Question

For a short time the bucket of the backhoe traces the path of the cardioid r = 25(1-cos) ft. The boom is rotating with an angular velocity of 8 = 2.3 rad/s and an angular acceleration of 8 = 0.22 rad/s at the instant shown. (Figure 1) Part A Determine the magnitude of the velocity of the bucket when 0 = 1200 Express your answer to three significant figures and include the appropriate units. v= Value Units Submit Request Answer Part B Figure < 1 of 1 > Determine the magnitude of the acceleration of the bucket when 0 = 120°. Express your answer to three significant figures and include the appropriate units. a= Value Units 0 = 120° Submit Request Answer Provide Feedback

Answer 1

Answer: Griven, 80 = 2.3 rad/s gol = 0.22 Yad/s2 required 9 = 120° Bucket path = 25(1-C058) ft 95(0-4-sine) you] »/8= 258 sine Again, y" s pohy 25 (*50 048* *x0 )} -> ØY" 25 (60)2 cos o + EcºSn09 At OC 190°, we can get ; Yo = 25(1-COS 1200) = -37.567 Y - 25 x 2.3 x sini20° = 49.79 A/S Y" = 25 (2.32 COS 120° + 6,99 Sin 120°)- = -61-36 R/52 Scanned with

(2) (a) magnitude of velocity is given as S v : Jer')2 +GiovjeJEM.as)2 + (37.5x2.3 12 v 99.5896 ft/s) :(b magnitues of acceleration ar -v@v2] + [ro" 4 28101]? =-61.36 -( 37.5 x 2.32)2 + (37.5%0.22 )+ (2x49.79x23)]2 -> 351.8038 ft (82)
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