Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance y, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.15 x 105 N/m, the helper spring constant is 3.80 x 105 N/m, and y₁ = 0.500 m. m Need Help? Truck body Main leaf spring (a) What is the compression of the leaf spring for a load of 4.90 × 10³ N? X Read It -"Helper" spring Axle (b) How much work is done in compressing the springs?

i.Considering the rod diagrammed below; calculate an equivalent spring constant or the rod using the length of the rod 1, its area A, and Young's nodulus E for a compressive force F that compresses the rod a distance x. Additionally, is a linear spring a useful model for a rod under compression? What if the rod is under tension? compressed rod

1 m 1 m 1 m b B 30° 0.5 m 0.5 m b -1m 75 mm- 75 mm A 25 mm Section b-b Figure 3 (not to scale) A drum is suspended from the wooden frame ABC as shown in Figure 3. The mass of the drum is 20 kg. The frame ABC is supported by the 2 mm diameter, A-36 steel cable DB and by a pin support at A. You are required to: a Calculate all the internal forces acting at the cross section b-b and in cable BD. b Calculate the orientation of the plane and the magnitude of the maximum in- plane shear stress at point F, on section b-b, and represent this condition using a stress element. с Determine the factor of safety (F.S.) of the cable BD for this loading based on the maximum-distortion energy theory (von Mises).

A cable and D-pulley system is used to bring a 230 kg (ACB) pole to the vertical position, as shown in part (a) of the figure. The cable is subjected to a pulling force T and is secured at C. The length L of the pole is 6.0 m, the outside diameter is d= 140 mm and the wall thickness is t= 12 mm. The post rotates around a pin at A shown in detail in figure (b). if the allowable shear stress in the pin is 60 Mpa, find the minimum diameter of the pin at A to support the weight of the pole in the position shown in (a). Pole 10m Cable Pulley 50m ACB Pin Pin sapport plates 40 m (a)

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 Options 8mg 1. O k 4 mg 2. O 5 k 8 mg 3. O 15 k 8mg 4. O 3k

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2. The mechanical system shown in figure is driven by the applied force fa(t). When x1 = x2 = x3 = 0, the springs are neither stretched nor compressed. a. Draw the free body diagram(s) and write the differential equations. X1 B₁ XXXXXX Hell M₁ K K B2 1 M3 fa(t) moo M₂ K relet K x2

A crank shaft is operated as shown in the figure. A load F1 = 9.73 N is applied and the operator %3D dz applies a load P to counter. The system is in equilibrium and all of the bearings are perfectly dz aligned such that they do not produce moments on the rotating crank. The geometry is given by, w = 7.31 [m), dl = 9.69 m], d2 = 7.57 m). 6.14 (m), d5 = 3.7 (m), %3D d1 d3 = 9.87 (m), d4 %3D F2 and h1 4.4 (m), find the following: %3D F1 Part 1. Express the reaction forces exerted on the bar by the journal bearing at point B. Use the coordinate system shown in the diagram 10 5% 100% Submit [N] Part 2. Express the reaction forces exerted on the bar by the journal bearing at Point A. Use the coordinate system shown in the diagram. 5% 100% 10 Submit [N]

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Problem 2 In the system below, two rigid bodies (Nodes 1 and 3) are connected by four springs to walls on either side, as shown in the figure. Nodes 2 and 4 are fixed (wall). An external force of 10 N is applied to body 1 (Node 1). The spring constants are given as kı=10 N/m, k2=20 N/m, k3=30 N/m, and k4=40 N/m. Assume that the bodies can only undergo translation in x-direction (1 DOF). Using the direct method: a) Find the displacements of the two rigid bodies (Nodes 1 and 3). Hint: units! b) Find the reaction force at the left wall (Node 4). Hint: units! E1 E2 3) F1 www 4 Е4 X