value of spring constant K needed
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- A small lab scale has a rigid L-shaped frame ABC consisting of a horizontal aim AB (length b = 30 cm) and a vertical arm BC (length c = 20 cm) pivoted at point B. The pivot is attached to the outer frame BCD that stands on a laboratory bench. The position of the pointer at C is controlled by two parallel springs, each having a spring constant k = 3650 N/m. that are attached to a threaded rod. The pitch of the threads is p = 1.5 mm. If the weight is 65 N. how many revolutions of the nut are required to bring the pointer back to the mark?A bumping post at the end of a track in a railway yard has a spring constant k = 8.0 MN/m (see figure). The maximum possible displacement d or the end of the striking plate is 450 mm. What is the maximum velocity vmaxthat a railway car of weight W = 545 kN can have without damaging the bumping post when it strikes it?Under some circumstances, when two parallel springswith constants k1 and k2 support a single mass, theeffective spring constant of the system is given byk 4k1k2/(k1 + k2). A mass weighing 20 pounds stretchesone spring 6 inches and another spring 2 inches. Thesprings are first attached to a common rigid supportand then to a metal plate. As the figure illustrates(see image), the mass is attached to the center of the plate in the distributiondouble spring. Determine the constant of theeffective spring for this system. find the equationof motion if the mass is initially released fromequilibrium position with downward speed of2 ft/sec.
- The controlling force curve of a spring controlled governor is a straight line. The weight of each governor ball is 40 N and extreme radii of rotation are 10 cm and 17.5 cm. If the values of the controlling force at above radli are 205 N and 400 N respectively and friction of mechanism is equivalent to 2.5 N at each ball. Find The extreme equilibrium speeds of the governor. (1) The equilibrium speed and coefficienct of insensitiveness at a radius of 15 cmPROBLEM The diameter of two pulleys are (0.3m)and (0.2m), center distance (1m).if we use open belt drive. Determine: 1- the length of V-belt (2ß = 60°). 2- the contact angle between belt and smaller pulley. 3- the horse power, if the smaller pulley turn with speed (400r.p.m) and the tension force in tight side (T1=900N), coefficient of friction ų=0.3 4- the speed of large pulley.Solve Sample Prob. 4.5, assuming that the spring is unstretched when 0 = 90°.(Reference to Sample Problem 4.5):
- A 30kg mass is tied to a uniform rod whose mass and length are 80-kg and 8-m, as shown below. The rod is attached to the floor via a hinge and makes an angle of 70° relative to the ground; a massless string is also attached to the rod at the ¼ point of the rod and makes an angle of 20° relative to the horizontal. What tension must be provided by the rope so that the system remains in stationary? If at some point the string breaks, what will be the angular acceleration of the system the instant that the string breaks?A wagon weighing 5100 Kg moving at a speed of 8 km/h has to be brought to rest. Springs made of wire diameter 25mm with a Dm of 250mm and with 24 turns are available. Find the number of springs required in buffer to stop the wagon at a compression of 180mm. b)A close coiled helical spring is made of diameter wire 25mm. The spring index is 8. Findthe number of turns required and maximum allowable load if the allowable shear stress is100 MPa and elongation is limited to 40mm. [G=80 GPaUsing the figure below for a mass-spring system and given that R2 = 2R1, derive the equation of motion for the system in terms of x. Assume that the pulleys are massless, and the answer should be a differential equation that must include x, f, and their (high-order)derivatives.
- The corediameter of the double start square threaded screw having a pitch of 12mm is 50 mm. A load of 18kN is lifted through a distance of 180mm. Find the work done(in Joule)in lifting the loadand the efficiency of the screw, when 1. The load rotates with the screw, and 2. The load rests on the loose head which does not rotate with the screw. The external and internal diameter of the bearing surface of the loose head are 60 mm and 10 mmrespectively. The coefficient of friction for the screw is 0.11,whilefor the bearing surface is 0.13.a helical compression spring with squared and ground ends is ti be made of a steel wire 79 gpa and presetting is to be used. the operation load of the spring can be considered static. If the maximum working force is 292 N and a force of 35 N is required when the spring is 30 mm longer, determine the spring constant kProblem 3: A helical spring is designed to have a stiffness of 500 N/m. The spring has a wire diameter of 5 mm and an outer diameter of 30 mm. Determine the number of coils required for the spring if the spring index is 6. Problem 4: A helical spring is compressed by a force of 100 N, resulting in a compression length of 20 cm. The spring has a wire diameter of 3 mm and a mean coil diameter of 15 cm. Determine the spring constant (stiffness) of the spring.