Lab M-4 Report

Community College of Philadelphia Philadelphia, Pennsylvania Experiment Number: M-4 Title: Moments in Static Systems Written by: Physics 140, Section 003 Lab Instructor: Professor Indu Das Date: February 11, 2022

Experiment M-4 2 Purpose The purpose of this experiment is to determine the effects of various forces and torques acting upon a rigid body in equilibrium. Procedure 1. Set up the Truss Boom making sure to weigh the boom and locate its center of gravity. 2. Set up the crane. 3. Record the load force L in gwt. 4. Take the zero reading of the boom and release/pull down weights when the lab required. Then, read the force S meas from the balance and make any required zero corrections before recording it. 5. Calculate the vertical and horizontal components V and H of the force F acting upon the boom at O. 6. Find the magnitude and angles of force F. 7. Calculate the percent difference between calculated results and measured results.

Experiment M-4 4 Calculations Sample calculations of trial 1 Tria l Masses Forces Distances m b m L w b L S meas OE OD OC kg kg N N N m m m 1 0.209 0.8 2.05 7.84 16 0.01 7 0.041 0.024 V = L + w b = 7.84 + 2.05 = 9.89 [N] H = S meas = 16 [N] F = √ V 2 + H 2 = √ 9.89 2 + 16 2 = 18.81 [ N ]  = tan − 1 ( V H ) = tan − 1 ( 9.89 16 ) = 31.72 S pred = OE ∗ w b + OD ∗ L OC = 0.017 ∗ 2.05 + 0.041 ∗ 7.84 0.024 = 14.85 [ N ] % Dif. in S = | S 2 − S 1 S 2 + S 1 2 | x 100 = | 14.85 − 16 14.85 + 16 2 | x 100 = 7.5%

Experiment M-4 5 Answer to Questions 1. Suppose that you were unaware of the balance of moments requirement for equilibrium (  = 0) and that the only requirements known to you were the balance of forces (  F x = 0,  F y = 0). In Figure 2 would it be possible for you to calculate the force S, knowing only the weights L and w and the various distances? How many unknowns and how many independent equations would you have? Is it possible to make this calculation with the additional equation for the balance of moments? If knowing only the weights L and w and the various distances, it would not be possible to calculate the force S because we have 3 unknowns (H, S, V) but only 2 independent equations. Therefore, it is possible to make this calculation with the additional equation for the balance of moments. 2. Any two forces acting on a body can be combined into a single resultant force having the same effect. Is this statement always true? Explain. No, this statement is not always true. If the forces act at different points on an object, this statement is false. 3. If the summation of moments had been made about point D would the results have been different? Explain. Yes, the results would have been different. The reasons are that the position vector and the direction of force will change from point to point, and the moment depends on the perpendicular distance from the axis to the line of action of the force.