A balsa wood glider wing has the following properties during flight:
Thickness= 0.3175 cm
I= 0.0733 cm^4
Moment= 4.2 N-cm
Find the bending stress in the wing. Express your answer in N/m^2.
Is the answer either 9.096 N/m^2 or 18.192 N/m^2
sigma = M y / Ix
max sigma is at outer fiber top and bottom y = .3175/2 = .159 cm = .00159 m
M = 4.2 N cm * 1 m/100 cm = .042 Nm
I = .0733 cm^4 *^10^-2 m/cm)^4 = .0733*10^-8 m^4
so
sigma = .042 Nm (.00159m)/.0733*10^-8 m^4
= 9.11*10^4 N/m^2
I see what happened, you used the whole depth of the wing, but the stress due to bending is proportional to the distance from the neutral axis, we assume the middle.
Also you dropped a couple of cm to meter type thingees I think
To find the bending stress in the wing, we can use the formula for bending stress:
Stress = (Moment * Distance from Neutral Axis) / (Section Modulus)
The Moment (M) is given as 4.2 N-cm, and the Distance from the Neutral Axis will be half of the thickness of the wing (t/2). The Section Modulus (S) is given by:
S = I / c
Here, I represents the moment of inertia and c is the distance from the Neutral Axis to the outermost surface of the wing, which is equal to the thickness of the wing (t).
From the given properties, the thickness of the wing (t) is 0.3175 cm, and the moment of inertia (I) is 0.0733 cm^4.
Let's calculate the section modulus (S):
S = I / c = I / t
Since c = t, we have:
S = I / c = I / t = 0.0733 cm^4 / 0.3175 cm = 0.2306 cm^3
Now, we can calculate the bending stress:
Stress = (Moment * Distance from Neutral Axis) / (Section Modulus)
The distance from the Neutral Axis is t/2 = 0.3175 cm / 2 = 0.15875 cm.
Stress = (4.2 N-cm * 0.15875 cm) / (0.2306 cm^3)
Stress = 0.66555 N-cm / 0.2306 cm^3
Stress ≈ 2.885 N/cm^2
To express the answer in N/m^2, we need to convert from cm to meters:
Since 1 m = 100 cm, the conversion factor is 10000.
So, the final answer in N/m^2 is:
Stress = 2.885 N/cm^2 * 10000 cm^2/m^2
Stress ≈ 28850 N/m^2
Therefore, the correct answer is 28850 N/m^2.
Neither of the options given (9.096 N/m^2 or 18.192 N/m^2) is correct. The correct answer is 28850 N/m^2.