Question

A meterstick is initially balanced on a fulcrum at its midpoint. You have four identical masses. Three of them are placed atop the meterstick at the following locations: 25cm , 43cm , and 99cm .

Answer 1

Where should the fourth mass be placed in order to balance the meterstick?

Answer 2

A meter stick as 100 cm, so the fulcrum would be placed at the 50 cm mark which is it's midpoint. Then we place our mass as so. We then find the moment around the midpoint, some will be negative since it will be providing a negative moment. \[\sum M _{0} = 0 = W _{D}(x) +W_{C}(99cm) - W_{A}(25cm) - W_{B}(43cm)\]we set the equation equal to 0 since we don't want the meter stick to turn or have a moment right? Since all the boxes have identical masses, we can cross out all the Weights(W) and then solve for "x"