View In: English v In the below arrangement, all the string and pulleys are massless and the inclined plane is frictionless. At t 0, spring is unstretched and a constant force F = mg starts to act. Find the maximum extension in the spring. (Assume incline to be sufficiently long). Question 11 F-mg m m2m 53 Options 8mg 1. O k 4 mg 2. O 5 k 8 mg 3. O 15 k 8mg 3k
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- 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 mmA 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 springA 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 stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed torque t1acting aver segment 1 and concentrated torque t2applied at C, as shown in the figure. Segment 1 of the shaft has a diameter of d1= 57 mm and length of L1= 0.75 m; segment 2 has a diameter d2— 44 mm and length L2= 0.5 m. Torque intensity /,"= 3100 N . m/m and T2= 1100 N. m. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: .x = L1/2 and at .x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams.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.)A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.
- Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.The tensional pendulum shown in the figure consists of a horizontal circular disk of a mass M = 60 kg suspended by a vertical steel wire (G = SOGPa) of a length L = 2 m and diameter d = 4 mm. Calculate the maximum permissible angle of rotation <£m:ls of the disk (that is, the maximum amplitude of torsional vibrations) so that the stresses in the wire do not exceed 100 MPa in tension or 50 MPa in shear.The piston in an engine is attached to a connecting rod AB, which in turn is connected to a crank arm BC (see figure). The piston slides without friction in a cylinder and is subjected to a force P (assumed to be constant) while moving to the right in the Figure. The connecting rod. with diameter d and length L, is attached at both ends by pins. The crank arm rotates about the axle at C with the pin at B moving in a circle of radius R. The axle at C, which is supported by bearings, exerts a resisting moment M against the crank arm. (a) Obtain a formula for the maximum permissible force Pallow. based upon an allowable compressive stress acin the connecting rod. (b) Calculate the Force Pallowfor the following data:
- 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.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?.17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C. Consider torsion effects only. Assume G = 4000 ksi is constant. Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.