Forces as Vectors – Tension in a Cable
Purpose: To determine how the tension in two weight bearing cables depends upon the angle between the cables.
Materials Needed: Vernier LabQuest (x2),
Force Meters (x2),
String (approx 2 meters),
Mass
Protractor
Procedures:
1) Tie a loop at each end of the string and MARK the center of the string with an ink spot.
2) Turn on the Vernier LabQuest device and connect the force meter (probe) at the top.
3) Ensure that the force meter (probe) is set to 50 N *** (Be Careful with this equipment!!!)
4) Attach each end of the string to one of the force meters (probes) and place the mass at the very center of the string – the place that you marked.
5) Starting with an angle of 25 degrees, record the tension in the table at the bottom of the page. If the two lab pro readings are different, then simply record the AVERAGE of the two readings. If the readings are more than 0.5 N apart, then your mass is probably not centered or your lab pro needs to be calibrated.
6) Increase the angle by about 10 degrees at a time by having the people holding the force meters move apart. You do not need to go up by exactly 10 degrees each time; however it is vital that you accurately measure each angle and each tension. For example: on the first measurement it is not necessary to waste time trying to make the angle exactly 25 degrees. If you have an angle of 23 degrees then, that is fine; but, you should record the angle as 23 degrees in your lab table (not 25 degrees).
7) Continue to do this and record these tensions in the string until you get to 165 degrees.
DO NOT ATTEMPT TO GO BEYOND 165 DEGREES
8) Use the graph paper to construct a graph of tension (vertical axis) vs angle (horizontal axis). When you draw a smooth curve through your data points, think twice before forcing your curve to go through the origin. Don’t forget such important points as a descriptive title and labeling the axes.
9) Use your graph to estimate the tension at 80 degrees = ________________.
10) Use your graph to estimate the tension at 150 degrees = ________________.
11) Look closely at the behavior of your graph as the angle between the cables gets close to 180 degrees. Could you ever pull hard enough to make the angle 180 degrees? If so, then how large would the tension have to be to get an angle of 180 degrees? If not, then what will determine how close to 180 degrees you can get?
12) Assuming that the two bridges shown below each had the same load on them, which bridge would be more likely to have the cables break? (EXPLAIN your reasoning).
13) Which of these roof trusses would be stronger? (EXPLAIN your reasoning)
14) Write a general statement the describes what you learned. We will call this
the First Law of Bridge Building.
Repeat the same procedures 5-8 for the set up described below (and graph your results):
Note: Start at 0 degrees and increase by increments of 5 degrees (you may not be able to get past 60 degrees)