Answer: 4 feet
Step-by-step explanation:
To find the distance Robert must sit from the fulcrum to balance Gene, we must set the torque (T) Robert applies equal to the torque Gene applies, since the torque they apply has to be equal for them to be balanced on the object. This is given by the equation:
[tex]T_{R} = T_{G}[/tex]
Torque is calculated as the product of the force (F) and the distance (d) from the fulcrum:
T = F×d
In this case, Robert and Gene's weights are the forces, and the distances are the distances from each person to the fulcrum. The equation becomes:
[tex]F_{T} d_{T} =F_{G} d_{G}[/tex]
Plugging in Robert and Gene's weights and distances into the formula, we get:
180·[tex]d_{T}[/tex] = 120·6
180·[tex]d_{T}[/tex] = 720
Now, solve for [tex]d_{T}[/tex], the distance from the fulcrum Robert must sit to balance Gene.
[tex]d_{T}[/tex] = 720/180
[tex]d_{T}[/tex] = 4
Therefore, Robert must sit 4 feet from the fulcrum to balance Gene.
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