Exercise A crane suspends a mass m2= 53 kg directly beneath its boom. The boom i

Question

Exercise A crane suspends a mass m2= 53 kg directly beneath its boom. The boom is rotating about the vertical axis through the origin at a constant w 0.2 rad/s, the mass is travelling at constant velocity of u 0.4 m/s outwards along the boom, and is being lowered at a rate of 0.2 m/s. What is the velocity of the mass relative to ground when the the mass is at coordinates (1, 1.2) in the x-y plane. Answer 1.2 2 3 Kinematics af Mechanisms Aditional Exercises nb From the description, and point O at the centre of rotation and z vertically upwards, we known that: 4 " "4 4.ooAi .TA2 4 00 Ai-n, 4 : 1.6 Substituting values: Norm[] Norn[t] 4m(0.0160738, 0.507289, -0.2}

Explanation / Answer

Here, velocity of mass in x direction = 1 - 1.2   + 0.21607

                                                             = 0.01607 m/sec

velocity of mass in y direction = 1 - 1.2   + 0.70728

                                                  = 0.50728 m/sec

velocity of mass in z direction = 1 - 1.2   + 0

                                                  = - 0.2    m/sec

=>   velocity of mass   =   (0.01607 i + 0.50728 j -   0.2 k) m/sec

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