A cardboard tube is loaded with a 15.3 N axial load. The tube has an outside diameter of 2.5 cm and a wall thickness of .035 cm. Find the axial stress in the cardboard tube.
Is the answer 75 N/cm^2?
If so can you show me your way of getting to this answer.
approximate area by 2 pi r dr
A = 2 pi (1.25)(.035) = .275 cm^2
15.3 / .275 = 55.6
To calculate the axial stress in the cardboard tube, we can use the formula:
Axial stress = Force / Area
First, we need to calculate the cross-sectional area of the cardboard tube. The cross-sectional area can be found by subtracting the area of the inner circle from the area of the outer circle.
Area = π * (outer radius^2 - inner radius^2)
We are given the outside diameter of the tube, which is 2.5 cm. Therefore, the outer radius (r_outer) can be calculated as r_outer = outer diameter / 2 = 2.5 cm / 2 = 1.25 cm.
The thickness of the wall is given as 0.035 cm. So, the inner radius (r_inner) can be calculated as r_inner = r_outer - thickness = 1.25 cm - 0.035 cm = 1.215 cm.
Now, we can substitute the values into the area formula:
Area = π * (1.25 cm^2 - 1.215 cm^2)
Using the value of π (approximately 3.14159):
Area = 3.14159 * (1.25^2 - 1.215^2) cm^2
Area ≈ 3.14159 * (1.5625 - 1.480225) cm^2
Area ≈ 3.14159 * 0.082275 cm^2
Area ≈ 0.25775 cm^2
Now that we have the area, we can calculate the axial stress using the given load:
Axial stress = 15.3 N / 0.25775 cm^2
Axial stress ≈ 59.4627 N/cm^2
Therefore, the correct axial stress in the cardboard tube is approximately 59.4627 N/cm^2, not 75 N/cm^2.