Answer:
The location of the center of mass of the system is approximately 117.31 cm.
Step-by-step explanation:
To find the center of mass of a system of two objects, you need to consider both their masses and positions. The center of mass (CM) can be calculated using the formula:
CM = (m1 * x1 + m2 * x2) / (m1 + m2)
Where:
CM is the center of mass position
m1 and m2 are the masses of the two objects
x1 and x2 are the positions of the two objects
Given:
m1 = mass of the first object
m2 = 6/7 * m1 (mass of the second object is 6/7 times the mass of the first object)
x1 = 73 cm (position of the first object)
x2 = 169 cm (position of the second object)
Let's plug in the values and calculate:
CM = (m1 * x1 + m2 * x2) / (m1 + m2)
Substitute the value of m2:
m2 = 6/7 * m1
CM = (m1 * x1 + (6/7 * m1) * x2) / (m1 + 6/7 * m1)
Simplify the expression:
CM = (7m1x1 + 6m1x2) / (7m1 + 6m1)
CM = (7x1 + 6x2) / 13
Now, plug in the values of x1 and x2:
x1 = 73 cm
x2 = 169 cm
CM = (7 * 73 + 6 * 169) / 13
CM = (511 + 1014) / 13
CM = 1525 / 13
CM ≈ 117.31 cm
So, the location of the center of mass of the system is approximately 117.31 cm.