The maximum compressional stress that a bone can withstand is `1.6xx10^(8)N//m^(2)` before it breaks. A thighbone (femur), which is the largest and longest bone in the human body, has a cross - sectional area of `7.7xx10^(-4)m^(2)`. What is the maximum compressional force that can be applied to the thighbone ?

Options

A. `2.1xx10^(11)N`
B. `1.2xx10^(5)N`
C. `4.8xx10^(12)N`
D. `3.0xx10^(3)N`

Answer

To find the maximum compressional force that can be applied to the thighbone (femur), we can use the relationship between stress, force, and area. The formula for stress is given by:

\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \]

Where:
- Stress is the maximum compressional stress that the bone can withstand, given as \(1.6 \times 10^8 \, \text{N/m}^2\).
- Force is the compressional force we want to calculate.
- Area is the cross-sectional area of the thighbone, given as \(7.7 \times 10^{-4} \, \text{m}^2\).

### Step 1: Rearranging the formula
We can rearrange the formula to solve for Force:

\[ \text{Force} = \text{Stress} \times \text{Area} \]

### Step 2: Substituting the given values
Now, we can substitute the values of stress and area into the equation:

\[ \text{Force} = (1.6 \times 10^8 \, \text{N/m}^2) \times (7.7 \times 10^{-4} \, \text{m}^2) \]

### Step 3: Performing the multiplication
Now, we will perform the multiplication:

\[ \text{Force} = 1.6 \times 7.7 \times 10^{8 - 4} \, \text{N} \]

Calculating \(1.6 \times 7.7\):

\[ 1.6 \times 7.7 = 12.32 \]

Now, adjusting the power of ten:

\[ \text{Force} = 12.32 \times 10^4 \, \text{N} \]

### Step 4: Converting to standard form
Converting \(12.32 \times 10^4\) to standard scientific notation:

\[ \text{Force} = 1.232 \times 10^5 \, \text{N} \]

### Final Answer
Thus, the maximum compressional force that can be applied to the thighbone is:

\[ \text{Force} = 1.232 \times 10^5 \, \text{N} \]