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The bowling ball shown rolls without slipping on the horizontal xz plane with an angular velocity,
Fig P15.184 and P15.185
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Vector Mechanics For Engineers
- B. In Fig. below; rod AB rotates about an axis through A and is connected to block D by a flexible and inextensible cable. Determine the linear velocity of block D when 0 = tan ( 3 /4 ), and the angular velocity of AB is 2.5 rad / sec counterclockwise. Fig.2.B B 1.5m 25marrow_forwardProblem 16.113 The disk has an angular acceleration a = 7 rad/s² and angular velocity w = 3 rad/s at the instant shown. It does not slip at A. (Figure 1) Figure y x @ α 0.5 m A 45° 45° с Barrow_forward5. The slider P can be moved inward by means of the string S, while the slotted arm rotates about point O. The angular position of the arm is given 12 where e is in radians and t is in 20 by 0 = 0.81 - %3D seconds. The slider is at r 1.6 m when t = 0 and thereafter is drawn inward at the constant rate of 0.2 m/s. Determine the magnitude and direction (expressed by the angle relative to the positive x- axis) of the velocity and acceleration of the slider when t= 4 s. %3D Ans. 0.377 m/s, 259.5°; 0.272 m/s, 19.4° y 1. Sarrow_forward
- At the instant shown in (Figure 1), rod AB has an angular velocity WAB = 2.2 rad/s and an angular acceleration AB = 5 rad/s². The collar at C is pin-connected to CD and slides over AB. Figure 60° @AB αAB 0.75 m D с 0.5 m B < 1 of 1 Part A Determine the angular velocity of rod CD at this instant. Express your answer in radians per second to three significant figures. Enter positive value if the direction of velocity is counterclockwise and negative value if the direction of velocity is clockwise. WCD= Submit Part B aCD = V Π| ΑΣΦ. 11 Submit Request Answer Determine the angular acceleration of rod CD at this instant. Express your answer in radians per second squared to three significant figures. Enter positive value if the direction of acceleration is counterclockwise and negative value if the direction of acceleration is clockwise. G| ΑΣΦ. 41 vec Request Answer vec ? wwwww rad/s ? rad/s²arrow_forwardThe piston of the hydraulic cylinder gives pin A a constant velocity v = 2.4 ft/sec in the direction shown for an interval of its motion. For the instant when 0 = 59°, determine i, ř, 0, and Ö where r = OA. A. 5.3" Answers: ft/sec ft/sec? rad/sec = rad/sec2arrow_forwardAt the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity w 6.5 rad/s, while at the same instant the arm is rotating upward at a constant rate w₂=3.9 rad/s (Figure 1) Figure 0-45° ▼ Part A If the conveyor is running at a rate r = 5 ft/s, which is increasing at F-8 ft/s². determine the velocity of the package Pat the instant shown. Neglect the size of the package. Enter the z, y, and z components of the velocity in feeet per second to three significant figures separated by commas. vp Part B Submit LVE| ΑΣΦ | 11 ap vec Submit Request Answer Determine the acceleration of the package P at the instant shown Enter the z, y, and a components of the acceleration in feet per second squared to three significant figures separated by commas. IVE] ΑΣΦ | 11 vec 52 C Request Answer ft/s ? ft/s²arrow_forward
- The conveyor belt is moving to the right at v = 12 ft/s, and at the same instant the cylinder is rolling counterclockwise at w = 7 rad/s while its center has a velocity of 4 ft/s to the left. (Figure 1) Figure -X B 1 ft A 1 of 1 Part A Determine the x and y components of the velocity of the point A on the disk at this instant. Express your answers using three significant figures separated by a comma. 17 ΑΣΦvec (VA) T. (VA)y= Submit Part B Request Answer (UB). (UB)y= Submit Determine the x and y components of the velocity of the point B on the disk at this instant. Express your answers using three significant figures separated by a comma. IVE ΑΣΦ | 11 Request Answer ? vec ft/s ? ft/sarrow_forwardThe base structure of the firetruck ladder rotates about a vertical axis through O with a constant angular velocity = 10.3 deg/s. At the same time, the ladder unit OB elevates at a constant rate = 8.3 deg/s, and section AB of the ladder extends from within section OA at the constant rate of 0.55 m/s. At the instant under consideration, = 22°, OA = 7.4 m, and AB = 5.1 m. Determine the magnitudes of the velocity v and acceleration a of the end B of the ladder. Answers: V= a = i i m/s m/s²arrow_forwardCollars A and B are attached by a rod of length 30 cm, as shown below. The joint at A is a ball-and-socket and at B a pin joint. Collar A moves in the z direction, while the guide bar for collar B is on xy plane. At the instant shown, collar A is at a height of 24 cm and collar B is moving with a speed of 3 m/s towards the x axis. Find the (a) angular velocity of the rod, and (b) the sliding of collar B. Use the image attached to solve the questionarrow_forward
- Problem 20.51 At the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity w₁ = 5.8 rad/s, while at the same instant the arm is rotating upward at a constant rate w₂= 3.8 rad/s. (Figure 1) Figure O 2 r = 6 ft 0-45° 1 of 1 Part A If the conveyor is running at a rate r = 5 ft/s, which is increasing at r = 8 ft/s², determine the velocity of the package P at the instant shown. Neglect the size of the package. Enter the x, y, and z components of the velocity in feeet per second to three significant figures separated by commas. vp = Submit Part B ap= IVE ΑΣΦ Submit ↓↑ Request Answer Determine the acceleration of the package P at the instant shown. Enter the x, y, and z components of the acceleration in feet per second squared to three significant figures separated by commas. vec AΣo↓↑vec 5 Request Answer < Return to Assignment ? Provide Feedback ft/s ? ft/s² 8 of 8 Reviewarrow_forward2. For a short period of time, the motor turns gear A with a constant angular acceleration, starting from rest. The cord is wrapped around pulley D which is rigidly attached to gear B. 2) if the radii are: A = 70 mm, r = 230 mm, and rp = 90 mm, the constant angular acceleration of gear A, AA is 4.4 rad/s², determine the angular acceleration of gear B, CB, in rad/s². Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. αA A P Your Answer: 1'B Answer -1'p'arrow_forwardThe base structure of the firetruck ladder rotates about a vertical axis through O with a constant angular velocity = 9.7 deg/s. At the same time, the ladder unit OB elevates at a constant rate = 7.6 deg/s, and section AB of the ladder extends from within section OA at the constant rate of 0.42 m/s. At the instant under consideration, p = 35°, OA = 8.8 m, and AB = 5.9 m. Determine the magnitudes of the velocity v and acceleration a of the end B of the ladder. Answers: V = a = i i m/s m/s²arrow_forward
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