Determine the relative and absolute velocity and acceleration
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Figure in the attachment shows an arrangement of a carriage system. A force P is applied on the carriage B, moving rightward at 3 m/s^2 constant acceleration. At the instant shown the velocity of B is 2 m/s.
(i) Determine the velocity of B relative to A.
(ii) Determine the acceleration of B relative to A.
(iii) Determine the absolute velocity of C, carriage A.
(iv) Determine the absolute acceleration of carriage A.
(v) Determine the force P and the tension in the rope if mass A = 50 kg and mass B = 40 kg. Neglect the masses of pulleys, rope and the friction forces at the wheels.
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This solution helps determine the relative and absolute velocity and acceleration.
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Please refer to the attachment.
Solution:
See attached file for diagram.
We take the fixed wedge as the reference for measuring distances. Fig. shows the initial distances of the carriages from the wedge.
i) In the initial positions of the carriages (at t = 0): 4a + 3b = L .......(1) where L = length of the rope
Let A move forward by a distance x and B by a distance y in the same time t. Distance of A from the wedge becomes (a - x) and that of B becomes (b+y)
At instant t: 4(a - x) + 3(b + y) = L .........(2) (as the length of the rope eamains unchanged)
Equating ...
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