A weightless rod, with length d = 5.5 m, supports three weights with masses m1 = 3 kg, m2 = 14 kg, and m3 = 4 kg as shown. Where is its center of gravity?

To determine the center of gravity of the weightless rod with the three weights, we need to calculate the position of the center of gravity. The center of gravity is essentially the point where the rod can balance perfectly.

The position of the center of gravity can be found using the principle of moments. The principle of moments states that the sum of the moments of forces acting on an object is equal to zero in equilibrium.

To get the answer, we need to calculate the moments of each weight and find their resultant moment.

1. Start by assigning a coordinate system. Let's assume that the left end of the rod is at position x = 0 and the right end of the rod is at position x = d.

2. Calculate the moment of each weight about the left end of the rod. The moment (M) of a weight is given by the product of its mass (m) and the distance (r) from the weight to the left end of the rod:

M1 = m1 * r1
M2 = m2 * r2
M3 = m3 * r3

Here, r1 is the distance of the first weight from the left end of the rod, r2 is the distance of the second weight from the left end of the rod, and r3 is the distance of the third weight from the left end of the rod.

3. Calculate the total moment by summing up the moments of all three weights:

Total Moment = M1 + M2 + M3

4. Calculate the position of the center of gravity (x_cg) by dividing the total moment by the sum of the masses of the weights (m_total):

x_cg = (Total Moment) / (m_total)

Here, m_total is the sum of the masses of all three weights: m_total = m1 + m2 + m3

Once you have calculated x_cg, you will have the position of the center of gravity. The center of gravity is the distance x_cg from the left end of the rod.

Please provide the distances r1, r2, and r3, and I can help you calculate the center of gravity.