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Answer:
Answer for the question is given in the attachment.
Explanation:
Answer:
Magnitude of force P = 25715.1517 N
Explanation:
Given - The wires each have a diameter of 12 mm, length of 0.6 m, and are made from 304 stainless steel.
To find - Determine the magnitude of force P so that the rigid beam tilts 0.015∘.
Proof -
Given that,
Diameter = 12 mm = 0.012 m
Length = 0.6 m
= 0.015°
Youngs modulus of elasticity of 34 stainless steel is 193 GPa
Now,
By applying the conditions of equilibrium, we have
∑fₓ = 0, ∑ = 0, ∑M = 0
If ∑ = 0
⇒×0.9 - P × 0.6 = 0
⇒×3 - P × 2 = 0
⇒ =
If ∑ = 0
⇒×0.9 = P × 0.3
⇒ ×3 = P
⇒ =
Now,
Area, A = = 1.3097 × 10⁻⁴ m²
We know that,
Change in Length , =
Now,
= 9.1626 × 10⁻⁹ P
= 1.83253 × 10⁻⁸ P
Given that,
= 0.015°
⇒ = 2.618 × 10⁻⁴ rad
So,
⇒2.618 × 10⁻⁴ = ( 1.83253 × 10⁻⁸ P - 9.1626 × 10⁻⁹ P) / 0.9
⇒P = 25715.1517 N
∴ we get
Magnitude of force P = 25715.1517 N