High School

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Four objects are situated along the y-axis as follows:

- A 197 g object is at +3.10 m
- A 2.90 kg object is at +2.53 m
- A 2.41 kg object is at the origin (0 m)
- A 4.08 kg object is at -0.493 m

Where is the center of mass of these objects?

Answer :

Using the formula Yc = (Σmiyi) / (Σmi), where 'mi' is the mass and 'yi' is the position of the mass in the system, we computed the precise center of mass which is 9587 grams.

The subject of this question falls under the topic of center of mass.

The center of mass of an object, or a system of objects, is the average position of all the mass in the system and can be found by summing up the multiplication of mass and position of each object, and divided by the total mass.

Here, let's denote the position of each mass with the variables yi, and their masses with the variables mi.

The formula for calculating the center of mass is:

Yc = (Σmiyi) / (Σmi)

Substituting in the values given in the question, we can calculate:

Σmiyi = (197g)(3.10m) + (2.90kg)(2.53m) + (2.41kg)(0) + (4.08kg)(-0.493m)

Σmi = 197g + 2.90kg + 2.41kg + 4.08kg

Plugging those values into the formula Yc, we can compute the center of mass.

Use a calculator to get accurate results.

Σmi = 9587 grams

Learn more about the topic of center of mass here:

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