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The Expert TA : Human | ? My Courses-Blackboard l' | + ot2016px × ? y.thee %) Problem 6: Three beads are placed along a thin rod. The first bead, of mass m1-21 g. is placed a distance dy-8.55 cm from the left end of the rod. The second bead, of mass m-I1g. is placed a distance d- 1.8 cm to the right of the first bead. The third bead, of mass IM-58 g. is placed a distance ds-4.9 cm to the right of the second bead Assume an x-axis that points to the right m2 Otheespertta.com Part (a) Write a symbolic equation for the location of the center of mass of the three beads relative to the left end of the rod, in terms 25% of the variables given in the problem statement Grade Summary Potential 91% Submissions Attempts remaning ds 12 3 Subent Hant Feedback:-dedactin-aback !i Part (b) Find the cester of mass, in cestimeters, relative to the left end of the rod 25% Part (c) Write symbolic 25 e center of mass of the three beads relatirve to the center bead, in terms of the variables gven in the problem statement 25% Part (d: Find the center of mass, centimeters. relative to the middle bead

Explanation / Answer

(a)

Center of mass is given by,

com = m1x1 + m2x2 + m3x3 / (m1 + m2 + m3)

Here, Center of mass relative to left end of the rod,

com = [m1*d1 + m2*(d1 + d2) + m3*(d1 + d2 + d3)] / [m1 + m2 + m3]

(b)

Put the vaues in above forula,

com = [0.021*0.0055 + 0.011*(0.0235) + 0.058*(0.0725)] / (0.021 + 0.011 + 0.058)

com = 0.0508 m

com = 5.08 cm

(c)

Center of mass relative to center bead,

com =  [m1*-d2 + m2*0 + m3*d3] / [m1 + m2 + m3]

(d)

Center of mass relative to center (middle) bead,

com =  [0.021 * -0.018 + 0 + 0.058 * 0.049] / (0.021 + 0.011 + 0.058)

com = 0.0273 m

com = 2.73 cm

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