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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?A 150-lb rigid bar AB. with friction less rollers al each end. is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A. (a) Find reactions at supports A and B. (b) Find the force in the cable.By what distance h does the cage shown in the figure move downward when the weight W is placed inside it? (See the figure.) Consider only the effects of the stretching of the cable, which has axial rigidity EA = 10,700 kN. The pulley at A has a diameter da= 300 mm and the pulley at B has a diameter dB= 150 mm. Also, the distance L1= 4.6 m, the distance L2=10.5 m, and the weight W = 22 kN. Note: When calculating the length of the cable. include the parts of the cable that go around the pulley sat A and B.
- Find support reactions at 4 and Band then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN.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 27‑kg sing is attached to the right end of a horizontal beam (the beam's mass m = 7.7 kg). The left end of the beam is mounted into a wall and it's right end is supported by a string which makes an angle θ = 32° with the beam, see the picture below. Find the magnitude of the tension in the string. 1. The tension in the string, T Find the reaction force exerted by the wall on the beam. 2. The x component of the wall's reaction force, Rx = 3. The y component of the wall's reaction force, Ry =
- The system in the figure is in equilibrium. A concrete block of mass 254 kg hangs from the end of the uniform strut of mass 66.8 kg. For angles o = 26.4° and e = 55.6°, find (a) the tension Tin the cable and the (b) horizontal and (c) vertical components of the force on the strut from the hinge. Strut LHinge (a) Number i Units ° (degrees) (b) Number i Units N (c) Number i Units N The angular position of a point on a rotating wheel is given by e = 6.69 + 1.54t2 + 3.82t, where e is in radians and tis in seconds. At t = O, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 8.46 s? (d) Calculate its angular acceleration at t = 2.77 s. (e) Is its angular acceleration constant? (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i UnitsIn the figure, AB is a rigid rod and CB is a cable. If M is 900kg, what is the pin reaction at A on the rod AB? What is the tension in the cable?draw free body diagram for the following figure and find the tension force in the cable and the reaction * 4 m 6 m 2 m W = 45 kN
- • A sphere weighing 100 N is tied to a smooth wall by a string as shown in Figure. Find the tension T in the string and the reaction R from the wall. 15 12Q1-A- A man stands on the middle rung of a 250 N ladder resting on a smooth floor and against a wall as shown in Figure. The ladder is prevented from slipping by a string OD and the tension force in the string is 50 N, and the reactions at A and B are 1.3 kN and 433 N respectively. Find the mass of the man. Fig. (1) A 250 N 30 2m 0 mTwo weights, A and C, are fixed to a bar, B. Their masses are: A = 60 kg, B = 230 kg,C = 45 kg. B is, in turn, connected to a fixed vertical post by a hinge and a support cableD. The geometry of the system is shown at right. Treat weights A and C as point masses a)What is the tension in support cable D? Be sure to include a detailed freebody diagram to accompany your analysis.b) What is the magnitude of the force provided by the hinge?c) What is the moment of inertia of the A + B + C as a rigid system, for rotationabout the hinge? For analysis, break the beam into a short piece to the left of thehinge, and a separate longer piece to the right of the hinge. If the support cable D on should break,d) what is the angular acceleration of the beam and weights at the moment the cable breaks?e) what is the magnitude of the linear acceleration experienced by each of the weights, A and C, at moment the cable breaks?