Bubba takes a uniform board of length L = 1.34 m and mass mB = 2.85 kg and nails

Question

Bubba takes a uniform board of length L = 1.34 m and mass mB = 2.85 kg and
nails three round objects to it. The first object, mass m1 = 3.03 kg is nailed a
distance d1 = 17.6 cm from the left end of the board. Mass m3 = 2.14 kg is nailed a
distance d3 = 11.6 cm from the right end of the board. Mass m2 = 1.78 kg is nailed
a distance d2 = 26.3 cm from mass m3, as shown below. Determine the location of
the center of mass of the entire system. Indicate from which end that you were
measuring the center of mass (left or right end).
(Note that the center of mass of the board itself is at its geometric center.)

Explanation / Answer

length of the board L = 1.34 m mass of the board M = 2.85 kg center of mass position of the board from left end  x = L / 2 = 0.67 m mass m1 = 3.03 kg distance of m1 from left end x1 = 17.6 cm = 0.176 m mass m3 = 2.14 kg distance of m3 from right end x ' = 11.6 cm = 0.116 m distance of m3 from left end x3 = 1.34 m - 0.116 m                                                 = 1.224 m mass m2= 1.78 kg distance of the m2 from left of m3 is x" = 26.3 cm =0.263 m distance of m2 from right end = 0.116 m + 0.263 m = 0.379 m distance of m2 from left end x2 = 1.34 m - 0.379 m = 0.961 m center of mass position X = [ Mx +m1x1+m2x2+m3x3 ] / [ M + m1+m2+m3]                                          = 0.691 m from left end length of the board L = 1.34 m mass of the board M = 2.85 kg center of mass position of the board from left end  x = L / 2 = 0.67 m mass m1 = 3.03 kg distance of m1 from left end x1 = 17.6 cm = 0.176 m mass m3 = 2.14 kg distance of m3 from right end x ' = 11.6 cm = 0.116 m distance of m3 from left end x3 = 1.34 m - 0.116 m                                                 = 1.224 m mass m2= 1.78 kg distance of the m2 from left of m3 is x" = 26.3 cm =0.263 m distance of m2 from right end = 0.116 m + 0.263 m = 0.379 m distance of m2 from left end x2 = 1.34 m - 0.379 m = 0.961 m center of mass position X = [ Mx +m1x1+m2x2+m3x3 ] / [ M + m1+m2+m3]                                          = 0.691 m from left end

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