. Find the resultant moment, which is the sum of the three individual moments (‚ąĎūĚĎÄ . Note that in this case the system may not be in rotational equilibrium. Label your resultant moment as positive or negative.

USD ENGR 101    Fall 2018

Homework #1: Mechanical Engineering Moments  Due:  Tuesday 9/18

Homework should be turned in individually, but you can work together with your classmates. Clearly  show all of your work and note anyone you worked together with on your assignment.

Note: Numerical solutions to the two problems are provided on the back. Submit worked out solutions to

the¬†assignment¬†on¬†Blackboard.¬†Show¬†requested¬†free¬†body¬†diagram¬†and¬†other¬†solutions¬† ¬† Problem¬†1¬†(parts¬†A‚ÄźD):¬†Consider¬†a¬†garlic¬†press¬†shown¬†below¬†in¬†Figure¬†1.¬†Focus¬†on¬†the¬†top¬†half¬† (the¬†bottom¬†half¬†can¬†be¬†thought¬†of¬†as¬†fixed¬†to¬†the¬†ground).¬†¬†The¬†arm¬†pivots¬†about¬†the¬†left¬†hinge.

Figure 1. Garlic Press Arm System

A. Draw a free body diagram to represent this system. Label the relevant forces and the

rotation point. Treat the forces as perpendicular to the lever of the garlic press.

B. Assume¬†that¬†the¬†distance¬†Dinput¬†=¬†4.0‚ÄĚ,¬†and¬†the¬†force¬†Finput¬†is¬†5¬†lb.¬†Consider¬†the¬†system¬†to¬†be¬† in¬†rotational¬†equilibrium,¬†so¬†the¬†sum¬†the¬†moments¬†(‚ąĎūĚĎÄ 0¬†.¬†Find¬†the¬†force¬†Foutput¬†that¬† results¬†on¬†the¬†clove¬†of¬†garlic.

 

USD ENGR 101    Fall 2018

C. Suppose¬†the¬†garlic¬†clove¬†requires¬†a¬†force¬†of¬†40¬†lb¬†to¬†be¬†pressed.¬†¬†If¬†Dinput¬†is¬†at¬†4.0‚ÄĚ,¬†what¬† input¬†force¬†is¬†required?

 

D. A manufacturer wants to design an ergonomic garlic press that only requires 5 lb to  operate.  If the garlic clove requires 40 lb to be pressed, how long must the handle (Dinput)  be?

Problem¬†2¬†(A‚ÄźB):

Forces on two arms with a center of rotation point at A are combined as shown in Figure 2.

Figure 2. Diagram for Problem 2

A. The center of rotation is at point A.  Find the three moments (M1, M2, M3) due to the three

forces.

B. Find¬†the¬†resultant¬†moment,¬†which¬†is¬†the¬†sum¬†of¬†the¬†three¬†individual¬†moments¬†(‚ąĎūĚĎÄ .¬†Note¬† that¬†in¬†this¬†case¬†the¬†system¬†may¬†not¬†be¬†in¬†rotational¬†equilibrium.¬†Label¬†your¬†resultant¬† moment¬†as¬†positive¬†or¬†negative.