Problem 12 128 r O A b Pin

Problem 12. 128 r O A b Pin B weighs 4 oz and is free to slide in a horizontal plane along the rotating arm OC and along the circular slot DE D B C friction. q of radius b = 20 in. Neglecting and assuming that q = 15 rad/s and. . b q = 250 rad/s 2 for the position q = 20 o, determine for that position (a) the radial and transverse components of E the resultant force exerted on pin B, (b) the forces P and Q exerted on pin B, respectively, by rod OC and the wall of slot DE.

Problem 12. 128 D B C Solving Problems on Your Own q Pin B weighs 4 oz and is free to slide O in a horizontal plane along the rotating b A arm OC and along the circular slot DE b of radius b = 20 in. Neglecting friction. E and assuming that q = 15 rad/s and. . q = 250 rad/s 2 for the position q = 20 o, determine for that position (a) the radial and transverse components of the resultant force exerted on pin B, (b) the forces P and Q exerted on pin B, respectively, by rod OC and the wall of slot DE. r 1. Kinematics: Examine the velocity and acceleration of the particle. In polar coordinates: e . q . v = r er + r q eq . . . 2 . . a = (r - r q ) er + (r q + 2 r q ) eq r = r er q er

Problem 12. 128 D B C Solving Problems on Your Own q Pin B weighs 4 oz and is free to slide O in a horizontal plane along the rotating b A arm OC and along the circular slot DE b of radius b = 20 in. Neglecting friction. E and assuming that q = 15 rad/s and. . q = 250 rad/s 2 for the position q = 20 o, determine for that position (a) the radial and transverse components of the resultant force exerted on pin B, (b) the forces P and Q exerted on pin B, respectively, by rod OC and the wall of slot DE. r 2. Kinetics: Draw a free body diagram showing the applied forces and an equivalent force diagram showing the vector ma or its components.

Problem 12. 128 D B C Solving Problems on Your Own q Pin B weighs 4 oz and is free to slide O in a horizontal plane along the rotating b A arm OC and along the circular slot DE b of radius b = 20 in. Neglecting friction. E and assuming that q = 15 rad/s and. . q = 250 rad/s 2 for the position q = 20 o, determine for that position (a) the radial and transverse components of the resultant force exerted on pin B, (b) the forces P and Q exerted on pin B, respectively, by rod OC and the wall of slot DE. 3. Apply Newton’s second law: The relationship between the forces acting on the particle, its mass and acceleration is given by S F = m a. The vectors F and a can be expressed in terms of either their rectangular components or their radial and transverse components. With radial and transverse components: . . . . 2 S Fr = m ar = m ( r - r q ) and S F q = m aq = m ( r q + 2 r q ) r

r D Problem 12. 128 Solution B C Kinematics. q O b A b B E r O . . . r = - 2 b sin q q 2 q q b r = 2 b cos q b A q = 20 o. . r = - 2 b sin q q - 2 b cos q q q = 15 rad/s 2 . . q = 250 rad/s 2

B r O b 2 q q A b r = 2 b cos q, For: q = 15 rad/s . . r = - 2 b sinq q, b = 20/12 ft, . Problem 12. 128 Solution . . . r = - 2 b sinq q - 2 b cosq q 2 q = 20 o, . . q = 250 rad/s 2 r = 2 (20/12 ft) cos 20 o = 3. 13 ft. r = - 2 (20/12 ft) sin 20 o (15 rad/s) = - 17. 1 ft/s. . r = -2(20/12 ft) sin 20 o (250 rad/s 2 ) - 2(20/12 ft) cos 20 o (15 rad/s)2. . r = - 989. 79 ft/s 2

Problem 12. 128 Solution r D B C q O b A b (a) Radial and transverse components of the resultant force exerted on pin B. Kinetics; draw a free body diagram. E maq Fq Fr r B q O = A mar r B q O A

Problem 12. 128 Solution maq Apply Newton’s second law. Fq Fr r = B q O A mar r B q A O. . . SFr = mar: Fr = m ( r - r q 2 ) (4/16) Fr = 32. 2 [- 989. 79 - ( 3. 13 )(152 )] = -13. 16 lb Fr = 13. 16 lb + + SFq = maq: . . Fq = m ( r q + 2 r q ) (4/16) Fq = [(3. 13)(250) + 2 (-17. 1)(15)] = 2. 1 lb 32. 2 Fq = 2. 10 lb

r B C D q O b A b Fq E r Fr q q O Problem 12. 128 Solution A = B Q r q O B q P A Fr = - Q cos q Fq = - Q sin q + P -13. 16 = - Q cos 20 o 2. 10 = - 14. 0 sin 20 o + P Q = 14. 00 lb 40 o P = 6. 89 lb 20 o q