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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1 Answer
Mar 21, 2018

Answer:

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#