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den301095 [7]
3 years ago
6

Consider the following distribution of objects: a 5.00-kg object with its center of gravity at (0, 0) m, a 3.00-kg object at (0,

4.00) m, and a 4.00-kg object at (3.00, 0) m. Where should a fourth object of mass 8.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0, 0)?
Physics
1 answer:
Minchanka [31]3 years ago
8 0

Answer:

(-1.5,-1.5)m

Explanation:

we know that:

X_{cm} = \frac{m_1x_1+m_2x_2....m_nX_n}{m_1+m_2...m_n}

where X_{cm} is the location of the center of gravity in the axis x, m_i is the mass of the object i and x_i the first coordinate of center of gravity of object i.

so:

0 = \frac{(5kg)(0)+(3kg)(0)+(4kg)(3)+(8kg)x_4}{5kg+3kg+4kg+8kg}

Where x_4 is the first coordinate of the center of gravity for the fourth object.

Therefore, solving for x_4, we get:

x_4 = -1.5m

At the same way:

Y_{cm} = \frac{m_1y_1+m_2y_2....m_ny_n}{m_1+m_2...m_n}

where Y_{cm} is the location of the center of gravity in the axis y, m_i is the mass of the object i and y_i the second coordinate of center of gravity of object i. replacing values we get:

Y_{cm} = \frac{(5kg)(0)+(3kg)(4)+(4kg)(0)+(8kg)y_4}{5+3+4+8}

Where y_4 is the second coordinate of the center of gravity for the fourth object.

solving for y_4:

y_4 = -1.5m

It means that the object of mass 8kg have to be placed in the  

coordinates (-1.5,-1.5) m.

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