Four very thin rods, each 5.9 m long, are joined to form a square, as part (a) of the drawing shows. The center of mass of the square is located at the coordinate origin. The rod on the right is then removed, as shown in part (b) of the drawing. What are the x- and y-coordinates of the center of mass of the remaining three-rod system?

Well, isn't that a tricky little puzzle! It sounds like we have a square made out of four thin rods, and then one of those rods gets removed. To find the x- and y-coordinates of the center of mass of the remaining three-rods, we'll need to do some calculations.

First, let's label the rods. We'll call the one on the left "A," moving clockwise, we have rods B, C, and D. Each rod has a length of 5.9 m.

Now, to find the x-coordinate of the center of mass of the three-rods system, we can average the x-coordinates of the individual rods. Rod A is at x = -2.95 m, Rod B is at x = 0 m, and Rod D is at x = 2.95 m. So, the x-coordinate of the center of mass is (-2.95 + 0 + 2.95)/3 = 0 m.

Next, let's find the y-coordinate of the center of mass. To do this, we'll also average the y-coordinates of the individual rods. Rod A is at y = 2.95 m, Rod B is at y = -2.95 m, and Rod C is at y = -2.95 m. So, the y-coordinate of the center of mass is (2.95 - 2.95 - 2.95)/3 = -0.95 m.

Therefore, the x-coordinate of the center of mass of the remaining three-rods system is 0 m, and the y-coordinate is -0.95 m. Voila!

To find the x- and y-coordinates of the center of mass of the remaining three-rod system, we can use the principle of symmetry.

In the original square configuration (part (a) of the drawing), each rod is identical and symmetrically placed. Therefore, the x-coordinate of the center of mass will be at the origin (0,0).

Now, when the rod on the right is removed (part (b) of the drawing), we can see that the symmetry is maintained in the x-direction, but not in the y-direction.

Since the three remaining rods are identical, the y-coordinate of the center of mass will be the average of the y-coordinates of the remaining rods.

Let's label the rods as follows:
A B C
-- -- --

From the symmetry in the x-direction, the x-coordinate of the center of mass remains 0.

To find the y-coordinate of the center of mass, we need to find the average of the y-coordinates of the remaining rods (A, B, C).

The y-coordinate of rod A is 0 since it is symmetrically placed about the origin.
The y-coordinate of rod B is also 0 since it is identical to rod A.
The y-coordinate of rod C can be calculated by splitting rod C into two halves and finding the center of mass of each half.

Considering that rod C is 5.9 m long, the center of mass of the left half (from the origin to the midpoint) would be at (0, 5.9/2) and the center of mass of the right half (from the midpoint to the end) would also be at (0, 5.9/2) due to symmetry.

Therefore, the y-coordinate of the center of mass of rod C is the average of the two halves:
y-coordinate of rod C = (5.9/2 + 5.9/2)/2 = 5.9/4 = 1.475

Since rods A and B have y-coordinate 0, and rod C has y-coordinate 1.475, the average of these three y-coordinates gives us the y-coordinate of the center of mass of the remaining three-rod system:

y-coordinate of center of mass = (0 + 0 + 1.475)/3 = 0.4917

Therefore, the x-coordinate is 0 and the y-coordinate is 0.4917 (approximately) for the center of mass of the remaining three-rod system.

To find the x- and y-coordinates of the center of mass of the remaining three-rod system, we need to consider the distribution of mass along each rod and the geometry of the system.

Let's assume that each rod has uniform mass distribution along its length, which means the mass is evenly distributed.

In part (a) of the drawing, the square is formed by joining four equal-length rods to form a closed shape. Since the center of mass of a square is at its geometrical center, the center of mass of the square is located at the coordinate origin (0, 0).

Now, in part (b) of the drawing, we remove one of the four rods. We are left with three rods forming an open shape.

To determine the new center of mass, we need to find the x- and y-coordinates by taking into account the mass distribution along each rod.

Since the rods are identical and have the same length, we can conclude that the remaining three rods are symmetric about the y-axis. The vertical line passing through the center of mass will also pass through the y-axis.

Therefore, the x-coordinate of the center of mass of the remaining three-rod system is 0.

Now, let's consider the y-coordinate of the center of mass. Since all three rods are identical, their masses are the same. Therefore, the y-coordinate of the center of mass will be at the midpoint of the y-coordinate of each rod.

Each rod has a length of 5.9 m, so the y-coordinate of the center of mass will be located at (0, 5.9/2) = (0, 2.95).

In conclusion, the x-coordinate of the center of mass is 0, and the y-coordinate of the center of mass is 2.95.