In a similar fashion to the case study described in Sec. 16.4, develop the potential energy function for the system depictedin Fig.P16.32. Develop cont our and surface plotsin MATLAB. Minimize the potential energy function in order to determine the equilibrium displacements
FIGURE P16.32
Two frictionless masses connected to a wall by a pair of linear elastic springs.
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Chapter 16 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The mass of Block(A) in Fig. below is( 6 kg ).The coefficient of friction between the block and the surface on which it rests is (0.25) .The weight (w) is (12N) and the system is in Equilibrium.(a)Find the friction force exerted on Block( A).//(b) Find the maximum weight of (W) for which the system will remain in Equilibriumarrow_forward68% @ uw 10:12 * Asiacell 1ı, docs.google.com 2. If a wooden block of weight W = 9.7 N placed on a smooth surface inclined at an angle 35 and is at rest, then the reaction (F) offered by the surface is * F 35° - 5.6 N ON 9.8 N 7.9 N 13. Find the angle between the horizontal and vertical forces acting in the given figure consisting of a beam with various sections.arrow_forward4. The specific weight of water in the ocean may be calculated from the empirical relation: y = y + Kh/2 (in which h is the depth below the ocean surface, and K is an empirical constant for seawater). Drive an expression for the pressure, P, at any depth h. Find the specific weight and pressure at a depth of 2.0 miles, assuming yo-64 lb/ft³, h in feet, and K = 0.025 lb/ft³.arrow_forward
- A fender is mounted on a automobile though dampers (to absorb collision energy) and springs (so that the fender can recover after low-speed collisions). During a crash-test, the automobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehicle mass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) The springs that mount the fender have a stiffness, k, of 1,000,000 N/m. y m barrier 1) Write a differential equation for the deflection of the springs when the fender is in contact with the barrier. 2) If the damping coefficient, c, is 30,000 N-s/m, what is the damping ratio of the mass-spring-damper system when the fender is in contact with the barrier? 3) For that damping coefficient, make a reasonably accurate sketch (with properly labeled axes) of the time-course of the force exerted on the barrier, starting from the moment of first contact. 4) Is there any value of the damping coefficient, c, that would yield no rebound of the vehicle from…arrow_forwardA three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length 200mm and has a thickness of 20mm. Plywood has a density of 0.37 g/cm^3. For the purposes of finding the platform weight, W, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts M1, M2, and M3 were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. • F₁: (-75,-75) F₂: (85,-75) F: (15,85) P WEDNE 0 Bottom view 0 M2 A coordinate system has been defined, such that middle of the board is 0,0. In this…arrow_forwardA three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length 200mm and has a thickness of 20mm. Plywood has a density of 0.3 g/cm^3. For the purposes of finding the platform weight, W, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts M1, M2, and M3 were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. Co • F: (-75,-75) F₂: (85, -75) • F3: (15,85) -17.4319 MAT 1.338758 3.18886 7 Top View A coordinate system has been defined, such that middle of the…arrow_forward
- (b) Figure Q.3(b) shows a 510 kg balloon with buoyancy force of F = 6 kN, and the air resistance is Fb = 100y N, where v is veloceity in m/s. (1) Draw a free body diagram and the kinetic diagram of the balloon. (ii) Express the acceleration of the balloon in term of v. (ii) If the balloon starts from rest, find the velocity of the balloon. UNIVERSITIT (iv) Using the expression of velocity obtained in (iii, determine the maximum velocity of the balloon. Fp = (100v)N F 6 kN Figure Q.3(b) ALAYSIA KERANA TUHarrow_forwardExample 1: Four masses m1, m2, m3, m4 are 200 kg. 300 kg. 240 kg and 260 kg, respectively. The corresponding radii of rotation are 0.2, 0.15, 0.25 and 0.3 meters, respectively, and the angles between successive masses are 45°, 75° and 135°. Find the position and magnitude of the balance mass required, if its radius of rotation is set to 0.2 m.arrow_forwardFind the equation of pressure, P exerted by a fluid as a function of density, r, gravity, g and height of the fluid, h.arrow_forward
- X₁ Find expression for X2 K₁ K₂ K3 00000 m, 00000 m₂ 00000 In the figure above, mass m1 = m2 and the spring constants k1=k3. When mass m1 is displaced slightly by a distance. x1, from equillibrium as shown, m2 also displaces by x2. a) the potential energy of the system, U(x1,x2)arrow_forwardE3. Suppose a mass-spring system is described by the ODE u"+9u = 0 with initial conditions u(0) = -1, and u' (0)I= 0. %3D a) How high up and how far down does the mass go? b) What is the velocity of the mass when it passes through equilibrium? c) Will the mass move slower as it passes through equilibrium the 5th time it passes through compared to the 1st time? d) Show that the time between a high point and the subsequent low point is 1/2 the period. e) Show that the time between a high point and the subsequent passage through equilibrium is 1/4 the period. (You might need the identity: arctan(2) + arctan(1/z) = /2.)arrow_forwardA mass of 300g hangs in a spring with a spring stiffness of 40 N/m (same situation as in Exercise 4.6). The mass is connected to the spring with a weightless cord, the rigidity of the cord can be considered infinite, ie it is so large that it does not affect the rigidity of the system. We start with a situation where the spring is not loaded and the weight is placed at the end of the spring. So the weight is ground free so that it falls from a height equal to the length of the string before it starts to act on the spring. 0 cm, 6.0 cm, 12 cm, 24 cm. That is, for situations when the length of the cord is 0 cm, 6.0 cm, 12 cm and 24 cm.arrow_forward
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