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 2.5 kg. The first stick is located on the x-axis and is placed from x = 0 to x = 1.3 m. The second stick is located on the y-axis and is placed from y = 0 to y = 1.3 m. The third stick is placed along the x-axis from x = 1.3 m to x = 2.6 m.
(a)
Calculate the location of the centre of mass of the sticks on the x-axis (x coordinate) in m.
(b)
Calculate the location of the centre of mass of the sticks on the y-axis (y coordinate) in m.
To calculate the location of the center of mass, we need to consider the mass and position of each stick.
(a) To calculate the x-coordinate of the center of mass, we can use the formula:
xcm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
Where:
- m1, m2, and m3 are the masses of the three sticks, which are all 2.5 kg.
- x1, x2, and x3 are the positions of the sticks along the x-axis.
From the given information, the positions of the sticks along the x-axis are:
x1 = 0 to x1 = 1.3 m
x2 = 1.3 m (located on the y-axis)
x3 = 1.3 m to x3 = 2.6 m
Using the formula, we can calculate the x-coordinate of the center of mass:
xcm = (2.5 kg * (0 + 1.3 m) + 2.5 kg * 1.3 m + 2.5 kg * (1.3 m + 2.6 m)) / (2.5 kg + 2.5 kg + 2.5 kg)
Simplifying the equation:
xcm = (3.25 m + 2.5 m + 9.75 m) / 7.5 kg
xcm = 15.5 m / 7.5 kg
xcm ≈ 2.067 m
Therefore, the x-coordinate of the center of mass of the sticks is approximately 2.067 m.
(b) Similarly, to calculate the y-coordinate of the center of mass, we can use the formula:
ycm = (m1y1 + m2y2) / (m1 + m2)
Where:
- m1 and m2 are the masses of the sticks on the y-axis, which are both 2.5 kg.
- y1 and y2 are the positions of the sticks along the y-axis.
From the given information, the positions of the sticks along the y-axis are:
y1 = 0 to y1 = 1.3 m
y2 = 1.3 m (located on the x-axis)
Using the formula, we can calculate the y-coordinate of the center of mass:
ycm = (2.5 kg * (0 + 1.3 m) + 2.5 kg * 1.3 m) / (2.5 kg + 2.5 kg)
Simplifying the equation:
ycm = (3.25 m + 3.25 m) / 5 kg
ycm = 6.5 m / 5 kg
ycm = 1.3 m
Therefore, the y-coordinate of the center of mass of the sticks is 1.3 m.