35 As the hydraulic cylinder rotates around O, the ex- posed length 1 of the piston rod P is controlled by the action of oil pressure in the cylinder. If the cyl- inder rotates at the constant rate = 60 deg/s and 1 is decreasing at the constant rate of 150 mm/s, calculate the magnitudes of the velocity v and ac- celeration a of end B when l = 125 mm. Ans. v = 545 mm/s, a = 632 mm/s²
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- 4. 4) The hydraulic cylinder D extends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. If the dimensions 1 = 1.1 ft, and 2 = 2.3 ft, VA = 4.7 ft/s, aa = 2.7 ft/s², and the angle 0 = 25°, determine the angular acceleration (in rad/s2) of rod ABC. Negative sign must be included if the angular acceleration is clockwise. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. %3D 12 D а Your Answer: AnswerFind: friction force between the spool and the ground. and the UNIT of measurement of the acceleration of the mass center of the spoolα v= A t = B Oh no! A very sad kitty is trapped on a little platform connected to a gear system, the little scoundrel! The cat is 10 feet below the cliff's edge and is too terrified to jump! Quick! Rotate the wheel at A at 4 rad/s to raise the poor creature to safety. At what speed does the platform raise? How long will it take the kitty to reach the top of the clliff's edge? The diameter of the crank and gears are dд = 1 ft, dß = 2 ft, dc = 6 ft, and dp = 2 ft D ft S www S
- 4. 3) The hydraulic cylinder D extends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. If the dimensions 4 = 1.0 ft, and 2 = 1.6 ft, VA = 3.6 ft/s, aa = 2.2 ft/s2, and the angle 0 = 27°, determine the speed of point C. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. %3D В 12 D Your Answer: Answer units 1,The rod OA rotates clockwise at a constant angular velocity of 0 = (3) rad -. Two pin-connected slider block, located at B, move freely on OA. The curved rod is described by the equationr = (250 · (8 - cos 0)) m. Hint: 1. Remember clockwise rotation is negative velocity. A d3 d1 d2 Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value 01 130 degrees di 0.45 m d2 dz 0.2 m 0.325 m Using cylindrical components, a. Determine the cylinders's radial and transverse components of velocity at the instant shown, vr and b. Determine the cylinders's radial and transverse components of acceleration at the instant shown, a, and ag. c. Determine the cylinder's magnitude of the velocity at the instant shown, v d. Determine the cylinder's magnitude of the acceleration at the instant shown, aThe piston of the hydraulic cylinder gives pin A a constant velocity v = 2.1 ft/sec in the direction shown for an interval of its motion. For where r = OA. the instant when = 54%, determine , r, 0, and 6.1" ✓ Answers: r = r = 0 = ÿ = i -1.6989 i 1.9645 i 2.425 10.623 ft/sec ft/sec² rad/sec rad/sec²
- 4. 4) The hydraulic cylinder Dextends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. If the dimensions/₁ 1.0 ft, and /2 = 2.0 ft, vµ = 5.5 ft/s, aµ = 2.1 ft/s², and the angle 0 = 30°, determine the angular acceleration (in rad/s²) of rod ABC. Negative sign must be included if the angular acceleration is clockwise. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Your Answer: 1₁ Answer B 12 ÏÏ a =4. 1) The hydraulic cylinder D extends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. Select the location of the instantaneous center of zero velocity (IC) for rod ABC. point F point E point B point G point D point A point C O O O D B B 0 v a v aA weight with mass mw=150 g is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R=4.00 cm and mass Ms=200 g. Find the magnitude ?a of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. Use ?=9.81 m/s2. Find the tension T in the thread.
- of fod mass 10 kg Tength L = 6 M anguiaŏ velocity w= 8 Bad's calculate comPonent of deaction magnitude of vedtical on the 8od at Point o Sign conventionFor the circular thin plate with a square hole as shown in the image below, its radius R = 0.32 m and the side of the square /= 0.22 m, and the material has a mass per unit area of 14 kg/m2. If at the instant shown, it is subjected to a force P= 44 N, and has a counterclockwise angular velocity of W = 3.8 rad/s, determine the angular acceleration (in rad/s?) of this plate. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s?. R PFor the circular thin plate with a square hole as shown in the image below, its radius R = 0.49 m and the side of the square /= 0.22 m, and the material has a mass per unit area of 14 kg/m². If at the instant shown, it is subjected to a force P= 43 N, and has a counterclockwise angular velocity of W = 2.3 rad/s, determine the angular acceleration (in rad/s²) of this plate. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². R @ Your Answer: Answer 5 3 P