Question

A thin solid rod of mass M and length L is connected to a wall by a hinge and hangs from the ceiling by a string which connects to the end of the rod at an angle of 30 degrees. The center of mass of the rod is located halfway from the hinge, and a block of mass m is placed on the rod 3/4 of the way from the hinge.

the string used to suspend the rod can support a maximum tension of 60N without breaking. If m=2kg and M=3kg, and using g=10m/s^2, what is the farther from the hinge that the block can be placed without breaking the string?

Answer 1

Sum of moments at the hinge:

$-\frac{1}{2}LMg-xmg+L\sin (30)60=0$

$x=\frac{(-0.5*3(10)+0.5*60)L}{2(10)}\rightarrow x_{max}=\frac{3}{4}L$