A block with mass m 1 hangs from a rope that is extended over an ideal pulley an

Question

A block with mass m1 hangs from a rope that is extended over an ideal pulley and attached to a second block with mass m2 that sits on a ledge. The second block is also connected to a third block with mass m3by a second rope that hangs over a second ideal pulley as shown in the figure below. If the friction between the ledge and the second block is negligible,

m1 = 2.20 kg,

m2 = 4.80 kg,

and

m3 = 8.80 kg,

find the magnitude of the tension in each rope and the acceleration of each block. (Enter the magnitude.)

Explanation / Answer

on m1: Fnet = m a

T12 - m1g = m1 a ...... (i)

on m2: T23 - T12 = m2 a ..... (ii)

on m3: m3 g - T23 = m3 a ..... (iii)

adding all three,

m3 g - m1 g = (m1 + m2 + m3 ) a

a = 9.8 (8.8 - 2.20) / (2.20 + 4.80 + 8.80)

a = 4.09 m/s^2 .......Ans

T12 = 2.20 (9.8 + 4.09) = 30.6 N ....Ans

T23 = 8.80 (9.8 - 4.09) = 50.2 N .....Ans

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