Passage IV
Physics students performed 3 studies to determine the forces that several doors exerted on their hinges. The doors had various weights, W, and widths, D. Each door had 2 hinges; the hinges could be moved to vary the distance, S, between them. None of the doors had a doorknob.
The 2 hinges on each door were equidistant from the center of mass of the door (see the diagram).
Each hinge was fitted with 2 force sensors. With the door attached to a door frame, one of the sensors detected the horizontal force exerted by the door on the hinge,
, and the other sensor detected the vertical force exerted by the door on the hinge,
. Once and were determined for each hinge, was averaged over the 2 hinges, yielding the average horizontal force per hinge,
, and was averaged over the 2 hinges, yielding the average vertical force per hinge,
· Fromand, the average net force per hinge,
could be calculated.
In the 3 studies, all forces were recorded in pounds (lb) and all lengths were recorded in inches (in).
Study 1
For a door with W=61 lb and D=30 in, the students determinedandat various S. The results are shown in Figure 1.
Study 2
For 3 doors, each with D = 30 in but a different W, the students determinedat various S. The results are shown in Figure 2.
Study 3
For 3 doors, each with W = 61 lb but a different D, the students determinedat various S. The results are shown in Figure 3.
23. If a door having W = 90 lb, D=30 in, and S=50 in had been tested in Study 2,for this door would most likely have been:
Your Answer is
Correct Answer is D
Explanation
Looking at figure 2, when the abscissa takes a fixed value, the vertical observation shows that F increases as W increases, so when S=50, W=76, the ordinate is about 45, so it is inferred that when W increases to At 90, the ordinate will be greater than 45