This physical model demonstrates how cables subjected to concentrated point loads establish equilibrium through geometry – i.e., the slope of each cable segment will change (as will the support reactions) as different loads are placed on the cable. This demonstration should take 10-20 minutes.
Cables subjected to concentrated loads are a great example of using static equilibrium to solve real-world problems. The solution method for this problem highlights many fundamental lessons in statics. Basic observations include that cables are two-force members that can be treated just like truss members, that the horizontal component of the tension is equal across all segments, and that the maximum tension must be in the segment with the greatest slope.
What You Need
Rope or Cord
Size and cost will vary depending on the size of the model constructed.
|Weight||2 to 3
These weights will act as the point loads on your supported cable.
Measuring tape or ruler
Used to establish the geometry and solve for the tensions in the system.
Using wood or metal, build a rigid support system to span the cable and support the weights acting on the cable.
**Only needed as part of the Additional Application**
How It’s Done
Build your support structure, tie off both ends of the cord, leave some slack, and hang the weights. Have your measurements and numerical values preplanned to simplify the problem solving process, but also be willing to allow the students to manipulate the weight values and locations within the system.
In Class: Keep a measuring stick nearby so that the students can measure the geometry of the system (Fig. 1, left). This can be used as an in-class problem where the students solve for the tension in the various segments of the rope, thereby realizing that when the loads are tied off, the tension varies in the rope (Fig. 1, right). It can also be demonstrated using a spring loaded scale at one end that as the rope shortens (taking the “belly” out of it), the tension goes up since the weights to be supported act only in the y-direction, and the y-component of the force at the ends must remain constant even as the angle of inclination goes down, causing a large increase in the x-component of the force.
Construct one model that looks similar to a problem being worked and construct another larger model that goes across the entire classroom (Fig. 2, top-left). In this case, instead of tying off both ends, one end is tied off and the other end is routed through a pulley and tied off to some weights (Fig. 2, right). Once loaded, show that if weight is added or subtracted from the “anchor point” or a load from the cable, the system will move up and down as it reestablishes equilibrium (Fig. 2, bottom-left). A weight can also be hung from a pulley along the rope, like a ski gondola, demonstrating that an x-direction stabilizing force is required at all points along the rope except when the “gondola” is at the very center.