Question

In order to construct a fort in your backyard, it is critical that you calculate location of the centre of mass of three sticks in particular, each of which is identical with mass 3.4 kg. The first stick is located on the x-axis and is placed from x = 0 to x = 1.7 m. The second stick is located on the y-axis and is placed from y = 0 to y = 1.7 m. The third stick is placed along the x-axis from x = 1.7 m to x = 3.4 m.

(a) Calculate the location of the centre of mass of the sticks on the x-axis (x coordinate) in m.
a. 0.96 m
b. 0.57 m
c. 0.28 m
d. 1.13 m
(b) Calculate the location of the centre of mass of the sticks on the y-axis (y coordinate) in m.
a. 0.48 m
b. 0.28 m
c. 0.85 m
d. 0.57 m

Answer 1

The center of mass for the sticks on the x-axis is 0.85 m, and for the y-axis, it is 0.28 m. The calculation is made using the weighted average position of all the masses involved. Therefore, the correct answers are: (a) 0.85 m and (b) 0.28 m.

Step-by-step explanation:

The problem at hand is a classic Physics question that involves calculating the center of mass of a system. To find the center of mass along the x-axis for the three identical sticks, we need to use the formula for the center of mass of a system, which is the weighted average position of all the masses involved.

For the x-coordinate of the center of mass (xcm):
xcm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
Since the sticks are identical and evenly placed, we can simplify:
xcm = (3.4 kg * 0.85 m + 3.4 kg * 1.7 m) / (3 * 3.4 kg)
xcm = (2.89 + 5.78) / 10.2
xcm = 0.85 m

For the y-coordinate of the center of mass (ycm), since only one stick contributes to the y-position:
ycm = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
ycm = (3.4 kg * 0.85 m) / (3 * 3.4 kg)
ycm = 0.85 m / 3
ycm = 0.28 m

Therefore, the correct answers are: (a) 0.85 m and (b) 0.28 m.