Torque Question

Question

A) A 372.4 N child and a 262.5 N child sit on either end of a 3.5 m long seesaw. How far from the 372.4 N child should the pivot be placed to ensure rotational equilibrium? Disregard the mass of the seesaw. Answer in units of m.

B) Suppose a 340 N child sits 0.284 m from the 372.4 N child. How far from the pivot must a 302 N child sit to maintain rotational equilibrium? Answer in units of m.

Answer 1

a) Draw a sketch:

Write the torque balance equation (clockwise torque is positive):

262.5(3.5 - x) - 372.4x = 0 (for rotational equilibrium)

918.75 - 262.5x - 372.4x = 0

918.75 = 634.9x

x = 1.447 m or, when rounded appropriately, x = 1.4 m

B) Repeat the process:

Let "x" be the distance from the pivot point to the 302 N child

From question a), we know that the 372.4 N child is 1.447 m from the pivot point and the 262.5 child is 3.5 - 1.447 or 2.053 m from the pivot point. Since the 340 N child is 0.284 m from the 372.4 N child, we know they are 1.447 - 0.284 or 1.163 m from the pivot point:

262.5(2.053) + 302x - 372.4(1.447) - 340(1.163) = 0

538.892 + 302x - 538.892 - 395.447 = 0

302x = 395.447

x = 1.309 m or when rounded appropriately, x = 1.3 m