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Vector Mechanics For Engineers
- Two blocks each have a mass 1.5 kg and are attached to links that are pin-connected to bar BC as shown. The masses of the links and bar are negligible, and the blocks can slide without friction. Block D is attached to a spring of constant = 720 N/m. Knowing that bloc k = 720 N/m. Knowing that block A is at rest when it is struck horizontally with a mallet and given an initial velocity of 250 mm/s, determine the magnitude of the maximum displacement of block D during the resulting motion.arrow_forwardA 36-lb motor is bolted to a light horizontal beam that has a static deflection of 0.075 in. due to the weight of the motor. Knowing that the unbalance of the rotor is equivalent to a weight of 0.64 oz located 6.25 in. from the axis of rotation, determine the amplitude of the vibration of the motor at a speed of 900 rpm, assuming (a ) that no damping is present, (b ) that the damping factor c/cc is equal to 0.055.arrow_forwardIt is shown in mechanics of materials that the stiffness of an elastic cable is k=AE It is shown in mechanics of materials that the stiffness of an elastic cable is L, where A is the cross-sectional area of the cable, E is the modulus of elasticity, and L is the length of the cable. A winch is lowering a 4000-lb piece of machinery using a constant speed of 3 ft/s when the winch suddenly stops. Knowing that the steel cable has a diameter of 0.4 in., E = 29 × 106 lb/in2, and when the winch stops L = 30 ft, determine the maximum downward displacement of the piece of machinery from the point it was when the winch stopped.arrow_forward
- An object of mass M is attached to a string. The length of the string is r and has no mass. The objects moves in a vertical circle counterclockwise as shown. When the ball is at point F, the string is horizontal. Point E is at the bottom of the circle and point D is at the top of the circle. Air resistance is negligible. Express all algebraic answers in terms of the given quantities and fundamental constants. Suppose that the string breaks at the instant the ball is at point F. Describe the motion of the ball immediately after the string breaks.arrow_forwardA 64-lb block is attached to a spring with a constant of k = 1 kip/ft and can move without friction in a vertical slot as shown. It is acted upon by a periodic force with a magnitude of P=Pm sin wf t = 10 rad/s. Knowing that the amplitude of the motion is 0.75 in., determine Pm.arrow_forwardA machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dash-pot at unit velocity ; 2. the ratio of the frequency of the damped vibration to the frequency of the undamped vibration ; and 3. the periodic time of the damped vibration.arrow_forward
- As a submerged body moves through a fluid, the particles of the fluid flow around the body and thus acquire kinetic energy. In the case of a sphere moving in an ideal fluid, the total kinetic energy acquired by the fluid is where p is the mass density of the fluid, V is the volume of the sphere, and v is the velocity of the sphere. Consider a 500-g hollow spherical shell of radius 80 mm that is held submerged in a tank of water by a spring of constant 500 N/m. (a ) Neglecting fluid friction, determine the period of vibration of the shell when it is displaced vertically and then released. (b) Solve part a, assuming that the tank is accelerated upward at the constant rate of 8 m/s2.arrow_forwardA sensitive electronic system, of mass 25 kg, is supported by a spring-damper isolator that rests on the floor of a manufacturing plant. The operation of nearby rotating equipment causes the floor to vibrate with an amplitude of 8 mm at a frequency of 35 Hz. The electronic system can only operate effectively if the amplitude of its acceleration is less than 40 m/s2. It is known that the damping ratio of the isolator is 0.1. i. Determine the maximum stiffness of the isolator needed for the transmitted acceleration level to be acceptable and hence facilitate effective operation of the electronic system. Using the calculated stiffness value, also determine the largest deformation of the spring in millimetres when the system is in motion. ii. If the damping ratio is allowed to increase by only increasing the equivalent damping coefficient (c) of the isolator, discuss the effect this change would have on the response of the electronic system when operating in the same environment. In your…arrow_forwardA vibrometer used to measure the amplitude of vibrations consists essentially of a box containing a mass-spring system with a known natural frequency of 120 Hz. The box is rigidly attached to a surface that is moving according to the equation y= δm sin wf t. If the amplitude zm of the motion of the mass relative to the box is used as a measure of the amplitude δm of the vibration of the surface, determine (a) the percent error when the frequency of the vibration is 600 Hz,(b) the frequency at which the error is zero.arrow_forward
- A 45-kg motor is bolted to a light horizontal beam that has a static deflection of 6 mm due to the weight of the motor. The unbalance of the motor is equivalent to a mass of 110 g located 75 mm from the axis of rotation. Knowing that the amplitude of the vibration of the motor is 0.25 mm at a speed of 300 rpm, determine (a) the damping factor c/cc(b) the coefficient of damping c.arrow_forwardA slender 10-kg bar AB with a length of l = 0.6 m is connected to two collars of negligible weight. Collar A is attached to a spring with a constant of k = 1.5 kN/m and can slide on a horizontal rod, while collar B can slide freely on a vertical rod. Knowing that the system is in equilibrium when bar AB is vertical and that collar A is given a small displacement and released, determine the period of the resulting vibrations.arrow_forwardUnder the action of a torsional moment of 3880 kg.cm, a transmission shaft undergoes an angular deformation of 0.25º / m. knowing that its length is 1200 mm and that the material used in its construction is a 1045 hot-rolled steel, it is requested:a) The diameter of the tree.b) Disregarding the angular deformation and with the diameter calculated in the previous item, what is the transmissible power at 120 rpm.Data: G = 8 x 104 kg / cm²; e X = πR4 / 2arrow_forward
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