Question

A red box (on the left) with a mass of 15 kg is attached to a string that goes over a massless, frictionless pulley and attaches to a green box with a mass of 4 kg. The green box has a second, separate string attached to its bottom which is attached to a blue box with a mass of 5 kg. (a) What is the acceleration of the system? (b) What is the tension in both strings?

Answer #1

**m1 ( red) = 15 kg**

**m2 ( green ) = 4 kg**

**m3 ( blue) = 5 kg**

**for m1**

**m1*g - T1 = m1*a**

**T1 = m1*g - m1*a**

**for m3**

**T2 - m3*g = m3*a**

**T2 = m3*g + m3*a**

**for m2**

**T1 - T2 - m2*g = m2*a**

**m1*g - m1*a - m3*g - m3*a - m2*g = m2*a**

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

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

**acceleration a = 9.8*(15 - 4 - 5)/(15+4+5) = 2.45
m/s^2**

**--------------------------**

**part(b)**

**tension T1 = m1*g - m1*a = 15*9.8 - 15*2.45 = 110.25
N**

**tension T2 = m3*g + m3*a = 5*9.8 + 5*2.45 = 61.25
N**

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