A cylinder weighing 400 lb is held against a smooth incline by means of the weightless rod AB in the figure. Determine the forces P and N exerted on the cylinder by the rod and the incline respectively. 55° P = 378 Ib, N, N = 418 lb P = 398 Ib, N, N = 408 lb OP = 387lb, N, N = 428 lb P = 378 Ib, N, N = 418 Ib
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- A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?The L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has a constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. (a) Obtain a formula for the elongation of the spring due to the weight of the arm. (b) Repeat part (a) if the pin support at A is moved to D.A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.
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- A crane boom of mass 450 leg with its center of mass at C is stabilized by two cables AQ and BQ (Ae= 304 mm2 for each cable) as shown in the figure. A load P = 20 KN is supported at point D. The crane boom lies in the y-z plane. (a) Find the tension forces in each cable: TAQand TBQ(kN}. Neglect the mass of the cables, but include the mass of the boom in addition to load P. (b) Find the average stress (s) in each cable..15 A hitch-mounted bicycle rack is designed to carry up to four 30-lb bikes mounted on and strapped to two arms Gil (sec bike loads in the figure part a) The rack is attached to the vehicle at A and is assumed to be like a cant silkier beam A BCDGII (figure part b) The light of fixed segment AB is U = 10 lb. centered 9 in. from A (see figure part b) and the rest of the rack highs W2 = 40 lb. centered 19 in. from A. Segment ABCDG is a steel tube o(2 X 2 in. with a thickness I = 118 in. Segment BCDGII pivots about a bolt at B with a diameter d1 = 0.25 in. to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright posit ion by a pin C(diameter o( pin d, = 5116 in.) (see phoo and figure part C). The of returning effect of the bikes on the rack is resisted by a force couple F h at BC. (a) Find the support reactions at A for the fully loaded rack. (b) Find forces in the bolt at B and the pin at C. (c) Find average shear stresses in both the bolt at Band the pin at C. (d) Find average bearing stresses o, in the bolt at B and the pin at C.A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.
- Solve the preceding problem for the following data: b = 8.0 in., k = 16 lb/in., a = 45°, and P = 10 lb.A soccer goal is subjected to gravity loads (in the - z direction, w = 73 N/m for DG, BG, and BC; w = 29 N/m for all other members; see figure) and a force F = 200 N applied eccentrically at the mid-height of member DG. Find reactions at sup ports C, D, and H.Solve the preceding problem for W = 1.0 lb. h = 12 in.,and k =0.511,/in.