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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?Solve the preceding problem for W = 1.0 lb. h = 12 in.,and k =0.511,/in.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 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 springRepeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.Two rigid bars are connected to each other by two linearly elastic springs. Before loads are applied, the lengths or the springs are such, that the bars are parallel and the springs are without stress. (a) Derive a formula for the displacement E4at point 4 when the load P is applied at joint 3 and moment PL is applied at joint 1. as shown in the figure part a. (Assume that the bars rotate through very small angles under the action of load P.) (b) Repeat part (a) if a rotational spring, kr= kL2, is now added at joint 6. What is the ratio of the deflection d4 in the figure part a to that in the figure part b ?
- 1. A helical compression spring is made of hard-drawn spring steel wire with a wire diameter d = 0.080 in and an outer coil diameter OD = 0.880 in. The ends are plain and ground, and there are 8 total coils. Determine the force F, required to close the spring, the spring constant k, the free length of this spring corresponding to n, = 1.2, and the pitch p.For the system of springs shown below derive the formula for the overallstiffness cΣ and calculate the overall displacement s if F=200 N, c1=2300 N/m, andc2=2100 N/m.Two coaxial closed coil springs make up a standard compound helical spring. When both springs are unloaded, they are not of equal length. If each spring's working stress is to be the same. The wire material has an 80 GPa modulus of rigidity. Find the diameter of steel wire for inner spring and stiffness of inner spring. Also find the stiffness of the compound spring. Outer spring a: Mean coil diameter = 100 mm No. of turns = 15 Wire diameter = 12.5 mm Inner spring b: mean coil diameter = 75 mm No. of turns = 20
- Find the equivalent torsional spring constant (up to two decimal points) of the system shown in the figure. Given : R = 0.2 m k1=1 kN.m/rad, k2 = 2 kN.m/rad , k3 = 3 kN.m/rad , k4 = 4 kN.m/rad , k5 = 5kN/m and k6 = 3.0 kN/mConsidering the figure shown, determine the equivalent spring constant of a spring that will represent all of the given springs such that its deflection is along a vertical path with the mass. k1=1N/m k2=2N/m k3=3N/m k4=4N/m and k5=5N/m. (answer in N/m) * k2 m k3 k5 k4The linkage shown is used in a vehicle suspension system. Find the forces indicated below when a static force of F = 820 lb is applied to the tire at point C at an angle of 0 = 22° as shown. Assume the connection of the wheel to member AB is rigid. hs hy hi F BY NC SA W4. W, Ws 2013 Michael Swanbom Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value Variable Value hi 10 in Wi 8.8 in h2 15.6 in W2 5.6 in h3 18.1 in W3 10.8 in h4 10.9 in WĄ 7.4 in h5 4.9 in W5 9.3 in For all answers, take x as positive to the right and y as positive upward. At point B, member AB exerts a force of B = j lbs on member BHE. At point A, member AD exerts a force of A + j lbs on member AB. At point H, shock GH exerts a force of H = i + i lbs on member ВНЕ. At point E, the magnitude of the force exerted on the car body by member BHE is lbs. At point D, the magnitude of the force exerted on the car body by member AD is lbs. At point G, the…