Question

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

Answer 1

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(cos 40^@, sin 40^@)`
`vec F_B = 2.8(-cos 50^@, sin 50^@)`
`vec F_G = m g (0,-1)`
`vec F = f(-1,0)`

`O = (0,0)`
`A = (0,1)`
`B = (2.5,1)`
`G =(x_G,y_G)` 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 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`