Question

Consider a steel cable with a diameter of 8.0 mm. Calculatethe stress in the cable when it holds a person weighing 850 N.Report your answer in MPa (106 Pa = 1 MPa).

Answer 1

Answer:

stress = 16.9 MPa

Explanation:

The stress in the cable can be calculated as:

$\text{Stress = }\frac{F}{A}$

Where F is the force and A is the area. So, the area can be calculated as:

$A=\pi^{}\cdot r^2$

Where r is the radius. Since the radius is half the diameter, the radius is 4.0 mm and the area will be equal to:

$\begin{gathered} A=3.14(4\operatorname{mm})^2 \\ A=50.24\operatorname{mm}^2 \end{gathered}$

Then, replacing the force F by 850 N, and A by 50.24 mm², we get that the stress is equal to:

$\text{stress = }\frac{850N}{50.24mm^2}=16.9\text{MPa}$

Therefore, the answer is 16.9 MPa