Frictionless Pulleys With Three Objects - Am I Right?

[Procrastinate]

I just want to check whether my answer is right because this worksheet has no answers. Thanks.

The following system of masses are connected by light inextensible strings as shown in the diagram. The string connecting the 5.0 kg mass to the 8.0kg mass passes over a frictionless pulley. Calculate the acceleration of the system and the magnitude of the tension forces T₁ and T₂.

 

[ideasrule]

T2 is supposed to be the magnitude of the tension, so it can't be negative. The mistake is in the step F2=mg-T1-T2. Since T2 acts in the same direction as gravity, it should be F2=mg-T1+T2.

 

[Procrastinate]

T2 is supposed to be the magnitude of the tension, so it can't be negative. The mistake is in the step F2=mg-T1-T2. Since T2 acts in the same direction as gravity, it should be F2=mg-T1+T2.

Why would T₂ act in the direction of gravity? I thought it would be oppose it.

 

[ideasrule]

Without the 6 kg mass, the 5 kg mass would move up instead of down. The 6 kg mass is dragging the 5 kg mass downwards, so T2 must act in the same direction as the gravity on the 5 kg mass.

 

[Procrastinate]

Well my new answers are: a= 1.55ms^-2 and for the tensions: T1 = 90.8N and T2 = 49.55N

Are they right?

If the 5kg mass was replaced by something heavier than the 8kg mass, would T2 act in accordance with gravity?