Question

In order to construct a fort in your backyard, it is critical that you calculate location of the center of mass of three sticks in particular, each of which is identical with mass 3.6 kg. The first stick is located on the x-axis and is placed from x = 0 to x = 2 m. The second stick is located on the y-axis and is placed from y = 0 to y = 2 m. The third stick is placed along the x-axis from x = 2 m to x = 4 m. a) Calculate the location of the center of mass of the sticks on the x-axis (x coordinate) in m.

Answer: 1.333

b) Calculate the location of the center of mass of the sticks on the y-axis (y coordinate) in m.

Answer: 0.333

Could you please help me by writing a clear full solution?

Answer 1

COM (Center of Mass) of each stick will be at

for a stick of length L, COM will be at L/2

for first stick

COM will be at x = (0 + 2)/2 = 1 m

for first stick

COM will be at x = (0 + 2)/2 = 1 m & y = 0

for 2nd stick

COM will be at x = 0 & y = (0 + 2)/2 = 1 m

for 3rd stick

COM will be at x = (2 + 4)/2 = 3 m & y = 0

Now COM of All sticks will be given by:

At x-axis

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

Since m1 = m2 = m3 = m

X = m*(x1 + x2 + x3)/3m = (x1 + x2 + x3)/3

X = (1 + 0 + 3)/3 = 1.333 m

Similarly at y-axis

Y = m*(y1 + y2 + y3)/3m = (y1 + y2 + y3)/3

Y = (0 + 1 + 0)/3 = 0.333

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