To solve the given expression:
[tex]$=m_2 \frac{m_0-\mu\left(m_1+m_2\right)}{m_0+m_1+m_2}+\mu m_2 g$[/tex]
we'll break it down into several steps. Here are the given values:
- [tex]\(m_2 = 2\)[/tex]
- [tex]\(m_0 = 10\)[/tex]
- [tex]\(\mu = 5\)[/tex]
- [tex]\(m_1 = 3\)[/tex]
- [tex]\(g = 9.81\)[/tex]
### Step 1: Calculate the first term
The first term of the expression is:
[tex]$term1 = m_2 \frac{m_0-\mu\left(m_1+m_2\right)}{m_0+m_1+m_2}$[/tex]
First, calculate the numerator:
[tex]$m_0 - \mu (m_1 + m_2) = 10 - 5(3 + 2) = 10 - 5 \cdot 5 = 10 - 25 = -15$[/tex]
Next, calculate the denominator:
[tex]$m_0 + m_1 + m_2 = 10 + 3 + 2 = 15$[/tex]
Now, divide the numerator by the denominator:
[tex]$\frac{-15}{15} = -1$[/tex]
Finally, multiply by [tex]\(m_2\)[/tex]:
[tex]$term1 = m_2 \cdot \left(-1\right) = 2 \cdot (-1) = -2$[/tex]
### Step 2: Calculate the second term
The second term of the expression is:
[tex]$term2 = \mu m_2 g$[/tex]
Substitute the given values:
[tex]$term2 = 5 \cdot 2 \cdot 9.81 = 10 \cdot 9.81 = 98.1$[/tex]
### Step 3: Add the two terms together
Finally, combine both terms to get the final result:
[tex]$term1 + term2 = -2 + 98.1 = 96.1$[/tex]
### Conclusion
The detailed step-by-step solution yields the following values:
- The value of the first term: [tex]\(-2.0\)[/tex]
- The value of the second term: [tex]\(98.1\)[/tex]
- The final result of the entire expression is: [tex]\(96.1\)[/tex]
