Materials Included In Kit

Additional Materials Required

Prelab Preparation

Fasten the screw through the hole in the half meter stick and through the bracket on the support stand clamp. Tighten the bolt assembly until the meter stick does not twist but can still be raised and lowered easily.

Safety Precautions

The materials in this lab are considered safe. Please follow normal laboratory safety guidelines.

Disposal

The materials should be saved for future classes.

Lab Hints

• Enough materials are provided in this kit for one student group. Additional kits should be purchased depending on the classroom goals. The experiment can be reasonably completed in two 50-minute class periods.
• Assume the mass of the boom and binding clips is negligible.
• If 500-g masses are not available, any small, heavy object can be used. A small bag of sand is one low-cost option. The design of the experiment may need to be changed slightly (e.g., having to hang the mass over the edge of a table if it is too large)
• To limit the metal fatigue in the binding clips, remove the clips from the meter stick before storing. Two additional clips have been provided if binding clips become too weak to securely clamp onto the meter stick. The binding clips can also be purchased at a local office supply.

Teacher Tips

• This lab can also be inquiry-based. Provide the students only with the necessary task and have them develop their own procedure, identifing the variables, developing a data table and analyzing their results.
• In order to determine the length of string, use simple right-triangle geometry. Assume that the attachment point of the string is directly above the pivot point.
  sin θ = opposite side/hypotenuse
  cos θ = adjacent side/hypotenuse
  tan θ = opposite side/adjacent side
  {13046_Tips_Figure_12}

Answers to Prelab Questions

1. Use simple right-hand triangle geometry to determine the length of string (l) needed to support a 40-cm-long boom when the string is held at a 30° angle and the boom is held parallel with respect to the ground. Assume the string is attached to the wall directly above the pivot point of the boom. Hint: Use right-angle triangle geometry (see Figure 3).

   l = (40 cm)/(cos 30°) = 46.2 cm

2. Using your solution to Prelab Question 1 as a guide, calculate the string lengths for the different string positions, and string angles given in the data table. Assume the string “attachment point” is directly above the pivot point of the boom. Record these values in the data table.

   See Data Tables. Note: The string lengths were calculated assuming the boom is 50 cm long. In this setup, however, the boom is actually 49 cm long because the pivot point is at the 1-cm mark, not the zero mark. So, the value of the positions of the string and mass will be one higher than their actual distance from the pivot. Some students may recognize this condition. Whether students use the value in the data table or the actual distance, the string length will not vary considerably (by at most 2) and will not affect the students’ conclusions as long as they are consistant.

Sample Data

Answers to Questions

1. Which boom setup completed the objectives in the best possible manner (i.e., the sign is hanging as far away from the wall as possible using the least amount of string)? How much did it cost for the cable?

   From the experimental results, the best setup is Test 17 in which the mass is positioned at 10 cm, and the string attachment is at 25 cm. This produced a string tension of 250 g. The position of the mass (“sign”) is at 10 cm from the ring stand (wall). The amount of string that was needed was 35 cm, resulting in a material cost of $165. This is the least expensive design.

2. In general, in order to provide the strongest support, where is the best place to hang the mass in relation to the string attachment?

   The best place to position the mass in relation to the string is to place the mass as close to the wall as possible and attach the string as far from the wall as possible.

3. How does the angle of the string affect the tension in the string?

   As the angle of the string increases, the tension in the string decreases (all other variables being equal).

4. Compare the force measurements for when the string and mass are attached at the same position.

   The force measurements for when the string and mass are attached at the same position are very similar. It does not matter where on the boom the string and mass are attached, so long as they are attached at the same point. Only the angle of the string affected the tension in the string.

5. Which boom would produce the most tension in the string? Why? Assume the mass in each figure is the same.

   The boom shown in Figure 8c would result in the highest string tension. This is because the angle of the string is the only important variable when the mass and string are attached at the same location. The smaller the angle of the string leads to a larger tension in the string. Therefore, Figure 8c would show the highest tension in the string.

Introduction

The ability to make strong, rigid structures has been important ever since the first buildings were constructed many thousands of years ago. In modern times, structural strength is even more important with the construction of complex bridges and skyscrapers. All these structures have the same physical property in common—they are all in static equilibrium. This laboratory activity introduces the concept of static equilibrium. Your task, as an engineer, will be to hang a “sign” over a sidewalk for the lowest material cost.

Concepts

• Trusses and boom supports
• Torque
• Second- and third-class lever arms
• Static equilibrium of a rigid body

Background

Static equilibrium occurs when all the forces acting on a structure are in perfect balance. That is, there is no linear or rotational movement. If a building or bridge is not in static equilibrium, the unbalanced forces, the most significant being from the force due to gravity, will eventually cause the structure to fall.

The ability to maintain static equilibrium becomes more difficult when an object must be supported from above instead of below. Long suspension bridges are generally supported by wire cables that attach to the tops of the supporting bases (see Figure 1). Overhanging signs and cranes are similar to suspension bridges and rely heavily on strong cables, a supporting lever, also called a boom or truss, and cable attachments. In order to save costs, engineers attempt to limit the amount of material used to support a structure, while still maintaining a high level of strength so that the structure stays in static equilibrium for many years to come.

