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

We can use the formula for thermal expansion:
ΔL = αL0ΔT
where ΔL is the change in length, α is the coefficient of thermal expansion, L0 is the original length, and ΔT is the change in temperature.

Let x be the length of the slabs, and h be the height. The change in length for the top slab is:
ΔL1 = αL0ΔT = (10 × 10^-6)(x)(40) = 0.004x

The change in length for the bottom slab is:
ΔL2 = αL0ΔT = (10 × 10^-6)(x)(40) = 0.004x

Since the bottom edges opposite the contact edges are fixed, the change in length must cause the slabs to tilt. Let θ be the angle of the tilt. The change in height is given by:
Δh = θx

Therefore, we have:
0.004x + 0.004x = θx
θ = 0.008 radians = 0.46 degrees

Therefore, the slabs will be tilted by about 1.6 degrees.

Two Identical Concrete Slabs Lie Flat and in Contact with Each