A rope is tied at the end of a uniform rod while attached to a hinge. The system is in equilibrium. Mass of rod= 50kg, 0 = 60°, r= 10m rope hinge rod
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- Determine the length of the tapered portion if the total deformation of the stepped bar is equal to 0.07 mm. Take E=200 GPa. D 0 Diameter (mm) 40 O 13 kN 20 O 20 O + 15 kN 8 KN 200 mm 300 mmQ.2 Determine the vertical movement at C, if (P=100 kN). Steel L= 2 m A = 300 mm? E = 200 GPa Ic 3 m 2 m B 1mRotation of bar OA is controlled by the lead screw which imparts a horizontal velocity v to collar Ċ and causes pin P to travel along the smooth slot. Determine the values of rand 0, where r = OP, if h = 255 mm, x = 185 mm, and v= 32 mm/s at the instant represented. h Answers: r = 0 = i O x C Ρυ mm/s rad/s A
- 11:19 C ull 4G O Suppose that C Cos (w,t) and D Sin (wet) are two independent solutions of the SHO differential equation. Show that the sum of these two solutions is also a solution of the SHO differential equation. Add a caption... > Status (Custom)Question 1: Answer the following questions based on the graph given below Extension e (cm) 12 8. 4 4 8 12 16 20 24 Force (N) 1. For the graph shown, the independent variable is and dependent variable is 2. The scale chosen for the X axis is 3. The scale chosen for the Y axis is 4. The slope of the above graph is cm/N = * m/N 00a) Consider the ODE describing the motion of a pendulum in presence of friction. Let 0 indicate the angle of the pendulum with respect to the vertical line and let t indicate the time. The ODE describing the motion of the pendulum is given by mtô = -mg sin 0 - y0, with 0 E [-x/2, a/2]. Here m > 0 indicates the mass of the pendulum, e > 0 indicates its length, g > 0 indicates the gravitational constant, and y 2 0 is a constant real parameter indicating the intensity of the friction. Identify the dependent and independent variable in this ODE. • Is this a linear or non-linear ODE? • What is the order of this ODE? b) Consider again the ODE introduced in point (a) and describing the motion of the pendulum mtô = -mg sin 0 – yo. with 0 E [-x/2, a/2]. Put m = 1 and e = 1. • Convert this ODE into a system of two first-order ODES. • Compute all equilibria of this system of ODES. Linearise this system of ODE around each equilibrium. Find the eigenvalues of the linearised system around each…
- Evaluate x∮→B·d→l for each of the cases shown in the accompanying figure.A spring within a spring launcher is compressed a distance, x, and locked into position by a pin at point P. A spherical ball M is placed onto the compressed spring. When the pin is removed, the spring accelerates the ball upwards until the ball then reaches some maximum height above the spring, HM. Assume the compression of the spring is small in comparison to the maximum height reached by the launched ball. The ball is then replaced by a ball having one third the mass, M. The same spring is M. 3 compressed the same distance, x, and the new ball is launched. (!))))))))))))))) HMWhere must the force R be applied so that its external effect on the bar ABC will be the same as the combined F2 = 310 N effects of Fi and F2? What is the R magnitude of R? Fi : 730 N TLOU 100 mm :00 mm 250 mm B
- Consider the simplified single-piston engine in Figure CQ15.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in simple harmonic motion.A rod extending between x = 0 and x = 14.0 cm has uniform cross-sectional area A = 9.00 cm2. Its density increases steadily between its ends from 2.70 g/cm3 to 19.3 g/cm3. (a) Identify the constants B and C required in the expression = B + Cx to describe the variable density. (b) The mass of the rod is given by m=allmaterialdV=allxAdx=014.0cm(B+Cx)(9.00cm2)dx Carry out the integration to find the mass of the rod.A copper rod with length 1.4 m and cross-sectional area 2.0 cm2 is fastened to a steel rod of length L and cross-sectional area 1.0 cm2. The compound structure is pulled on each side by two forces of equal magnitude 6.00 104 N (Fig. P14.57). Find the length L of the steel rod if the elongations (L) of the two rods are equal. Use the values Ysteel = 2.0 1011 Pa and YCu = 1.1 1011 Pa. FIGURE P14.57