A uniform rod of length 176 cm is bent at its midpoint into a right angle. Then the bent rod is placed along the negative x and positive y axes, with the "bend point" located at the origin. What are the x and y coordinates of the center of mass of this object?
my thoughts were that the coordinates were just (.44, .44) but it's incorrect. can someone help?
the cm along the x axis is 1/2 (-176/2) or -.44 m, and along the y axis .44m
You missed the sign.
Why is it negative?
I just plugged them into the computer, and it isn't accepting that answer. (-.44m, .44m), that is.
Perhaps they want the answer in cm.
The x coordinate of the C.M. is negative because half of the bent rod is in the -x region and the other half is along the x=0 axis.
I definitely missed that. Thanks.
I got an answer of -22 cm on x, and 22cm on y, put it into the computer, and it's right.
To find the center of mass of the bent rod, we need to consider the distribution of mass along its length.
Let's assume that the rod has uniform linear density, which means the mass per unit length is constant.
To solve the problem, we divide the rod into two parts: the lower part (lying along the negative x-axis) and the upper part (lying along the positive y-axis).
The length of each part is half of the total length of the rod, which is 176 cm divided by 2, equal to 88 cm.
Now, let's calculate the x-coordinate of the center of mass:
For the lower part, its mass is proportional to its length, which is 88 cm. Thus, its mass is 88cm times the linear density.
For the lower part, the x-coordinate of its center of mass is at the midpoint of its length, which is at x = -88/2 = -44 cm.
For the upper part, its mass is also proportional to its length, which is again 88 cm.
For the upper part, the x-coordinate of its center of mass is at the end of the rod, which is x = 0 cm.
Next, we need to calculate the y-coordinate of the center of mass:
For both the lower and upper parts, their y-coordinates of the center of mass are at the midpoint of their respective lengths. Since the lengths of both parts are the same, their y-coordinates of the center of mass are equal.
The center of mass of the lower and upper parts of the rod lie on the y-axis, so their x-coordinates are both zero.
Now, we can calculate the overall center of mass:
To find the x-coordinate of the center of mass, we use the principle of moments. The total moment about the y-axis must be zero since the rod is in equilibrium:
(88 cm) * (-44 cm) + (88 cm) * (0 cm) = 0
Simplifying:
-44 * 88 = 0
From this, we find that the x-coordinate of the center of mass is 0.
Finally, since the y-coordinate of the center of mass is at the midpoint of the lengths of both parts, it is equal to half of the length of each part:
(88 cm) / 2 = 44 cm
Therefore, the coordinates of the center of mass of the bent rod are (0, 44).