Two blocks of mass and are suspended from a pulley with string . The pulley is hung from ceiling through another string . The tension in strings and are and newtons respectively. The blocks move with an acceleration .
Find the sum of the magnitudes of , , and .
Assumptions and Details:
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By Newton's second law , the acceleration of the two blocks is given by:
m 1 g − m 2 g ⟹ a = ( m 1 + m 2 ) a = m 1 + m 2 m 1 − m 2 g = 5 + 3 5 − 3 × 1 0 = 2.5 m/s 2
The tension in string A : T A = m 1 g − m 1 a = 5 ( 1 0 − 2 . 5 ) = 37.5 N .
The tension in string B : T B = 2 T A = 75 N .
Therefore, ∣ a ∣ + ∣ T A ∣ + ∣ T B ∣ = 2 . 5 + 3 7 . 5 + 7 5 = 1 1 5 .