Explanation Given information: The engine hoist is used to support the 200-kg engine. Assumption: Consider the state of member as tension where the force is pulling the member and as compression where the force is pushing the member. Consider the force indicating the right side as positive and left side as negative in horizontal components of forces. Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces. Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable. Apply the Equation of equilibrium wherever applicable. Acceleration due to gravity is g = 9.81 m/sec 2 . The member AB is a two-force member. Conversion: Convert the mass into weight using the relation: W = m g Substitute 200 kg for m and 9.81 m/sec 2 for g . W = ( 200 × 9.81 ) N Geometry ABC : Show the free-body diagram of the geometry ABC as in Figure 1. Using Figure 1, Length of member AB : Determine the length of member AB using the relation: l A B = l A C 2 + l B C 2 − 2 ( l A C ) ( l B C ) cos 80 ° (I) Determine the angle θ 1 using sine rule: sin θ 1 850 = sin 80 ° l A B (II) Conclusion: Substitute 350 mm for l A C and 850 mm for l B C in Equation (I). l A B = 350 2 + 850 2 − 2 × 350 × 850 × cos 80 ° = 122 , 500 + 722 , 500 − 103 , 320.67 = 861.21 mm Substitute 861.21 mm for l A B in Equation (II). sin θ 1 850 = sin 80 ° 861.21 sin θ 1 = sin 80 ° 861.21 × 850 θ 1 = 76.41 ° Segment GAC : Show the free-body diagram of the segment GAC as in Figure 2. Using Figure 2, Moment about point C : Determine the force in the member AB by taking the moment about point C . ∑ M C = 0 200 × 9.81 × 1.60 − F A B sin θ 1 ( 0.35 ) = 0 (III) Along the vertical direction: Determine the vertical reaction at point C by resolving the vertical component of forces. ∑ F y = 0 F A B sin θ 1 − 200 × 9.81 − C y = 0 (IV) Along the horizontal direction: Determine the horizontal reaction at point C by resolving the horizontal component of forces. ∑ F x = 0 C x − F A B cos θ 1 = 0 (V) Conclusion: Substitute 76.41 ° for θ 1 in Equation (III). 3 , 139.2 − F A B sin 76.41 ° ( 0.35 ) = 0 F A B = 3 , 139.2 0.35 × sin 76.41 ° F A B = 9 , 232.94 N × 1 kN 1,000N F A B = 9

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 6.6, Problem 81P

To determine

The force acting in the hydraulic cylinder AB, the horizontal and vertical components of force at the pin C, and the reactions at the fixed support D.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 80P

Chapter 6.6, Problem 82P

Students have asked these similar questions

Bài 1. Cho cơ hệ như hình 1. Hình biểu diễn lược đổ cơ hệ tại vị trí cân bằng tĩnh. Trục tọa độ Oy hướng theo phương chuyển động của vật 1, gốc O đặt tại vị trí cân bằng của vật 1(tức khi lò xo biến dạng tĩnh). Bỏ qua khối lượng của thanh số 3. Vật rắn 2 là pulley 2 tầng đồng chất có bán kính ngoài 21, bán kính trong I, bán kính quán tính đối với trục qua tâm P-1.5, khối lượng m:. Vật rắn 4 là thanh thắng đồng chất có khối lượng m, chiều dài 1. Cho các số liệu: m = 2kg, m= = 5kg, m = 4kg, k=40(N/cm), ! – 0.8(m),r=0.1(m). Điều kiện đầu y; =0.5 cm );j = 10 cm/s) . Giả sử hệ dao động bé, Vật rắn 2 chuyển động lăn không trượt trên mặt phẳng ngang. 1. Viết phương trình chuyển động của hệ. 2. Xác định tần số dao động tự do của hệ. 3. Xác định đáp ứng dao động tự do của hệ. dây dây 1 2r Hình 1 y 3 -2 I k www. -2

Hints: Find the closed loop transfer function and then plot the step response for diFerentvalues of K in MATLAB. Show step response plot for different values of K. Auto Controls Show solutions and provide matlab code NO COPIED ANSWERS OR WILL REPORT

Obtain the response of the system shown below for a parabolic or acceleration input r(t);where Auto Controls Show full solution

Chapter 6 Solutions

Engineering Mechanics: Statics

Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 3FP Ch. 6.3 - Determine the greatest load P that can be applied...Ch. 6.3 - Identify the zero-force members in the truss....Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Determine the force in each member of the truss,...Ch. 6.3 - Determine the force in each member of the truss,...

Knowledge Booster

The force acting in the hydraulic cylinder AB , the horizontal and vertical components of force at the pin C , and the reactions at the fixed support D .

The force acting in the hydraulic cylinder AB, the horizontal and vertical components of force at the pin C, and the reactions at the fixed support D.

Want to see the full answer?

Chapter 6 Solutions