Teacher Notes


Teacher Notes
Publication No. 12662
Simple Form Truss—Classroom SetAdvanced Inquiry Laboratory KitMaterials Included In Kit
Binder clips, 4
Meter stick, half, with hole String, thin, 2 m Support clamp with bracket, screw and bolt Additional Materials Required
(for each setup)
Cclamp, 3" (optional, recommended) Hooked mass, 500g Protractor Ruler or meter stick Scissors Spring scale, 1000g Support stand Prelab PreparationFasten 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. {12662_Preparation_Figure_11}
Safety PrecautionsThe materials in this lab are considered safe. Please follow normal laboratory safety guidelines. DisposalThe materials should be saved for future classes. Lab Hints
Teacher Tips
Correlation to Next Generation Science Standards (NGSS)^{†}Science & Engineering PracticesAsking questions and defining problemsDeveloping and using models Planning and carrying out investigations Analyzing and interpreting data Using mathematics and computational thinking Constructing explanations and designing solutions Obtaining, evaluation, and communicating information Disciplinary Core IdeasMSETS1.A: Defining and Delimiting Engineering ProblemsMSETS1.B: Developing Possible Solutions MSETS1.C: Optimizing the Design Solution HSETS1.A: Defining and Delimiting Engineering Problems HSETS1.B: Developing Possible Solutions HSETS1.C: Optimizing the Design Solution Crosscutting ConceptsSystems and system modelsStability and change Structure and function Performance ExpectationsMSPS12: Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred. Answers to Prelab Questions
Sample Data{12662_Data_Table_1}
{12662_Data_Table_2}
Answers to Questions
DiscussionWhen a lever arm is made to pivot around a fulcrum, a rotational force must act on the lever arm. This rotational force is called torque. A torque is actually the perpendicular force (F) multiplied by the distance (D) between where the force is applied and the position of the pivot point (Equation 1). {12662_Discussion_Equation_1}
The “sin θ” term is included to make sure only the perpendicular components of the force and lever arm distance are multiplied together. When the angle between the force and the lever arm is perpendicular (90°) then the sin θ term becomes 1 (sin 90° = 1). The conditions for static equilibrium occur when the net force acting on the rigid body and the net torque about any point on the rigid object are both equal to zero (Equations 2 and 3). {12662_Discussion_Equation_2}
{12662_Discussion_Equation_3}
The freebody diagram for a general simple form truss is shown in Figure 13.
{12662_Discussion_Figure_13}
The equations for the torque produced by the hanging mass (τ_{m}) and the cable (τ_{c}) are shown in Equations 4 and 5.
{12662_Discussion_Equation_4}
{12662_Discussion_Equation_5}
Where mg is the weight of the mass (g = 9.81 m/s^{2}), D is the distance the mass hangs from the pivot point; T is the tension in the cable; L is the distance of the cable attachment location from the pivot point. β is equal to (90 – θ). The “positive” direction is chosen to be in the counterclockwise direction. Therefore, the net torque equation is equal to
{12662_Discussion_Equation_6}
Rearranging to solve for the tension in the cable
{12662_Discussion_Equation_7}
Equation 7 is the general equation for the tension in the string of a simple form truss. If the simple form truss is held horizontally and the mass and cable are at the same location on the boom then Equation 7 simplifies to
{12662_Discussion_Equation_8}
There is more to the simple form truss than simply the tension in the string. The wall at the pivot point also applies a force in order to maintain static equilibrium. The net force must also be equal to zero. The force provided by the wall at the pivot point can be determined by separating the force into the x and ycomponents.
{12662_Discussion_Equation_9}
{12662_Discussion_Equation_10}
Where W_{x} and W_{y} represent the x and ycomponents of the force applied by the wall.
{12662_Discussion_Equation_11}
{12662_Discussion_Equation_12}
As an example, suppose a 1000g mass is hanging at a distance of 25 cm from the pivot point of the boom and that the boom is at a 30° angle. The boom is supported by a cable at a 45° angle and attached 40 cm from the pivot point of the boom. What is the tension in the string and the force applied by the wall?
T = (1 kg)(9.81 m/s^{2})(0.25 m) sin (90° – 30°)/(0.40 m) sin (45° + 30°) = 5.5 N {13047_Discussion_Equation_13}
It should be noted that the forces provided by the wall and the tension in the string are greater than the overall weight of the hanging mass—7.1 N + 5.5 N > 9.8 N.
Recommended Products 
Student Pages


Student PagesSimple Form TrussIntroductionThe 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
BackgroundStatic 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. {12662_Background_Figure_1}
A simple truss is a supporting structure consisting of a lever arm (boom) and a supporting cable. A simple truss can act as either a Class II lever or a Class III lever, depending on where the supporting cable is in relation to the supported load (see Figure 2). The fulcrum of the truss is the pivot point where it is connected to the supporting wall.
{12662_Background_Figure_2}
Experiment OverviewLaboratory Objective Guidelines
Materials
Binding clips, 2
Cclamp, 3" (optional, but recommended) Hooked mass, 500g Meter stick, half, with support stand clamp (Simple Form Truss) Protractor Ruler or metric stick Scissors Spring scale, 1000g String Support clamp with bracket Support stand Prelab Questions
Safety PrecautionsThe materials in this lab are considered safe. Please follow normal laboratory safety guidelines. Procedure
Student Worksheet PDF 