When using center of gravity to solve for an unknown variable, the general form used is:
(weight_"1")*(displacement_"1")=(weight_"2")*(displacement_"2")(weight1)⋅(displacement1)=(weight2)⋅(displacement2)
It's very important to note that the displacements, or distances, used are relating to the distance the weight is from the fulcrum (the point the object is balanced at). That being said, since the axis of rotation is at 45"cm":45cm:
45"cm"-12"cm"=33"cm"45cm−12cm=33cm color(blue)(" Fulcrum" - "distance" = "displacement" Fulcrum−distance=displacement
5"g"*2=10"g"5g⋅2=10g color(blue)(" 2 coins of 5g each = 10g") 2 coins of 5g each = 10g
It's important to remember that we can't neglect the original center of gravity of 50"cm"50cm, meaning that since there was a 5"cm"5cm shift:
(50"cm"-45"cm") = 5"cm"(50cm−45cm)=5cm color(blue)("Displacement due to coins")Displacement due to coins
So, to follow our original equation of
(weight_"1")*(displacement_"1")=(weight_"2")*(displacement_"2")(weight1)⋅(displacement1)=(weight2)⋅(displacement2)
We substitute with:
(10"g")*(33"cm") = (weight_"2")*(5"cm")(10g)⋅(33cm)=(weight2)⋅(5cm)
(330g*cm)=(5"cm")(weight_"2")(330g⋅cm)=(5cm)(weight2) color(blue)("Solve for unknown weight")Solve for unknown weight
(weight_"2")=66"g"(weight2)=66g color(blue) ((
330"g"* cancel("cm"))/ (5cancel("cm")))