A boy of mass 25.5 kg is sitting on one side of a seesaw while his older sister,

Question

A boy of mass 25.5 kg is sitting on one side of a seesaw while his older sister, who has a mass of 33.0 kg, is sitting on the other side. Each child is 1.80 m from the center of the seesaw. (Assume that the positive direction is from the center towards the sister.) (a) Where is the center of mass of the two children relative to the center of the seesaw? (Indicate the direction with the sign of your answer.) (b) The older sister moves so that the center of mass of the two children is directly above the center of the seesaw. How far did she move and in which direction? Did she move closer to or further from the center? (Indicate the direction with the sign of your answer.)

Explanation / Answer

if we take center of see saw as origin (0,0)

then co ordinates of boy = (-1.8,0)

co ordintes of sister = (1.8,0)

Xcom = (33(1.8) +25.5(-1.8))/(25.5+33) =0.23

so the center of mass is 0.23 m towards sister from the center

b) let the new distance of older sister from center be x

as the center of mass is at the origin

0 = (33(x) - 25.5(1.8))/58.5

that gives x =1.39

so the sister has to move 1.8 -1.39 = 0.41m towards the center

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