If a force is applied to the end bb of the member and causes it to rotate by θ=0.45∘θ=0.45∘, determine the normal strain in the cable. express your answer to three significant figures.

Q) Part of a control linkage for an airplane consists of a rigid member CB and a flexible cable AB ' 800 mm 600 mm Originally the cable is unstretched. If a force is applied to the end of the member and causes it to rotate by θ = 0.45°, determine the normal strain in the cable. Express your answer to three significant figures. (I believe this is the complete question)

Normal Strain = 0.00376 mm/mm

Explanation:

Here we are given with the length AC which is L_AB= 600 mm and the length BC which is L_BC = 800mm and the angle of rotation ∅ = 0.45°

First we will find the unstretched length AB by applying Pythagoras theorem:

L_AB = sqrt( (L_AC)^2 + (L_BC)^2)

L_AB = sqrt((600^2) + (800^2)

L_AB = 1000 mm

Now in order to find the stretched length we will use the cosine formula:

L_AB' = sqrt ( (L_AC)^2 + (L_AB)^2) - 2(L_AC)(L_AB)cos∅)

L_AB' = sqrt( (600)^2 + (800)^2 - 2(600)(800)cos(90+0.45))

L_AB' = 1003.762 mm

Now we will use the strain formula:

∈ = (L_AB' - L_AB)/L_AB

∈ = (1003.762 - 1000)/1000

∈ = 0.00376 mm/mm