ES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division

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1 ES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division Exam 1 Study Guide Exam 1: Tuesday, February 6, :30 to 8:30pm Kirby Room 104 Exam Format: 50 minute time limit. Closed book. Students are allowed to have a calculator,, pencils, etc. Students may also bring a protractor and ruler, but this is not essential. Exam Coverage: Lessons 1 through 7. LESSON 1 THE BIG PICTURE I LESSON 2 THE BIG PICTURE II Know that, for any 2D object that is in Static Equilibrium (i.e., not accelerating),,,, where A can be any point in space. Determine the unknown forces acting on a beam in 2D space, using the 3 equations of Static Equilibrium. Determine the internal forces that are acting on the top and bottom members of a trussed girder by taking a cut at the position of interest and applying the equations of Static Equilibrium. Not on the exam Define stress. LESSON 3 VECTORS: THE PARALLELOGRAM LAW Determine the magnitude and direction of a resultant force (or other vector quantity) using the Parallelogram Law and trigonometry (the Sine Law or the Cosine Law), given its component vectors. Solve for any two unknown quantities (magnitude and/or direction) in a force vector addition problem using the Parallelogram Law; e.g., given the resultant magnitude and direction and the component directions, find the component magnitudes; e.g., given the magnitudes of the component vectors and the resultant magnitude and direction, find the directions of the component vectors; etc. LESSON 4 VECTORS: CARTESIAN COMPONENTS Resolve 2-D vectors into Cartesian components and utilize Cartesian components to solve for unknown magnitudes or directions in either the resultant or component vector for 2D vector addition problems. Write the force vector in 3D space, determine the vector magnitude, write the unit vector, and specify the vector s angles with respect to x, y, and z axes. Determine the resultant of a system of forces LESSON 5 CONCURRENT EQUILIBRIUM IN 2D Define a concurrent free-body-diagram (FBD) and Explain why there are only two equations of equilibrium for a concurrent FBD in two dimensions. Draw the free-body-diagram (FBD) of a particle in equilibrium. Compute the unknowns (forces, angles, distances) for two-dimensional concurrent statics problems. LESSON 6 DEFINITION OF STRESS AND DIRECT STRESS PROBLEMS Define Stress. Compute the normal and shear stresses on a member, if the stress is uniform. Determine the Factor of Safety for a member, given the failure stresses for the material. Know that the formulae = F/A and = F/A are not applicable to bending problems because the stresses are not uniform. LESSON 7 - CONCURRENT EQUILIBRIUM IN 2D II Compute the unknowns (forces, angles, distances) for two-dimensional concurrent statics problems when the number of unknowns requires consideration of equations in addition to the equilibrium equations: spring deformation, the geometry of right triangles (e.g., Pythagorean relations, similar triangles, etc.), or pulleys. Page 1

2 Compute the unknowns (forces, angles, distances) for 2D concurrent statics problems when multiple free-body-diagrams are required. Compute the unknowns for 2D concurrent statics problems when multiple cases (e.g., failure cases ) must be considered. Solve equations by trial-and-error, when necessary. YOU SHOULD: Review lesson notes and homeworks for Lessons 2 through 5 Solve problems from Hibbeler sections 2.3 to 2.6 and 3.3 Solve the problems in this guide. Given Formulae (provided on the exam): Sine Law: A a sin B C [Cc, Bb, Aa] sin b sin c A c B a Cosine Law: 2 2 C A B 2AB cos c [SAS] b C Sample Problems FOR ADDITIONAL PROBLEMS, SEE HIBBELER TEXTBOOK 1. (15 points) Determine the unknown forces F A and F C acting on the beam. 5000N 1000N A FA B 2.5m 4m C F C 2m D 2. (20 points). Determine the magnitude of the resultant of the two vectors F 1 and F 2 and report the angle this resultant makes with respect to F 1. Page 2

3 F 2 =400N F1=500N (25 points). Determine the angle if the resultant of F 1 and F 2 has a magnitude of 300N. F 2 =400N F1=500N Page 3

4 4. (20 points). Determine the magnitude of F 1 and the angle if the resultant has a magnitude of 700N at an angle of 20 (counterclockwise) with respect to F 1. F 2 =400N F1 Page 4

