Consider the thin rod of length l moving in the x-y plane as shown in Fig. P26.13. The rod is fixed with a pin on one end and a mass at the other. Note that
FIGURE P26.13
Let
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Chapter 26 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The piston of the hydraulic cylinder gives pin A a constant velocity v = 2.1 ft/sec in the direction shown for an interval of its motion. For where r = OA. the instant when = 54%, determine , r, 0, and 6.1" ✓ Answers: r = r = 0 = ÿ = i -1.6989 i 1.9645 i 2.425 10.623 ft/sec ft/sec² rad/sec rad/sec²arrow_forwardA shaft is rotating at a uniform speed with four masses m1, m2, m3 and m4 of magnitudes 300 kg, 450kg, 360kg and 390 kg respectively. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250mm and 300mm. The angles made by these masses with respect to horizontal are 0°, 45°, 120° and 255° respectively. 1) Check the magnitude and position of balance mass if it radius of rotation is 200mm, and 2) Evaluate the effect of adding the balance mass to the system. solve it using garphical methodarrow_forwardA wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) isarrow_forward
- Question 27 Notyet an A circular wheel of mass 50 kg and radius 200 mm is rotating at 300 r.p.m. Find its kinetic energy. A- =|三 Enter your answer here....arrow_forwardHW3) PQRS is a four bar chain with link PS fixed. The lengths of the links are PQ = %3D 62.5 mm ; QR = 175 mm ; RS = 112.5 mm ; and PS = 200 mm to be vertical. %3D The crank PQ rotates at 10 rad/s clockwise. Draw the velocity and acceleration diagram when angle QPS = 120° and Q and R lie on the same side of PS. Find the angular velocity and angular acceleration of links QR and RS.arrow_forwardIf VA = 96.2 i in/sec in the figure below, find w2, the angular speed of bar B2. By 12 in. Bs B8 in. i -10 in. To calculate the angular speeds of the two bars B2 and B3, you need to use the two point formula: 1) fırst on rigid body B2 to calculate the velocity of point B (since you know velocity at point A) 2) then on rigid body B3 to calculate the velocity of point D (since you know velocity at point B) 3) Note that the velocity at point D has to be zero. Thus the two components of the velocity are zero giving you two equations to solve for the two unknown angular velocities. Figure is from "Engineering Mechanic An Introduction to Dynamics", McGill and King.arrow_forward
- A double collar C is pin connected together such that one collar slides over a fixed rod and the other slides over a rotating rod. The geometry of the fixed rod for a short distance can be defined by a lemniscate, ² = (4 cos 20) ft². Rod OA is rotating at a constant rate of 0 = 5.6 rad/s. (Figure 1) Figure Part A Vr, vg = Submit ²2² = 4 cos 20 OF ΠΆΓΙ ΑΣΦ 0 Determine the collar's radial and transverse components of velocity at the instant = 0° as shown Express your answers in feet per second to three significant figures separated by a comma View Available Hint(s) 11 vec A ? 1 of 1 ft/sarrow_forwardThis most likely is made to be a probelm about mx''+bx'+kx=f(t) m = mass b = friction k = spring constant 4. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is atequilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a mediumwhere friction is small, and we assume it is zero. Note that the acceleration due to gravity near theearth’s surface where the experiment takes place can be taken as 32 ft/s2.(a) Suppose that in addition to the conditions described above, a hammer strikes the mass everyπ/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models theforce of each blow to the mass. Find the function x(t) for the displacement from equilibrium infeet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use ofunit step or Heaviside functions and such that in each time window it is a different multiple of the samesinusoidal function.(b) Now assume the same spring-mass…arrow_forwardA shaft is rotating at a uniform speed with four masses mı, m2, m3 and m4 of magnitudes 300 kg, 450kg, 360kg and 390 kg respectively. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250mm and 300mm. The angles made by these masses with respect to horizontal are 0°, 45º, 120° and 255° respectively. 1) Check the magnitude and position of balance mass if it radius of rotation is 200mm, and 2) Evaluate the effect of adding the balance mass to the system.arrow_forward
- The following diagram shows a piston moving in a cylinder with rod AB. Point B is rotating clockwise with an angular velocity of w. cylinder piston A connecting rod crank bearing B ResearchGate The motion of B is given by the equation r = C cos(wt) + Dsin(wt) Were r is the horizontal +vertical distance of B from O, and C, D are constants. For C=D=42mm and w = 20 rad/s. (i) Write r in the form Rcos (wt ± ß) and state the amplitude and period of r. (ii) Sketch one complete cycle of r. (iii) Explore the differences between the derived form and drawn formarrow_forwardIn a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 7.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as 0 = 2.10t? - 0.800r where 0 is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. rad/s (b) What is the maximum tangential speed of a point on the rim of the roller? m/s (c) At what time t should the driving force be removed from the roller so that the roller does not reverse its direction of rotation? |s (d) Through how many rotations has the roller turned between t = 0 and the time found in part (c)? | rotationsarrow_forwardA Ferris wheel with radius 30 ft is decelerating such that at t = 0 s, the tangential speed of a point P on the rim is v=10ft/s and dv/dt = ct. c=-0.4ft/s^3 . What is the acceleration of P at t= 3 s?arrow_forward
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