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.
15. The results of Study 1 are best represented by which of the following graphs?
Your Answer is
Correct Answer is D
Explanation
Look at table 1, where I is the independent variable and should be placed on the X-axis, D is the dependent variable and should be placed on the Y-axis, so exclude A & B;
From table 1 It can be seen from the numerical value that as I increases, D decreases, so C is excluded