How to Calculate Tension in a Two-Block System with Upward Acceleration?

[babbagee]

Hello

The question is
The blocks are now accelerating upward (due to the tension in the strings) with acceleration of magnitude a.

Find T₂, the tension in the lower rope.

I really don't know where to start with this one. Would T2 equal the force that is applied on block one plus the weight that is pulling down. Point me in the right direction please.

Thanks

 

[mezarashi]

What is the difficulty you are having, or what about the problem do you understand or not understand so far. What principles do you think you should use?

 

[babbagee]

Would the tension be T2 = M₁g + (M₁ + M₂)a

beccause there is a downward force of gravity and then an upward force which is acting on both block 1 and 2. So their force would be (M₁ + M₂)a and the tension would be the sum of these two forces.

 

[Doc Al]

Rather than try to solve it in your head, why not apply Newton's 2nd law to each block. What forces act on each?

 

[babbagee]

Block one
W=mg
T1=ma
force of block 2 pulling on block 1 which is the opposite of T2, right

Block two
W=mg
T2=ma

I drew the free body diagrams for the two blocks and these are the forces I came up with.

 

[Doc Al]

Careful: Don't equate a specific force with ma. Newton's 2nd law says that the net force will equal ma.

The forces on block 1: its weight, the tension T1, the tension T2.

The forces on block 2: its weight, the tension T2.

I'll leave it to you to specify the direction of these forces. Now find the net force on each block and apply Newton's 2nd law.