Physics Tension system?! Help!!?
Three boxes are arranged as shown. The middle box has mass M2 and accelerates to the right with acceleration a on a horizontal frictionless table. The boxes to the left and right hang freely, suspended by strings over massless, frictionless pulleys. The box to the left has mass M1 and the box on the right has mass M3. The tension in the left string is T1.
What is M3 in terms of M2, T1, a, and g ?
M3 = M2a/g
M3 = (T1 +M2a)/(g+a)
M3 = (T1 +M2a)/(g-a)
M3 = (T1 +M2g)/a
M3 = (T1 +M2a)/g
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Verified answer
The acceleration of all the boxes is the same. Take forces to the right/downward as positive
Forces on the right box, accelerating downward
T2 = M3*(g - a)
Forces on the middle block
M2*a = T2 - T1
Forces on the left block
M1(g + a) = T1
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From T2 = M3*(g - a) get M3 = T2/(g - a)
from M2*a = T2 - T1 get T2 = M2*a + T1
then
M3 = [M2*a + T1]/(g - a)