Scales Lumber

Center of Gravity PHYSICS Question!!?! equilibrium Please help me figure it out!?

You have a turkey to cook for Thanksgiving. It came with no label. Betty Crocker told you to cook it ___ many hours for an 8 pound turkey, ___ many hours for a 10 pound turkey, and so on and so forth. But you don't have a scale. Let's say you take a two by four (piece of lumber) and balance it on the arm of your sofa. You then take a brand new,
unopened 5 [lb] bag of sugar and place it 74 [cm] from the sofa arm.
The sugar/board/turkey system balances when you place the turkey 37 [cm] from the sofa arm.
How much does the turkey weigh?

Let weight of turkey = w
Let us calculate torques along the soft arm.
Torque by w has magnitude = w * 37 cm
Torque by sugar bag's weight has magnitude = 5 lb * 74 cm
The two torques are in opposite direction. There is balance. Therefore, total torque = 0
Therefore,
w * 37 cm = 5 lb * 74 cm
Or w= 5 * 74/37 lb = 5 * 2 lb = 10 lb
Ans: 10 lb

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