Question

center of mass lecture participation one - day: problem 1
(2 points)
point - masses ( m _ { i } ) are located on the ( x ) - axis as follows. answer the following questions.

point - mass	mass ( m _ { i } )	position ( x _ { i } )
( m _ { 2 } )	50	9
( m _ { 3 } )	35	2.5
( m _ { 4 } )	25	- 6

1. find the moment ( m ) of the system.

answer: ( m = )

1. find the center of mass ( overline { x } ) of the system.

answer: ( overline { x } = )

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Explanation:

Step1: Calculate the moment \(M\)

The formula for the moment \(M\) of a system of point - masses on the \(x\) - axis is \(M=\sum_{i = 1}^{n}m_ix_i\).
For \(m_1 = 30,x_1=-4\); \(m_2 = 50,x_2 = 9\); \(m_3=35,x_3 = 2.5\); \(m_4 = 25,x_4=-6\)

$$
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$$

Step2: Calculate the total mass \(m\)

The formula for the total mass \(m\) of a system of point - masses is \(m=\sum_{i = 1}^{n}m_i\)

$$
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$$

Step3: Calculate the center of mass \(\overline{x}\)

The formula for the center of mass \(\overline{x}\) of a system of point - masses on the \(x\) - axis is \(\overline{x}=\frac{M}{m}\)
Since \(M = 267.5\) and \(m = 140\)

$$ \overline{x}=\frac{267.5}{140}=1.910714\approx1.91 $$

Answer:

1. \(M = 267.5\)
2. \(\overline{x}\approx1.91\)