Experiment Overview

Laboratory Objective Guidelines 
The boom used to hang the sign must be attached to the wall of the building at a specific location. The sign should be hung as far away from the building as possible in order to maximize its visibility and marketing potential. Also, in order to keep the costs of the project down and still maintain building code, the “cable” material used can only support half the weight of the sign. If the “cable” attempts to support more than half the weight of the sign (250 g; 2.45 N), the “cable” will snap. In order to accomplish this task, experiment with the position of the sign on the boom, the angle of the boom and the position of the supporting rope. Hint: Hang the mass and attach the string at 10 cm, 25 cm and 40‑cm on the meter stick, and use boom angles of 30°, 45° and 60°.

• Sign mass: 500 g
• Boom attachment height on wall: 20 cm
• Maximum supporting weight of cable: 250 g
• Cost of supporting cable: $5/cm

Materials

Prelab Questions

1. Use simple right-hand triangle geometry to determine the length of string (l) needed to support a 40-cm-long boom when the string is held at a 30° angle and the boom is held parallel with respect to the ground. Assume the string is attached to the wall directly above the pivot point of the boom. Hint: Use right-angle triangle geometry (see Figures 3 and 4).
   {13046_PreLab_Figure_3}
2. Using your solution to Prelab Question 1 as a guide, calculate the string lengths for the different string positions, and string angles given in the data table. Assume the string “attachment point” is directly above the pivot point of the boom. Record these values in the data table.

Safety Precautions

The materials in this lab are considered safe. Please follow normal laboratory safety guidelines.

Procedure

1. Obtain the Simple Form Truss, two binding clips, support stand, 500-g hooked mass, string, scissors, protractor, ruler and 1000-g spring scale.
2. Use scissors to cut two pieces of string—one approximately 50 cm and the other approximately 15 cm.
3. Tie one end of the 50-cm string to the spring-scale handle.
4. The setup for the Simple Form Truss is shown in Figures 5 and 6.
   {13046_Procedure_Figure_5}
   Note 1: The spring-scale scale should face the measurer.
   Note 2: Tie the 15-cm string around the binder clip to form a loop that is just large enough to allow the string to slide along the meter stick (see Figure 7). The hooked mass will hang from the string and the binder clip will prevent the string from slipping. The spring-scale binder clip should be clipped on the bottom edge of the meter stick. This will prevent the clips from being pulled off the meter stick.
   {13046_Procedure_Figure_7}
   Note 3: (Optional) Clamp the support stand to the tabletop using a C-clamp.
   Note 4: Figure 6 shows how to use the mass binder clip when the mass and string are attached at the same position on the meter stick. Only one binder clip is used for this setup.
5. Lab partner responsibilities:
   Lab partner 1: Hold the base of the support stand with one hand and pull on the string with your other hand to lift the boom so it is parallel to the ground as well as keep the string at the proper angle. (If a C-clamp is used, the support stand should be secure and it will not be necessary to hold it down with one hand.)
   Lab partner 2: Measure and record the angle of the string with the protractor and the force measurement from the spring scale.
6. Follow steps 7–10 to collect spring-scale force data for each particular test given in the data table. When the mass and string are connected at the same position, set up the boom as shown in Figure 6. All other tests will be set up similar to Figure 5. Hang the mass from the string, making sure the mass clip is secured to the meter stick and does not slip. Both clips should be centered around the appropriate mark on the meter stick (see Figure 8).
   {13046_Procedure_Figure_8}
7. With the ring stand firmly held down with one hand, slowly pull on the string toward the ring stand rod in order to raise the boom until it is parallel to the ground. Pull the string in the same plane as the boom in order to prevent the boom from spinning around the support stand rod. Note: It may be easier to raise the boom with one hand first and then pull on the spring scale until there is enough tension to support the boom.
8. Slowly raise or lower the string angle, while maintaining the parallel boom, until the string is at the appropriate angle according to the value in the data table. Use a protractor to measure the approximate angle of the string (see Figure 9). The angle should be within ±3° of the value in the data table for the specific test. All angles should be measured with respect to the horizontal.
   {13046_Procedure_Figure_9}
9. When the boom and string are at the proper angles, measure and record the force indicated on the spring scale. Note: Depending on the mass used, some tests may result in a force greater than 1000 g. If this occurs, record >1000 g in the data table.
10. When all the data has been collected for a particular mass position and string angles, slowly lower the mass to the tabletop.
11. Repeat steps 6–10 for each test in the data table, using the appropriate clip positions, and string angle for each test. Measure and record the force on the spring scale when the string angle is at the appropriate value (within ±3°). Note: It is easier to move the mass clip and looped string when the mass is removed from the string.
12. Consult your instructor for appropriate storage procedures.

Student Worksheet PDF

13046_Student1.pdf