Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_3

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/3 For the given vectors and of Prob. 1/2, determine the magnitude of the vector difference and the angle which makes with the positive -axis. Complete both graphical and algebraic solutions. Given data from Problem 1/2: Vector : Magnitude units, direction defined by a slope triangle with horizontal leg 4 and vertical leg 3 (1st quadrant). Vector : Magnitude units, direction makes an angle of with the negative -axis (2nd quadrant). Problem 1/3 (a) Algebraic Solution ● Calculation Process 1. Determine the components of and : For , using the slope triangle (3-4-5): For , the angle with the positive -axis is : 2. Calculate the vector difference : 3. Calculate the magnitude of : V 1 V 2 V= ′ V − 2 V 1 θ x V ′ x V 1 V = 1 10 V 2 V = 2 1260 ∘ x V 1 V 2 V 1 cosα = 1 = 5 4 0.8,sinα = 1 = 5 3 0.6 V = 1 V cosα i+ 11 V sinα j= 11 10(0.8)i+10(0.6)j=8i+6j V 2 x180− ∘ 60= ∘ 120 ∘ V = 2 12cos(120)i+ ∘ 12sin(120)j= ∘ 12(−0.5)i+12(0.8660)j=−6i+ V= ′ V − 2 V 1 V= ′ (−6−8)i+(10.392−6)j V= ′ −14i+4.392j V ′ V= ′ = (V )+(V ) x ′2 y ′2 (−14)+(4.392) 22 4. Calculate the angle with the positive -axis: Since and , the vector is in the 2nd quadrant. ● Final Conclusion: The vector difference has a magnitude of units and its direction angle with the positive -axis is . (b) Graphical Solution ● Calculation Process 1. Vector Triangle Construction: The vector difference can be represented by the side of a triangle that connects the tip of to the tip of when bo