Question

Four objects are situated along the y axis as follows: a 1.99-kg object is at 2.99 m, a 2.96-kg object is at 2.57 m, a 2.43-kg object is at the origin, and a 3.96-kg object is at -0.502 m. Where is the center of mass of these objects

Answer 1

The center of mass for the object is
`y_c = 1.063 \ m` from the origin

Step-by-step explanation:

From the question we are told that

The mass of the first object is
`m_1 = 1.99 \ kg`

The position of first object with respect to origin
`y_1 = 2.99 \ m`

The mass of the second object is
`m_2 = 2.96 \ kg`

The position of second object with respect to origin
`y_2 = 2.57 \ m`

The mass of the third object is
`m_3 = 2.43 \ kg`

The position of third object with respect to origin
`y_3 = 0 \ m`

The mass of the fourth object is
`m_3 = 3.96 \ kg`

The position of fourth object with respect to origin
`y_3 = -0.502 \ m`

Generally the center of mass of the object along the x-axis is zero because all the mass lie on the y axis

Generally the location of the center mass of the object is mathematically represented as

`y_c = (m_1 * y_1 + m_2 * y_2 + m_3 * y_3 + m_4 * y_4)/(m_1 + m_2 + m_3 + m_4)`

=>
`y_c = (1.99 * 2.99 + 2.96 * 2.57 + 2.43 * 0 + 3.96 * (-0.502))/(1.99+ 2.96 + 2.43 + 3.96)`

=>
`y_c = 1.063 \ m`