Question

A basketball has a 300-mm outer diameter and a 3-mm wall thickness. Determine the normal stress in the wall when the basketball is inflated to a 108-kPa gage pressure. (Round the final answer to two decimal places.)

Answer 1

2.65 MPa

Step-by-step explanation:

To find the normal stress (σ) in the wall of the basketball we need to use the following equation:

`\sigma = (p*r)/(2t)`

Where:

p: is the gage pressure = 108 kPa

r: is the inner radius of the ball

t: is the thickness = 3 mm

Hence, we need to find r, as follows:

`r_(inner) = r_(outer) - t`

`r_(inner) = (d)/(2) - t`

Where:

d: is the outer diameter = 300 mm

`r_(inner) = (300 mm)/(2) - 3 mm = 147 mm`

Now, we can find the normal stress (σ) in the wall of the basketball:

`\sigma = (p*r)/(2t) = (108 kPa*147 mm)/(2*3 mm) = 2646 kPa = 2.65 MPa`

Therefore, the normal stress is 2.65 MPa.

I hope it helps you!