Physics students performed 3 studies to determine the forces that several doors exerted on their hinges
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, Fh, and the other sensor detected the vertical force exerted by the door on the hinge, Fv. Once Fh and Fv were determined for each hinge, Fh was averaged over the 2 hinges, yielding the average horizontal force per hinge, Fh, av, and Fv was averaged over the 2 hinges, yielding the average vertical force per hinge, Fv, av. From Fh, av and Fv, av, the average net force per hinge, Fn, av, 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 determined Fh, av and Fv, av at 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 determined Fn, av at 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 determined Fn, av at various S. The results are shown in Figure 3.
21. In which study, if any, was the door with the greatest mass tested?
A. Study 1
B. Study 2
C. Study 3
D. None of the studies; all the doors tested in the 3 studies had the same mass.
22. Which of the following statements regarding W and D best describes a difference between Study 2 and Study 3 ? In Study 2:
F. W was varied while D was held constant, whereas in Study 3, W was held constant while D was varied.
G. W was held constant while D was varied, whereas in Study 3, W was varied while D was held constant.
H. both W and D were varied, whereas in Study 3, both W and D were held constant.
J. both W and D were held constant, whereas in Study 3, both W and D were varied.
23. If a door having W = 90 lb, D = 30 in, and S = 50 in had been tested in Study 2, Fn, av for this door would most likely have been:
A. less than 20 lb.
B. between 20 lb and 30 lb.
C. between 30 lb and 45 lb.
D. greater than 45 lb.
24. For the door tested in Study 1, when S was less than 30 in, was Fh, av less than Fv, av or greater than Fv, av, and when S was greater than 30 in, was Fh, av less than Fv, av or greater than Fv, av ?
S less than 30 in | S greater than 30 in
F. less | less
G. less | greater
H. greater | less
J. greater | greater
25. In Studies 2 and 3, which combination of W, D, and S resulted in the lowest Fn, av ?
W (lb) | D (in) | S (in)
A. 51 | 30 | 20
B. 51 | 30 | 70
C. 61 | 24 | 20
D. 61 | 24 | 70
26. In Study 1, which average force, Fh, av or Fv, av, was independent of S ?
F. Fh, av, because as S increased, Fh, av decreased.
G. Fh, av, because as S increased, Fh, av remained constant.
H. Fv, av, because as S increased, Fv, av decreased.
J. Fv, av, because as S increased, Fv, av remained constant.
27. Suppose that, due to a manufacturing defect, a particular pair of hinges will break when a net force greater than 57 lb is exerted on each hinge. Based on Study 3, the hinges will most likely break if used on a 61 lb door with which of the following combinations of D and S ?
D (in) | S (in)
A. 30 | 20
B. 30 | 70
C. 36 | 20
D. 36 | 70
Answers
21. The best answer is B. Because the weight of an object is related to its mass, the door with the greatest mass is the door with the greatest weight. According to the passage, the door with the greatest weight had a weight of 76 lb and was used in Study 2.
22. The best answer is F. According to the passage, in Study 2, D was held constant, and W and S were varied. In Study 3, W was held constant, and D and S were varied.
23. The best answer is D. According to the results of Study 2, when D = 30 in and S = 50 in, Fn,av increases as W increases. When W = 76 lb, Fn,av = 46 lb. If an additional door with W = 90 lb had been tested, Fn,av would most likely have been greater than 46 lb.
24. The best answer is H. Figure 1 shows that Fv,av remained constant at all values of S. Figure 1 also shows that Fh,av was greater than Fv,av for all S < 30 in, equal to Fv,av for S = 30 in, and less than Fv,av for all S > 30 in.
25. The best answer is B. According to Figure 2, in Study 2, the lowest Fn,av was 27 lb. According to Figure 3, in Study 3, the lowest Fn,av was 33 lb. The lowest value for Fn,av of 27 lb was measured when W = 51 lb, D = 30 in, and S = 70 in.
26. The best answer is J. Figure 1 shows that as S was varied, there was no change in Fv,av, while Fh,av decreased as S increased. Fv,av was independent of S.
27. The best answer is C. A is incorrect; according to Figure 3, under these conditions, the net force on each hinge was 55 lb and the hinge would not break.