Question

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a log. Express the strength of the beam as a function of the angle θ in the figures.

Answer 1

The strength of the beam can be expressed as a function of the angle θ using the given information. It can be represented as S = k * w * h^2 / cos^2(θ), where k, w, and h are constants.

Step-by-step explanation:

The strength of the beam can be expressed as a function of the angle θ using the given information. According to the question, the strength of the beam is proportional to the width and the square of the depth. Let's assume that the width of the beam is w and the depth is d. Then the strength of the beam can be represented as S = kw * d^2, where k is a constant of proportionality.

Now, we need to express the width and the depth in terms of the angle θ. Since the beam is cut from a log, we can consider the depth as the perpendicular distance from the surface of the log to the bottom of the beam. If we consider the angle θ, then the depth can be expressed as d = h / cos(θ), where h is the height of the log.

Substituting the value of d in the equation for the strength, we get S = kw * (h / cos(θ))^2. Hence, the strength of the beam can be expressed as a function of the angle θ as S = k * w * h^2 / cos^2(θ).