PROLEM 15.38 An automobile traels to the right at a constant speed of 48 mi/h. If the diameter of a wheel is 22 in., determine the elocities of Points, C,, and E on the rim of the wheel. A 48 mi/h 70.4 ft/s C 0 d d 22 in. r 11 in. 0.91667 ft 2 A 70.4 76.8 rad/s r 0.91667 r A / A / EA / (0.91667(76.8 70.4 ft/s + / [70.4 ft/s ] + [70.4 ft/s ] A A 140.8 ft/s + / [70.4 ft/s ] + [70.4 ft/s 30 ] A A + / [70.4 ft/s ] + [70.4 ft/s ] E A E A 136.0 ft/s E 99.6 ft/s 15.0 45.0 PROPRIETARY MATERIAL. 2013 The McGraw-Hill Companies, Inc. All rights resered. No part of this Manual may be displayed, distribution to teachers and educators permitted by McGraw-Hill for their indiidual course preparation. If you are a student using this Manual, 1052
PROLEM 15.50 Arm A rotates with an angular elocity of 20 rad/s counterclockwise. Knowing that the outer gear C is stationary, determine (a the angular elocity of gear, (b the elocity of the gear tooth located at Point. Arm A: Gear : (a E 0.05 m: + / 0 + ( E E 2.4 m/s 0 + (0.05 m (b E (0.05 2: E+ / E 0 + ( E 0 + (0.05 2(48 48 rad/s 48 rad/s 3.39 m/s 3.39 m/s 45 PROPRIETARY MATERIAL. 2013 The McGraw-Hill Companies, Inc. All rights resered. No part of this Manual may be displayed, distribution to teachers and educators permitted by McGraw-Hill for their indiidual course preparation. If you are a student using this Manual, 1067
PROLEM 15.57 A straight rack rests on a gear of radius r and is attached to a block as shown. enoting by the clockwise angular elocity of gear and by θ the angle formed by the rack and the horizontal, derie expressions for the elocity of block and the angular elocity of the rack in terms of r, θ, and. Gear : Rack A: Rotation about. Tooth E is in contact with rack A. E r θ r le Plane motion Translation with E + Rotation about E. raw elocity ector diagram. + E / E [ ] [ E E / A E r E r l E / E r r 2 tan θ θ ] + [ E / θ ] r tan θ A 2 PROPRIETARY MATERIAL. 2013 The McGraw-Hill Companies, Inc. All rights resered. No part of this Manual may be displayed, distribution to teachers and educators permitted by McGraw-Hill for their indiidual course preparation. If you are a student using this Manual, 1074
PROLEM 15.76 A 60-mm-radius drum is rigidly attached to a 100-mm-radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that end E of the cord is pulled to the left with a elocity of 120 mm/s, determine (a the angular elocity of the drums, (b the elocity of the center of the drums, (c the length of cord wound or unwound per second. Since the drum rolls without sliding, its instantaneous center lies at. 120 mm/s E, r A A/ / (a 120 3 rad/s 100 60 / 3.00 rad/s (b A (100(3 300 mm/s Since A is greater than, cord is being wound. A 300 120 180 mm/s 300 mm/s A (c Cord wound per second 180.0 mm PROPRIETARY MATERIAL. 2013 The McGraw-Hill Companies, Inc. All rights resered. No part of this Manual may be displayed, distribution to teachers and educators permitted by McGraw-Hill for their indiidual course preparation. If you are a student using this Manual, 1104
PROLEM 15.83 Rod A is guided by wheels at A and that roll in horizontal and ertical tracks. Knowing that at the instant shown β 60 and the elocity of wheel is 40 in./s downward, determine (a the angular elocity of the rod, (b the elocity of Point. Rod A: We locate the instantaneous center by drawing lines perpendicular to A and. (a Angular elocity. (b Velocity of : In ΔCE: ( C 40 in./s (12.99 in. 3.079 rad/s 3.08 rad/s 1 7.5 25.98 γ tan 16.1 ; C 27.04 in. 25.98 cosγ ( C (27.04 in.(3.079 rad/s 83.3 in./s 83.3 in./s 16.1 83.3 in./s 73.9 PROPRIETARY MATERIAL. 2013 The McGraw-Hill Companies, Inc. All rights resered. No part of this Manual may be displayed, distribution to teachers and educators permitted by McGraw-Hill for their indiidual course preparation. If you are a student using this Manual, 1112
PROLEM 15.88 Rod A can slide freely along the floor and the inclined plane. enoting by A the elocity of Point A, derie an expression for (a the angular elocity of the rod, (b the elocity of end. Locate the instantaneous center at intersection of lines drawn perpendicular to A and. Law of sines. AC C sin[90 ( β θ] sin(90 θ l AC C cos( β θ l cos( β θ AC l C l (a Angular elocity: cos( β θ A ( AC l A l cos( β θ (b Velocity of : θ ( C l l cos( β θ A cos( β θ PROPRIETARY MATERIAL. 2013 The McGraw-Hill Companies, Inc. All rights resered. No part of this Manual may be displayed, distribution to teachers and educators permitted by McGraw-Hill for their indiidual course preparation. If you are a student using this Manual, 1118