a cable 10 cm in diameter has a strength of 1018.6 MPa and the design engineer has specified a factor of safety of 2. what is the maximum allowable mass the cable can support?

To determine the maximum allowable mass the cable can support, we first need to follow these steps:

### 1. **Convert the cable diameter into radius**:
   The diameter of the cable is given as 10 cm, so the radius \( r \) is:
   \[
   r = \frac{10}{2} = 5 \, \text{cm} = 0.05 \, \text{m}
   \]

### 2. **Calculate the cross-sectional area**:
   Assuming the cable has a circular cross-section, its area \( A \) can be calculated using the formula for the area of a circle:
   \[
   A = \pi r^2
   \]
   Substituting \( r = 0.05 \, \text{m} \):
   \[
   A = \pi (0.05)^2 = 7.854 \times 10^{-3} \, \text{m}^2
   \]

### 3. **Determine the allowable stress**:
   The allowable stress \( \sigma_{\text{allowable}} \) is the strength of the material divided by the factor of safety \( FS \):
   \[
   \sigma_{\text{allowable}} = \frac{\sigma_{\text{material}}}{FS} = \frac{1018.6 \, \text{MPa}}{2} = 509.3 \, \text{MPa}
   \]
   Converting this into pascals (since \( 1 \, \text{MPa} = 10^6 \, \text{Pa} \)):
   \[
   \sigma_{\text{allowable}} = 509.3 \times 10^6 \, \text{Pa}
   \]

### 4. **Calculate the maximum allowable force**:
   The maximum allowable force \( F_{\text{max}} \) is given by:
   \[
   F_{\text{max}} = \sigma_{\text{allowable}} \times A
   \]
   Substituting the values for \( \sigma_{\text{allowable}} \) and \( A \):
   \[
   F_{\text{max}} = (509.3 \times 10^6) \times (7.854 \times 10^{-3}) = 4.000 \times 10^6 \, \text{N}
   \]

### 5. **Determine the maximum allowable mass**:
   The maximum allowable mass \( m_{\text{max}} \) is related to the maximum force by the equation:
   \[
   F_{\text{max}} = m_{\text{max}} \times g
   \]
   where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). Solving for \( m_{\text{max}} \):
   \[
   m_{\text{max}} = \frac{F_{\text{max}}}{g} = \frac{4.000 \times 10^6}{9.81} \approx 407,749.74 \, \text{kg}
   \]

### Conclusion:
The maximum allowable mass the cable can support is approximately **407,750 kg**.

Would you like more details or have any questions?

### 5 Related Questions:
1. How does the factor of safety affect the allowable stress in the cable?
2. How would a different material strength change the maximum allowable mass?
3. What would happen if the factor of safety was reduced?
4. How can we design a cable to support more weight while keeping the same diameter?
5. How would environmental factors, such as temperature, affect the cable’s strength?

### Tip:
When designing with factors of safety, always ensure to consider dynamic loads and environmental conditions for maximum safety.

A cable 10 cm in diameter has a strength of 1018.6 MPa and the design engineer has specified a factor of safety of 2. What is the maximum allowable mass the cable can support?

Find out how to calculate the maximum allowable mass a 10 cm diameter cable with a strength of 1018.6 MPa can support, factoring in a safety factor of 2. This detailed solution covers key physics concepts, including stress, strength, cross-sectional area, and force calculations.

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