Question

A car has side window made of glass (shear strength 40 MPa) having size 40 cm x 40 cm. The car is travelling with a velocity of 40 m/s in still air. Density of air can be assumed to be 1.25 kg/m³. The windows are closed.

• A. If the glass is very thin, it may break and fall into the car.
• B. If the glass is very thin, it may break & fall out of the car.
• C. If we want that glass should not break, it's thickness should be greater than 2.5 µm.
• D. If we want that glass should not break, it's thickness should be greater than 8.75 µm.

Answer 1

Answer: (A), (C)

(A) and (C)

Answer 2

The dynamic pressure created by the car's motion is $P_{dyn} = \frac{1}{2} \rho v^2 = \frac{1}{2} \times 1.25 \times (40)^2 = 1000$ Pa. This pressure acts on the window area $A = (0.4 \text{ m})^2 = 0.16 \text{ m}^2$, resulting in a force $F = P_{dyn} \times A = 1000 \times 0.16 = 160$ N. This force pushes the window inwards. The shear stress on the glass edges is $\tau = \frac{F}{A_{shear}}$, where $A_{shear} = \text{perimeter} \times \text{thickness} = (4 \times 0.4 \text{ m}) \times t = 1.6t$. For the glass not to break, $\tau \le \tau_{max}$. Thus, $\frac{160}{1.6t} \le 40 \times 10^6$ Pa. Solving for $t$, we get $t \ge \frac{160}{1.6 \times 40 \times 10^6} = \frac{100}{40 \times 10^6} = 2.5 \times 10^{-6}$ m, or $2.5$ µm. If the thickness is less than $2.5$ µm, it will break and fall inwards. If the thickness is greater than $2.5$ µm, it will not break.