Passage III

In 3 studies, students investigated the stiffness of rectangular metal beams (see Figure 1).

Using the apparatus shown in Figure 2, the students deformed each beam under a variety of conditions.

In each trial, the beam being tested was supported at 2 points that were 0.10 m apart and equidistant from the midpoint of the beam. The beam was subjected to a load, W, measured in newtons (N), at the midpoint of the beam. W was provided by weights placed on the platform of the apparatus. During deformation, each beam became slightly U-shaped (see Figure 3).

A dial on the apparatus registered the distance, D, the beam was deformed in multiples of 10^-6 m. After D was measured, the load was removed, and the beam returned to its original shape.

The intrinsic stiffness of the metal composing a beam was represented by Young's modulus, E. The effect of the width and height of a beam (see Figure 1) on D was represented by the quantity I, given in m⁴.

Study 1

In Trials 1-4, students determined D for beams with different I (see Table 1). In every trial, W=20 N and E = 50×10⁹ N/m².

Study 2

In Trials 5-8, students determined D for beams composed of Metals S-V, respectively. Each metal had a different value of E (see Table 2). In every trial, W = 20 N and I = 2.0 × 10^-9 m⁴.

Study 3

In Trials 9-12, students determined D for different W (see Table 3). In every trial, I = 2.0 × 10^-9 m⁴ and E = 50 × 10⁹ N/m².