Question

A 4.0-m long steel beam with a cross-sectional area of 1.0 x 10² m² and a Young's modulus of 2.0 x 10⁹ N/m² is wedged horizontally between two vertical walls. In order to wedge the beam, it is compressed by 0.020 mm. If the coefficient of static friction between the beam and the walls is 0.70, what is the maximum mass (including its own) that it can bear without slipping?

Answer 1

To determine the maximum mass a wedged beam can support without slipping, one must calculate the compression force, apply the static friction formula, and then find the maximum supported mass, but the beam's mass must be known to give an exact answer.

Step-by-step explanation:

The question at hand involves calculating the maximum mass that a steel beam can bear without slipping, given that it is wedged between two walls. We are given the length, cross-sectional area, compression, Young's modulus, and coefficient of static friction for the beam. To find the maximum supported mass, first, we calculate the force needed to compress the beam using Hooke's Law. Then, using that force, we apply the formula for static friction to find the maximum force the friction can hold. Finally, this force is used to calculate the maximum mass, including the mass of the beam itself. As no mass of the beam is provided, the answer would consider only the mass it can bear besides its own weight (if known).

However, as the mass of the beam is not provided, we can only determine how this calculation is approached but are unable to provide the actual final answer without the weight of the beam itself.