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A plastic dowel has a Young's Modulus of 1.50 ✕ 1010 N/m2. Assume the dowel will break if more than 1.50 ✕ 108 N/m2 is exerted.

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Answer:

(A) The maximum force is 85.8 kN.

(B) Dowel shorten by 2.79 mm

Explanation:

Given:

Young modulus $E = 1.50 \times 10^{10}$ $\frac{N}{m^{2} }$

Pressure fracture $P = 1.50 \times 10^{8}$ $\frac{N}{m^{2} }$

Diameter $D = 2.70 \times 10^{-2}$ m

Radius $r = 1.35 \times 10^{-2}$ m

(A)

From the formula of force in terms of pressure,

$F=PA$

Where $A =$ area of dowel

$F = 1.50 \times 10^{8} \times \pi (1.35 \times 10^{-2} ) ^{2}$

$F = 85.8 \times 10^{3}$

$F = 85.8$ kN

(B)

From young modulus formula,

$E = \frac{FL}{A\Delta L}$

Where $L = 28 \times 10^{-2}$ m

$\Delta L = \frac{FL}{AE}$

$\Delta L = \frac{85.8 \times 10^{3} \times 28 \times 10^{-2} }{\pi (1.35 \times 10^{-2} )^{2} \times 1.50 \times 10^{10} }$

$\Delta L = 2.79 \times 10^{-3}$

$\Delta L = 2.79$ mm

Therefore, the maximum force is 85.8 kN and dowel shorten by 2.79 mm

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