A block with mass m1 hangs from a rope that is extended over an ideal pulley and

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 m3 by 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 = 2.60 kg, m2 = 4.00 kg, and m3 = 8.20 kg, find the magnitude of the tension in each rope and the acceleration of each block. (Enter the magnitude.) a = m/s2 T12 = N T23 = N

Explanation / Answer

For the mass m1 ,

T1 - m1*g = m1*a ..........(1)

For the mass m2

T2 - T1 = m2*a

For mass m3 ,

m3*g - T2 = m3*a .....(3)

add eq(1) and (2)

T2 - m1*g = (m1 + m2)*a

add the above equation to the eq(3)

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

a = (m3 - m1)*g / (m1+ m2+m3) = (8.20 - 2.60)*9.8/(2.60+4+8.20)

a = 3.70 m/s2

substitute the value of a in eq(1)

T1 = m1(a+g) = 2.60*(9.8+3.70)

T1 = 35.12 N

substitute the value of a in eq(3)

T2 = m3(g-a) = 8.20*(9.8 - 3.7)

T2 = 50.02 N

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