Given the force in spring AD (150N), final length of spring EC (0.8m), spring constant k = 9 N/cm, and ¤= 72° in the spring and pulley system shown, calculate for the following if a= 75', B= 15', d= 2.4m a. the load P in N b. the initial length or spring Lu In mm
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- A bumper for a mine car is constructed with a spring of stiffness k = 1120 lb/in. (see figure). If a car weighing 3450 lb is traveling at velocity v = 7 mph when it strikes the spring, what is the maximum shortening of the spring?A safety valve on the top of a tank containing steam under pressure p has a discharge hole of diameter d(see figure). The valve is designed to release the steam when the pressure reaches the value Pmax If the natural length of the spring, is L and its stiffness is k, what should be the dimension ft of the valve? (Express your result as a formula for h.)The inclined ladder AB supports a house painter (85 kg) at C and the weight iq = 40 K/m} of the ladder itself. Each ladder rail (t5= 4 mm) is supported by a shoe (ts= 5 mm) that is attached to the ladder rail by a bolt of diameter d = 8 mm
- A cable and pulley system in the figure part a supports a cage of a mass 300 kg at B. Assume that this includes the mass of the cables as well. The thickness or each of the three steel pulleys is t = 40 mm. The pin diameters are dPA= 25 mm, dB= 30 mm. and dc= 22 mm (see figure part a and part b). (a) Find expressions for the resultant forces acting on the pulleys at A, B. and C in terms of cubic tension T. (b) What is the maximum weight W that can be added to the cage at B based on the following allowable stresses? Shear stress in the pins is 50 MPa; bearing stress between the pin and the pulley is 110 MPa.A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?A polyethylene tube (length L) has a cap that when installed compresses a spring (with under-formed length L1) by an amount ?? = (L1 = L). Ignore deformations of the cap and base. Use the force at the base of the spring as the redundant. Use numerical properties given in the boxes. (a) What is the resulting Force-in the spring, Fk? (b) What is the resulting Force in the tube, Ftl (c) What is the filial length of the tube, Lf? (d) What temperature change ?T inside the tube will result in zero force in the spring
- Solve the preceding problem if the collar has mass M = 80 kg, the height h = 0.5 m, the length L = 3.0 m, the cross-sectional area A = 350mm2. and the modulus of elasticity E = 170 GPa.A bungee jumper having a mass of 55 kg leaps from a bridge, braking her fall with a long elastic shock cord having axial rigidity EA = 2.3 kN (see figure). If the jumpoff point is 60 m above the water, and if it is desired to maintain a clearance of 10 m between the jumper and the water, what length L of cord should be used?A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)
- 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?The device shown in the figure consists of a prismatic rigid pointer ABC supported by a uniform translational spring of stiffness k = 950 N/m. The spring is positioned a distance P = 165 nun from the pinned end A of the pointer. The device is adjusted so that, when there is no load P, the pointer reads zero on the angular scale. (a) If the load P = 11 N, al what distance .v should the load be placed so that the pointer will read ?? = 2.5° on the scale (see figure part a)? (b) Repeal part (a) if a rotational spring E1= kb-6 is added al A (see figure part b). (c) Lel.x = 7b/8.What is P maxif 0 cannot exceed 2"? Include spring krin your analysis. (d) Now, if the weight of the pointer ABC is known to be W =3N and the weight or the spring is Ws= 2.75 N, what initial angular position (Left in degrees) of the pointer will result in a zero reading on the angular scale once the pointer is released from rest? Assume P = kr=0. (e) If the pointer is rotated lo a vertical position (see figure part c), find the required load P applied at mid-height of the pointer that will result in a pointer reading of 0 = 2.5" on the scale. Consider the weight of the pointer W. in your analysis.A hollow circular pipe (see figure} support s a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1= 50 mm, d2= 60 mm, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.