Question

find the central of mass of a 120 cm long rod makde of 60 cm of iron and 60 cm of alluminum density 2.5 g/cm³ express location of the center of mass as measured from the left of the rod

Answer 1

To find the center of mass of the rod, calculate the position of the center of mass for each segment and then combine them.

Step-by-step explanation:

To find the center of mass of the rod, we need to calculate the position of the center of mass for each segment of the rod and then combine them. The center of mass for each segment can be found using the formula: x = (m1 * x1 + m2 * x2) / (m1 + m2), where x is the position of the center of mass, m is the mass, and x1 and x2 are the positions of the segment ends.

For the iron segment, the mass is 60 cm * 2.5 g/cm³ = 150 g = 0.15 kg. The position of the center of mass is x1 = 0 cm and x2 = 60 cm.

For the aluminum segment, the mass is 60 cm * 2.5 g/cm³ = 150 g = 0.15 kg. The position of the center of mass is x1 = 60 cm and x2 = 120 cm.

Combining the center of mass for each segment, we get x = (0.15 kg * 0 cm + 0.15 kg * 60 cm) / (0.15 kg + 0.15 kg) = 30 cm. Therefore, the center of mass is located 30 cm from the left of the rod.