Question

D) A system consists of the following masses in the xyz plane: 4.0kg at coordinates (0m, 5m, 1m), 7kg at (3m, 8m, 2m),and 5.0kg at (-3m, -6m, -4m). Find the position of its center of mass. (6marks)

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Answer 1

the answer is above (5798. m)

Step-by-step explanation:

check it

Answer 2

To find the position of the center of mass of a system of point masses, you need to use the following formula1:

rcm​= ∑i=1n​mi / ​∑i=1n​mi​ri​​

where mi​ is the mass of the i-th point and ri​ is its position vector.

In your case, you have three point masses in the xyz plane, so you need to find the x, y, and z components of the center of mass separately. For example, the x component is given by:

xcm​=∑i=13​mi​∑i=13​mi​xi​​=4+7+54(0)+7(3)+5(−3)​=166​=0.375

Similarly, you can find the y and z components by replacing the x coordinates with the y and z coordinates, respectively. The final answer is:

rcm​=(0.375,0.75,−0.375)

This means that the center of mass of the system is located at the point (0.375, 0.75, -0.375) in the xyz plane.

I hope this helps you understand how to solve this problem. Have a nice day!