Pulley Block

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Frequently Asked Questions...

what is the tension in the cord at the right?

three blocks attached by cords that loop over frictionless pulleys. Block B lies on a frictionless table; the masses are mA = 4.90 kg, mB = 9.40 kg, and mC = 13.0 kg. When the blocks are released, what is the tension in the cord at the right?


Best Answer...

Answer:

The blocks are attached. So the experience the same displacement , move at the same velocity and undergo the same acceleration in the direction the can move.
Set up the instationary force balance for each block:, with the tensions in the cord acting as drag force on the block

Block A at the left moves upwards, dragged by the rope T_AB, while gravity acts downwards. Hence
m_A · a = T_AB - m_A · g
=>
The tension in the cord between A and B is
T_AB = m_A · (a + g)

Block B in the middle moves to the right, left moves upwards, dragged by the rope T_AB, while gravity acts downwards:
m_B · a = T_BC - T_AB
=>
With tension AB from above
m_B · a = T_BC - m_A · (a + g)
The acceleration of the blocks is:
=>
a = (T_BC - m_A · g)) / (m_a + m_B)

Block C at the right moves downwards, dragged by the rope T_AC, while gravity acts downwards. Hence
m_C · a = m_C · g - T_BC
=>
with acceleration from above
m_C · (T_BC - m_A · g)) / (m_a + m_B) = m_C · g - T_BC
<=>
m_C · (T_BC - m_A · g)) = (m_C · g - T_BC ) ·(m_a + m_B)

Solve for the tension at the cord to the right T_BC:

T_BC = m_C · g · (2·m_a + m_B) / (m_A + m_B + m_C)
= 13kg · 9.81m/s² · (2·4.9kg + 9.4kg) / (4.9kg + 9.4kg + 13kg)
= 89.7N

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Pulley Block

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