Lecture 31: Mid-Term Review ENGI 1313 Mechanics I Lecture 31: Mid-Term Review

Overall Mid-Term Results Class Statistics (259) Average 67% Standard deviation 17% Standard deviation between sections 3% Solution Posted

Term A/B Exam (Mon. Oct 22) Results are not Back Student Numbers 200600816 200641421 200641728 200643385 200714459 200737914 200749075

No Record of Mid-Term Exam Contact Me Immediately to Resolve Student Numbers 200643849 200626752 200402782 200565687 200672285

Problem 1 Determine the components of the F force acting along the u and v axes. Given: 1 = 70 2 = 45 3 = 60 F = 250N

Problem 1 (cont.) Problem Characteristics Solution Method Force vectors No right rectangular coordinate system Forces on specified axes Solution Method Parallelogram or triangle construction Law of sines

Problem 1 (cont.) Force Triangle  Fv F = 250 N 1 = 70 2 = 45 Fu

Problem 2 The three cables are used to support the lamp of weight W. Determine the force developed in each cable for equilibrium. Given: a = 4 m b = 4 m c = 2 m W = 600 N 4 m 2 m 4 m W = 600 N

Problem 2 (cont.) Problem Characteristics Solution Method Particle Equilibrium Scalar or vector approach Solution Method Summation of Forces 4 m 2 m 4 m W = 600 N

Problem 2 (cont.) FBD and Unit Vectors FAD 4 m 2 m 4 m FAB FAC W = 600 N

Problem 2 (cont.) Equilibrium Equation Three Equations FAD 4 m 2 m 4 m FAB FAC W = 600 N

Problem 3 Force F is applied to the handle of the wrench. Determine the angle  between the tail of the force F and the handle AB. Given: a = 0.30 m b = 0.50 m F = 80 N 1 = 30 2 = 45 F = 80N  1 2 0.3 m 0.5 m

Problem 3 (cont.) Problem Characteristics Solution Method Vector projection Solution Method Dot product F = 80N  1 2 0.3 m 0.5 m

Problem 3 (cont.) Unit Vectors Dot Product F = 80N  30 0.3 m 0.5 m 45 0.3 m 0.5 m

Problem 4 The hood of the automobile is supported by the strut AB, which exerts a force F on the hood. Determine the moment of this force about the hinged axis y. Given: a = 0.60 m b = 1.50 m c = 0.25 m d = 1.00 m F = 100 N

Problem 4 (cont.) Problem Characteristics Solution Method Moment about a specified axis Solution Method Triple scalar product

Problem 4 (cont.) Unit Vector Moment about Y-axis