Three balls with masses of 4 g, 6 g, and 4 g,respectively, are connected by massless rods. The balls are located (in meter intervals).What is the x-coordinate of the center of mass?

Answer in units of m

To find the x-coordinate of the center of mass, we need to calculate the weighted average of the x-coordinates of the individual masses.

Let's assume that the balls are located at x1, x2, and x3.

The center of mass equation is given by:

x_cm = (m1*x1 + m2*x2 + m3*x3) / (m1 + m2 + m3)

where m1, m2, and m3 are the masses of the balls.

In this case, the masses are 4 g, 6 g, and 4 g, respectively.

Converting the masses to kilograms:

m1 = 4 g = 4/1000 kg = 0.004 kg
m2 = 6 g = 6/1000 kg = 0.006 kg
m3 = 4 g = 4/1000 kg = 0.004 kg

Let's assume that the balls are located at x1 = 0 m, x2 = 1 m, and x3 = 2 m.

Plugging in the values into the equation:

x_cm = (0.004 kg * 0 m + 0.006 kg * 1 m + 0.004 kg * 2 m) / (0.004 kg + 0.006 kg + 0.004 kg)

Simplifying the equation:

x_cm = (0 + 0.006 kg + 0.008 kg) / 0.014 kg

x_cm = 0.014 kg / 0.014 kg

x_cm = 1 m

Therefore, the x-coordinate of the center of mass is 1 m.

To find the x-coordinate of the center of mass, we need to calculate the weighted average of the x-coordinates of the individual masses.

The x-coordinate of the center of mass (x_c) can be found using the formula:

x_c = (m1 * x1 + m2 * x2 + m3 * x3) / (m1 + m2 + m3)

Where m1, m2, and m3 are the masses of the balls, and x1, x2, and x3 are their respective x-coordinates.

Given:
m1 = 4 g = 0.004 kg
m2 = 6 g = 0.006 kg
m3 = 4 g = 0.004 kg

Let's assume the x-coordinate of the leftmost ball is 0 m, so x1 = 0 m.
As the balls are connected by massless rods, the distances between the balls will remain constant. Let's consider the distance between the leftmost and middle ball to be 0.5 m. So x2 = 0.5 m. Similarly, let's assume the distance between the middle and rightmost ball is also 0.5 m. Therefore, x3 = 1 m.

Now, we can substitute the values into the formula:

x_c = (0.004 kg * 0 m + 0.006 kg * 0.5 m + 0.004 kg * 1 m) / (0.004 kg + 0.006 kg + 0.004 kg)

Simplifying the expression further, we get:

x_c = (0 + 0.003 + 0.004) / 0.014

x_c = 0.007 / 0.014

x_c = 0.5 m

Therefore, the x-coordinate of the center of mass is 0.5 m.

The middle ball is at the center of mass in this case. That is obvious from the symmetry.

What its x-coordinate is depends upon what you choose for the origin of coordinates.