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

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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