5 5. (20 points) A car is towed with two ropes. The tension in AB is 400 lb and the angle is 20. Knowing that the resultant of the two forces applied at A is directed horizontally along the axis of the car, determine the tension in rope AC and the magnitude of the resultant of these two forces. (ans: AC=585 lbs, F R = 896 lbs) 6. (20 points) Determine the tension in rope AC and the value of so that the resultant force is 800-lb, directed along the x-axis. Given: The tension in rope AB is 500 lb. Page 5

6 7. (20 points) Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. (ans: 25.1 N) Page 6

7 8. (25 points) Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis (ans: 546 N, ) 9. (20 points). Determine the magnitude and the coordinate direction angles ( ) of the force F acting on the stake. (Ans: F=50N, =74.1º, =41.3º, =53.1º). THIS WAS INCLUDED ON THE STUDY GUIDE, ACCIDENTLY (BUT IT IS NOT BEING REMOVED BECAUSE, WELL, IT S GOOD STUFF TO KNOW). THIS IS LESSON 8. THIS MATERIAL WILL NOT BE ON EXAM 1. Page 7

8 10. (30 points) Determine the magnitude and the coordinate direction angles of the resultant force.(ans: F R =39.4lb, =52.8º, =141º, =99.5º). THIS WAS INCLUDED ON THE STUDY GUIDE, ACCIDENTLY (BUT IT IS NOT BEING REMOVED BECAUSE, WELL, IT S GOOD STUFF TO KNOW). THIS IS LESSON 8. THIS MATERIAL WILL NOT BE ON EXAM 1 Page 8

9 11. (25 points). The stock mounted on the lathe is subjected to a force of 60 N. Determine the coordinate direction angle and express the force as a Cartesian Vector.(Ans: =90º, F = <-30, 0, -52.0>). THIS WAS INCLUDED ON THE STUDY GUIDE, ACCIDENTLY (BUT IT IS NOT BEING REMOVED BECAUSE, WELL, IT S GOOD STUFF TO KNOW). THIS IS LESSON 8. THIS MATERIAL WILL NOT BE ON EXAM (35 points) Determine the Factor of Safety F.S. for the AB and AC ropes. Given: The lift sling is used to hoist a container having a mass of 500 kg. The angle is 60 degrees. The 10-mm diameter ropes fail at a stress 50 MPa. Page 9

10 13. (30 points) Two forces P and Q are applied as shown to an aircraft connection. Knowing that the force P = 500-lb and Q=650-lb, determine the magnitude of the forces exerted on the rods A and B. (partial ans: F A =1303 lb) Page 10

11 14. (30 points) Determine the forces in cables AC and AB needed to hold the 20-kg ball D in equilibrium. Ans: AB=98.6, AC=267 1 m 300 N Page 11

12 15. (30 points) Determine the tension in cables A, B, and C and the mass of the body being lifted. Given: The cable system shown is being used to lift body m. The cable system is in equilibrium when a 500 N force is applied vertically at joint 1. 20º B 10º C 1 A N D 3 m Page 12

13 16. (30 points) If a 100 N load hangs at joint E, determine all of the unknown cable forces and the unknown force F that keeps the system in equilibrium. Given: cable ABC wraps around a small pulley at point B. D A B C 45º 30º E F F 100 N Page 13

14 17. (25 points) Determine the maximum force P that can be applied to the small pulley that is free to move on cable ACB if it is known that cable ACB can sustain a maximum tension force of 750 lbs, without breaking. Also, determine the angle. (ans: 913N, 7.5 degrees) Page 14

15 18. (25 points) Two cables are tied together as shown at C. Knowing that the maximum allowable tension is 1200 N in cable AC and 600 N in cable BC, determine the maximum force P and the corresponding angle. (partial ans: 1294 N) 19. (40 points) If the rubber band has k=4 lb/inch, what force does the band exert on the pellet and hand if the total length of the rubber band is 5-inches when unstretched? Page 15

16 SOLUTION Page 16

17 20. (35 points) Two cables are tied together as shown at C. Knowing that the maximum allowable tension is 800 N in cable AC and 400 N in cable BC, determine the maximum force P and the corresponding angle. SOLUTION Page 17