Answer
A) The counterweight needs to be 2.3m away from the crane.
B) The maximum load that can be lifted is 4200kg.
Work Step by Step
Part A) Let x be the distance between the counterweight and the crane. To determine the distance, we will sum the torques about any point on the main crane shaft;
$(+ \circlearrowleft) \sum\tau=0$
$9500kg*x-2800kg*7.7m=0$
$x=\frac{2800kg*7.7m}{9500kg}$
$x\approx2.3m$
The counterweight needs to be 2.3m away from the crane.
Part B) We set x to be 3.4m and then solve for the maximum load possible by again summing the torques about the crane. Let M be the mass of the load to be lifted.
$(+ \circlearrowleft) \sum\tau=0$
$9500kg*3.4m-7.7m*M=0$
$M=\frac{9500kg*3.4m}{7.7m}$
$M\approx4200kg$
The maximum load that can be lifted is 4200kg.
