4 Block Pulley System | Newton's 2nd Law | Engineering Dynamics

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Welcome to Engineering Hack! In today's video we are still exploring pulley systems. This time with 4 blocks and an overwhelming 6 unknowns. However, in these cases (unless you can use a computer to solve the linear system for 6 unknowns) there will always be a catch or a way you can eliminate some of the unknowns and make the whole problem easier to solve. To solve this question, we are interested in the motion and also in the forces that cause the motion to start with. Thus, expect at least 4 free body diagrams. We'll be applying Newton's second law to be able to arrive at conclusions in regard to the whole system and then again to be able to calculate the forces and accelerations for the individual components. We are using free body diagrams to isolate these components and evaluate them as individual control volumes. This is problem 12.32.

Problem statement: The masses of blocks A, B, C and D are 9 kg, 9 kg, 6 kg and 7 kg, respectively. Knowing that a downward force of magnitude 120 N is applied to block D, determine
(a) the acceleration of each block
(b) the tension in cord ABC.
Neglect the weights of the pulleys and the effect of friction.

Answer:
T = 84.61N
Acc of A = 1.073 m/s² downwards
Acc of B = 1.073 m/s² downwards
Acc of C = 4.29 m/s² upwards
Acc of D = 1.073 m/s² downwards

To learn more please watch the video till end and if you have a question just ask in the comments section.
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