How far along the plank, measured from the pivot, can the center of gravity of a

Question

How far along the plank, measured from the pivot, can the center of gravity of an 950kg piece of heavy machinery be placed before the rope snaps?

The figure shows a 100 kg plank supported at its right end by a 7 mm diameter rope with a tensile strength of 6.0 x 10^7 N/m^2.

6.0

How far along the plank, measured from the pivot, can the center of gravity of an 950kg piece of heavy machinery be placed before the rope snaps? The figure shows a 100 kg plank supported at its right end by a 7 mm diameter rope with a tensile strength of 6.0 times 10^7 N/m^2.

Explanation / Answer

Max. possible force that rope can take is =stress * area

= 6*10^7 * (pi/4*0.007^2)

= 2307.9 N

Balancing moment about pivot, 950*9.81*x + 100*9.81*(3.5/2)= 2307.9*3.5

9319.5 X +1716.5 = 8077.65

X = (8077.65-1716.5)/9139.5

x =0.683

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