A nail projects 25.0 mm horizontally outward from a wall. A picture is hung from the end of the nail and the nail deflects downward by 2.00 × 10⁻⁶ m. The shear strain of the nail is A) 7.00 × 10⁻⁵. B) 8.00 × 10⁻⁵. C) 9.00 × 10⁻⁵. D) 10.0 × 10⁻⁵. E) 12.0 × 10⁻⁵.

Question

Quizplus · Accepted Answer

We can use the formula for shear strain:
shear strain = (deflection)/(length of nail)
The length of the nail is not given, but we can use the Pythagorean theorem to find it:
length of nail = sqrt((25.0 mm)^2 + (2.00 × 10^-6 m)^2) = 25.0 mm
(Note that we converted the deflection to meters for consistency.)
Plugging in the values, we get:
shear strain = (2.00 × 10^-6 m)/(25.0 mm) = 8.00 × 10^-5
Converting to scientific notation with proper units, we get:
shear strain = 8.00 × 10^-5 (unitless) = 8.00 × 10^-5 m/m = 8.00 × 10^-5 or 8.00 × 10^-5 S^-1
The closest answer choice is B, which is 8.00 × 10^-5 or 8.00 × 10^-5 S^-1.

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