Assuming an ideal pulley, calculate the acceleration of system (a) and the tension (T) in the string connecting the two blocks. (APPHYS)?
Use the photo below for reference.

Answer options:

1) a=6m/s^2 , T=16N
2) a=6m/s^2 , T=4N
3) a=8m/s^2 , T=18N
4) a=8m/s^2 , T=8N
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answers:
oldschool say: We know Fnet = (4-1)*g so a = Fnet/mass = 3g/(1+4) = 0.6g or about 6m/s²
The tension on the left = 1kg(g+a) = 1.6g or about 16N
The tension on the right = 4kg(g-a) = 4*0.4g = 1.6g or about 16N which is
choice A. <<<<<<<<
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oubaas say: acceleration a = g(m4-m1)/(m4+m1) = 10*(4-1)/(4+1) = 6 m/sec^2
Tension T4 = m4*(g-a) = 4*(10-6) = 16 N
Tension T1 = m1*(g+a) = 1*(10+6) = 16 N

Pls note that tension T is equal on both sides of the pulley because pulley has been assumed massless ; if pulley has a mass , then tension T4 whould be greather than tension T1 and the difference T4-T1 is just what needed for accelerating the pulley
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Andrew Smith say: The total driving force is (4-1) g = 3 kg * g
the total mass is ( 4+1) = 5kg
so the acceleration is 3g/5 ( about 6 m/s^2)

The tension in the string can be calculated by finding the gravitational force + acceleration force on the 1 kg mass
= 1 *(3g/5 +g) = 8g/5 N

Or by finding the gravitational force on the 4 kg and subtracting the acceleration force on it.
= 4( g - 3g/5) = 4 * 2g/5 = 8g/5N
Both methods agree so I have not made a mistake.
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