Problem Two uniform rods each of weight W and length L are maintained in the position shown by a couple M 0 applied to rod CD. Knowing that the coefficient of static friction between the rods is 0.40, determine the range of values of M 0 for which equilibrium is maintained. A B C D M0M0 30 o

Solving Problems on Your Own When the motion is impending and  s is known; you must find some unknown quantities, such as a distance, an angle, the magnitude of a force, or the direction of a force. a. Assume a possible motion of the body and, on the free-body diagram, draw the friction force in a direction opposite to that of the assumed motion. Two uniform rods each of weight W and length L are maintained in the position shown by a couple M 0 applied to rod CD. Knowing that the coefficient of static friction between the rods is 0.40, determine the range of values of M 0 for which equilibrium is maintained. A B C D M0M0 30 o Problem 8.154

Solving Problems on Your Own b. Since motion is impending, F = F m =  s N. Substituting for  s its known value, you can express F in terms of N on the free- body diagram, thus eliminating one unknown. c. Write and solve the equilibrium equations for the unknowns. Two uniform rods each of weight W and length L are maintained in the position shown by a couple M 0 applied to rod CD. Knowing that the coefficient of static friction between the rods is 0.40, determine the range of values of M 0 for which equilibrium is maintained. A B C D M0M0 30 o Problem 8.154

Problem Solution Assume a possible motion of the body and,on the free-body diagram, draw the friction force in a direction opposite to that of the assumed motion. Impending Motion: Assumed clockwise A B C D M0M0 W L2L2 L cos  L sin  N F N F (L /2)cos  W Free-Body Diagrams CxCx CyCy AxAx AyAy

Since motion is impending, F = F m =  s N. Substituting for  s its known value, you can express F in terms of N on the free-body diagram, thus eliminating one unknown. Assume a possible motion of the body and,on the free-body diagram, draw the friction force in a direction opposite to that of the assumed motion. Impending Motion: Assumed clockwise Free-Body Diagrams A B D M0M0 W L2L2 L cos  L sin  N N F =  s N C (L /2)cos  W CxCx CyCy AxAx AyAy Problem Solution

+ Write and solve the equilibrium equations for the unknown. A B W L2L2 L cos  N F =  s N  M A = 0: N (Lcos  ) - W (L/2) = 0 W 2 cos  N = F =  s N =  s W 2 cos  AxAx AyAy Problem Solution

Write and solve the equilibrium equations for the unknown. D M0M0 L sin  N C F =  s N F =  s N =  s W 2 cos  (L /2)cos  W +  M C = 0: M 0 - N (Lcos  ) + F (Lsin  ) - W (L/2)(cos  ) = 0 W 2 cos  N = M 0 - (Lcos  ) + (Lsin  ) - W (L/2)(cos  ) = 0 W 2 cos   s W 2 cos  M 0 = WL (cos   s tan  ) 1212 = (0.5)WL (cos 30 o tan 30 o ) M 0 = 0.818WL CxCx CyCy Problem Solution

D M0M0 L sin  N C F =  s N (L /2)cos  W M 0 = WL (cos   s tan  ) 1212 = (0.5)WL (cos 30 o tan 30 o ) M 0 = 0.818WL For Impending Counterclockwise Motion of the rods, we change the sign of  s. Therefore, M 0 is M 0 = WL Range of M 0 for Equilibrium: 0.818WL < M 0 < 1.048WL CxCx CyCy Problem Solution