How Do Tensions in a Massless, Frictionless Pulley System Compare?

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In a massless, frictionless pulley system, the tensions in the rope sections T1, T2, and T3 are equal due to the nature of the pulleys. The equations governing the system include T1 - F = 0, T4 - T1 - T3 = 0, T2 + T3 - T5 = 0, and T5 - Mg = 0. Since the pulleys are massless and frictionless, they cannot create a difference in tension; thus, T1 = T2 = T3. This equality is essential for solving for the applied force F and understanding the overall dynamics of the system. The analysis confirms that the tensions must remain constant throughout the rope sections.
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A mass M in held in place by the applied force F and the pulley system shown below. The pulleys are massless and frictionless. Determine the tension in each section in each section of rope and the applied force F

Taking upwards as positve

-T1 - F = 0

T4 - T1 - T3 = 0

T2 + T3 - T5 = 0

T5 - Mg = 0

Now this is where I confused about the tension
To me, I think T1 = T2 = T3
but again, am not sure, can anyone tell me if it was right or wrong ? so I can go on with my problem. Thank you
 

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As the pulleys are massless and frictionless, and T1, T2, T3 are the tensions in the same rope, they must be equal. The massless pulleys would rotate with infinite angular speed otherwise.

ehild
 

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