3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortex and a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and a Poisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107 kN. Use 9.8 m/s 2 for the acceleration due to gravity. Consider the cross-section shown (you can look these up). Pay attention to the coordinate system given in the drawing. d) where is the centroid? e) what is the area? f) Calculate the shear modulus

A 4.8 m-long from fixed point, 0.5 m wide and ssumed a thickness of 30 mm troughout a springboard made of high strengh S-2 glassfiber material which weighs 3.6-kN/m. If a diver impacts 30-kN at the free-end of the board when about to dive, calculate: i. the reaction at the fixed-end of the cantilever and bending moment diagram. ii. the maximum bending moment in the beam. if the material Young's Modulus of elasticity is 93.8 GPa find: iii the maximum slope of the beam. iv. the maximum deflection in the beam. v.  the maximum strength in the material

Two street lights are mounted as shown in the figure one at A and the other at C. The member AD is able to freely rotate about D. Member BE is a steel cable. B. EACH street light has a mass of 5 kg, AB=20cm, BC=20cm, CD=10cm, DE=17.32cm. Assume gravity is 9.81 N/kg. h=4cm Draw the shear force profile (a) between point A and D. On the diagram, clear indicate the values on the diagram. (b) member just to the right of point B. Calculate the maximum bending shear stress. At what distance from the bottom does it occur? Consider a cross-section of the (c) distance from the bottom does the minimum bending shear stress occur? What is its value? For the same cross-section, at what

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following.   (4) the work done by the reaction force of the pin.____________ (J)

A uniform beam of mass ? = 140.0 kg and length ? = 2.40 m is supported by twocolumns at each end. The beam supports a heavy block of mass ? = 220.0 kg, whose center of gravity is at adistance ? = 0.720 cm from the left end of the beam. 1. Draw a free body diagram for the beam. 2. Find the forces exerted by the columns on the beam

- Two pipes, each with a diameter of Im, are supported every 10m by a frame, as shown in the figure. Each pipe (including its contents) weighs 2.0 kN/m. All contact surfaces are assumed to be frictionless. Determine the support reactions. 1.8m A 2.4 m B 2.4 m

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following.   (2) ) the work done by the couple moment. __________(J) (two decimal places)

In the figure below, the equivalent force-couple at point O is: O-123.3î – 176.8ĵ N, 397 N- m ccw F2 = 300 N N O-123.3î - 216.5ĵ N, 233 N- m ccw 1.0 т 45° O-123.3î –176.8ĵ N, 146.7 N- m ccw 45° O-773î – 176.8ĵ N, 1494 N- m ccw F = 250 N 1.5 m

A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure.   Since the floor is rough, it exerts both a normal force N1 and a frictional force f1 on the ladder. However, since the wall is frictionless, it exerts only a normal force N2 on the ladder. The ladder has a length of L = 4.0 m, a weight of WL = 69.0 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90 kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 =     N N2 =     N f1 =     N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.) N1 =         N N2 =         N f1 =         N

P=6 M=4 W=0.7 L=12