A 50-kg air conditioner is placed on top of a concrete pad that is 20 cm thick and has a cross-sectional area of 3.0 m².What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is 2.3 × 10¹⁰ N/m². A)1.4 × 10^-9 m B)2.8 × 10^-9 m C)1.4 × 10^-8 m D)1.4 × 10^-7 m E)2.8 × 10^-8 m

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Quizplus · Accepted Answer

The change in thickness ($\Delta L$) can be calculated using the formula $\Delta L = \frac{F \cdot L}{A \cdot Y}$, where $F$ is the force applied (weight of the air conditioner), $L$ is the original length (thickness of the pad), $A$ is the cross-sectional area, and $Y$ is Young's modulus. The force $F$ is the weight of the air conditioner, which is $mg = 50 \times 9.8 = 490$ N. The original length $L = 20 \times 10^{-2}$ m, $A = 3.0 \, m^2$, and $Y = 2.3 \times 10^{10}$ N/m$^2$. Plugging these values into the formula gives $\Delta L = \frac{490 \cdot 20 \times 10^{-2}}{3.0 \times 2.3 \times 10^{10}} = 1.4 \times 10^{-9}$ m.

A 50-Kg Air Conditioner Is Placed on Top of a Concrete