The answer is:
The second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.
Since we are given two forces acting at distance, torque will be created. We are given two forces and one distance, so, to calculate the other distance required to balance the system (solve this fulcrum problem), we need to write the following equation:
[tex]Torque_{1}=Torque_{2}[/tex]
Where,
[tex]Torque=F*Distance[/tex]
We are given,
[tex]Force_{1}=Weight_{1}=150lb\\Force_{2}=Weight_{2}=30lb\\distance_{1}=15ft\\[/tex]
So, substituting and calculating, we have:
[tex]Torque_{1}=Torque_{2}[/tex]
[tex]Weight_{1}*distance_{1}=Weight_{2}*distance_{2}[/tex]
[tex]150lb*15ft=300lb*distance_{2}[/tex]
[tex]distance_{2}=\frac{150lb*15ft}{300lb}=7.5ft[/tex]
Hence, the second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.
It's a logical solution since the second force is twice the first force and it means that the second distance must be equal to half the first distance in order to maintain the equilibrium condition.
Have a nice day!
