Page 211 - Dynamics of Mechanical Systems

0593_C06_fm Page 192 Monday, May 6, 2002 2:28 PM

192 Dynamics of Mechanical Systems

P6.4.6: See Problem P6.4.5. Find the torque of the couple.
P6.4.7: See Problems P6.4.5 and P6.4.6. Find the moment of the force system about points
O, A, D, and G.
P6.4.8: Show that the magnitude of the torque of a simple couple (two equal-magnitude
but oppositely directed forces) is simply the product of the magnitude of one of the forces
multiplied by the distance between the parallel lines of action of the forces. Show further
that the orientation of the torque is perpendicular to the plane of the forces, with sense
determined by the right-hand rule.
P6.4.9: Show that a set of simple couples is also a couple. Show further that the torque of
this composite couple is then simply the resultant (sum) of the torques of the simple
couples.

6.5 Equivalent Force Systems
P6.5.1: See Problem P6.3.1. Consider again the force system exerted on the box of Problem
P6.3.1 as shown in Figure P6.5.1, where the magnitudes and lines of action of the forces
are listed in Table P6.5.1. Suppose this force system is to be replaced by an equivalent
force system consisting of a single force F passing through O together with a couple having
torque T. Find F and T. (Express the results in terms of the unit vectors n , n , and n of
2
3
1
Figure P6.5.1.)

FIGURE P6.5.1
A force system exerted on a box.

TABLE P6.5.1
Forces, Their Magnitudes, and Lines of Action
for the Force System of Figure P6.5.1
Force Magnitude (N) Line of Action
18 BA
F 1
25 BO
F 2
30 AO
F 3
10 CB
F 4
12 OC
F 5
26 OG
F 6
20 DH
F 7
25 EO
F 8
16 DG
F 9
24 CD
F 10