\vec{F}}_{G} = m g \left(0 , - 1\right)$
$\vec{F} = f \left(- 1 , 0\right)$

$O = \left(0 , 0\right)$
$A = \left(0 , 1\right)$
$B = \left(2.5 , 1\right)$
$G = \left({x}_{G} , {y}_{G}\right)$ Brass plate mass center

we have

Null force resultant

${\vec{F}}_{A} + {\vec{F}}_{B} + {\vec{F}}_{G} + \vec{F} = \vec{0}$

Null resulting moment regarding point $O$

${\vec{F}}_{A} \times \left(A - O\right) + {\vec{F}}_{B} \times \left(B - O\right) + {\vec{F}}_{G} \times \left(G - O\right) = \vec{0}$

or equivalently

{(3.5cos 40^@-2.8 cos50^@=f), (3.5sin 40^@+2.8sin 50^@= m g), (3.5 cos 40^@-2.8 cos 50^@-2.5 xx 2.8 sin 50^@+x_G m g = 0):}

Solving for $f , m , {x}_{G}$ we obtain

$f = 0.88 N$
$m = \frac{4.39}{g}$
${x}_{G} = 1.02$