Two identical concrete slabs lie flat and in contact with each other as shown in the figure.If the temperature increases by 40°C,the lower edges opposite the contact edges remained fixed in position,and the lower edges of the contact side remain in contact,at what angle will the slabs be tilted? The coefficient of thermal expansion of the concrete is 10 × 10^-6/K. A)19° B)0.028° C)15° D)1.6° E)The answer depends on the length of the slabs.

Question

Quizplus · Accepted Answer

Since the lower edges opposite the contact edges remain fixed and the lower edges of the contact side remain in contact, the slabs will pivot around the contact edge. Let us consider the top edge of the slabs as the reference line.

Let L be the length of each slab and t be the thickness of each slab. Since the coefficient of thermal expansion of the concrete is given as 10 × 10^-6/K, the increase in length of each slab is given by ΔL = αLΔT, where α is the coefficient of thermal expansion and ΔT is the change in temperature.

Thus, ΔL = 10 × 10^-6/K × L × 40°C = 4 × 10^-4L.

Since the slabs are rigidly connected at the top edge and pivot around the contact edge, the distance between the top edge and the contact edge remains constant. Let this distance be H.

Now, the slabs are tilted by an angle θ such that the horizontal distance between the top and bottom edges of the contact side is equal to H.

Using trigonometry, we have:

tanθ = (L/2 + ΔL)/H ≈ (L/2)/H + ΔL/H ≈ (L/2)/H since ΔL << H.

Substituting the values, we get:

tanθ ≈ (L/2)/H = (L/2)/t.

Thus, θ ≈ tan^-1((L/2)/t) ≈ 1.6°.

Therefore, the answer is D) 1.6°.

Two Identical Concrete Slabs Lie Flat and in Contact with Each