Question

Calculate the center of mass for the following collection of point masses on the real number line.

m₁ = 7 at x₁ = -3
m₂ = 3 at x₂ = -5
m₃ = 5 at x₃ = -2

Answer 1

The center of mass for this collection of point masses on the real number line is approximately −3.067.

To find the center of mass for a collection of point masses on the real number line, you can use the formula:

Center of Mass=
`(\sum m_ix_i)/(\sum m_i)`

where:

m_i represents the mass of the ith point mass.

x_i represents the position of the ith point mass.

For your given masses and positions:

m_1 =7 at x_1 =−3

m_2 =3 at x_2= -5

m_3 =5 at x_3 =−2

Let's plug these values into the formula:

Center of Mass= (7×(−3))+(3×(−5))+(5×(−2))/ 7+3+5

​Calculating the numerator first:

(7×(−3))+(3×(−5))+(5×(−2))=(−21)+(−15)+(−10)=−46

Now, the denominator:

7+3+5=15

Finally, calculate the center of mass:

Center of Mass= −46/ 15 ≈−3.067

Therefore, the center of mass for this collection of point masses on the real number line is approximately −3.067.