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

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

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Answer 1 · 2018-03-21T12:00:34

See below.

Explanation:

Assuming

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

Calling

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

$O = (0, 0)$ $O = (0,0)$
$A = (0, 1)$ $A = (0,1)$
$B = (2.5, 1)$ $B = (2.5,1)$
$G = (x_{G}, y_{G})$ $G =(x_G,y_G)$ Brass plate mass center

we have

Null force resultant

${\to F}_{A} + {\to F}_{B} + {\to F}_{G} + \to F = \to 0$ $vec F_A+vec F_B+vec F_G+ vec F = vec 0$

Null resulting moment regarding point $O$ $O$

${\to F}_{A} \times (A - O) + {\to F}_{B} \times (B - O) + {\to F}_{G} \times (G - O) = \to 0$ $vec F_A xx (A-O)+vec F_B xx( B - O) + vec F_G xx (G-O) = vec 0$

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

$f = 0.88 N$
$m = 4.39/g$
$x_G = 1.02$

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

1 Answer

Explanation:

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