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Figure P8 shows a spring-mass system consisting of multiple linear springs arranged in a combination of series and parallel connections.
The top three springs with stiffness k are connected in parallel to a rigid bar. This bar is then connected to the mass M through three identical springs (each of stiffness 2k) arranged in parallel configuration.
Which of the following correctly represents the , of the system?
Assume all springs are linear, massless, and deform only in the vertical direction.
Select the correct answer.
Figure P8. Spring and mass system.
Consider the spring system shown in Figure P7 . A mass is placed on top of a vertical spring and comes to rest after causing a vertical deflection .
If and the spring stiffness is = 5.9 N/m, which of the following is the ?
Assume the system is in equilibrium and the acceleration due to gravity is
Figure P7. Mass–spring system in static equilibrium
Consider the pulley system shown in . The system consists of six pulleys, three fixed pulleys (A, B and C) and three moveable pulleys (D, E and F), and a single mass . The pulley arrangement is designed to increase the input force ( ) in order to lift the mass (M).
The of the system is defined as the ratio of the output force (the force acting on the mass) to the input force (the force applied to the cable).
Which of the following correctly represents the of this system?
Assume the system is in equilibrium, and that the pulleys and cables are massless and frictionless.
Figure P6. Pulley system
Now consider the cantilever beam shown in Figure P5 with different loading. A force F3 is applied at point B and acts in the positive y direction. An applied moment M1 acts at the tip of the beam (point C), acting in direction shown.
If F
Select the correct answer (All answers are in N·m)
Figure P5. Cantilever beam with applied moment and force.
Consider the cantilever beam shown in Figure P4. Two forces are applied on the beam: F1 acts at point B in the positive y-direction, and F2 acts at point C in the negative x-direction, as shown.
If F1 = 1655 N and F2 = 2148 N, determine the reaction moment (MA) at the fixed support A. Use the sign convention for forces and moments shown in the figure (i.e. a counter clockwise moment is considered positive).
Select the correct answer (All answers are in N·m)
Figure P4. Cantilever beam with applied forces
Consider the free-body diagram of the beam shown in Figure P3 . The beam is in equilibrium. The support reactions are shown, together with the external force
Which of the following correctly represents the moment equilibrium equation about point B?
Use the sign convention for forces and moments shown in the figure.
Figure P3. Beam free-body diagram
. Two ropes are attached to an eyelet.
Each rope is in tension, with forces
F1 and F2 acting along the ropes as shown.
For select which of the following is the correct expression for the magnitude of the resultant force .
Select the correct answer.
Figure P2. Rope connection
. Using the dimensions provided in the figure,
determine the value of the angle
θ.
Figure P1. Truss
Which of the following correctly identifies the point of application (distance from A ) of the equivalent resultant force
Consider the free-body diagram of the beam shown in . The beam is in equilibrium. The support reactions are shown, together with the external uniformly distributed load , applied at the position indicated.
Which of the following correctly represents the
Use the sign convention for forces and moments shown in the figure.
Figure P3. Beam free-body diagram