A compound metal bar has 4 kg of copper making up the first third of the bar, while the remainder is made of 12 kg of lead. The bar is 3 meters in length. In addition, a mass of 2 kg is hung 1m from the left end of the bar, and a mass of 6 kg is hung 2m from the left end of the bar.

Question

A compound metal bar has 4 kg of copper making up the first third of the bar, while the remainder is made of 12 kg of lead.  The bar is 3 meters in length.  In addition, a mass of 2 kg is hung 1m from the left end of the bar, and a mass of 6 kg is hung 2m from the left end of the bar.

Where would a single rope have to be tied in order to hang the bar and masses so they would be in complete equilibrium?

bobpursley · Accepted Answer

The cg of the bar is at the 1.5m mark.

Summing moments about the left end.
2*1-Weight*x+16*1.5+6*2=0 check this. Clockwise moments
weight of bar is 16kg+8kg, the string pulls counterclockwise with force weight.
x= (2+24+12)/24= 38/24 m from the left end. check this.