Physics Block Tension 4 part problem. Please help!

Question

Two blocks with masses M1 and M2 hang one under the other. For this problem, take the positive direction to be upward, and use g for the magnitude of the free-fall acceleration.

(For Parts A and B assume the blocks are at rest.)

PART A:

-Find T2, the tension in the lower rope.

Express your answer in terms of some or all of the variables M1, M2, and g.

PART B:

Find T1, the tension in the upper rope.

Express your answer in terms of some or all of the variables M1, M2, and g.

For Parts C and D the blocks are now accelerating upward (due to the tension in the strings) with acceleration of magnitude a.

PART C:

-Find T2, the tension in the lower rope.

Express your answer in terms of some or all of the variables M1, M2, a, and g.

PART D:

Find T1, the tension in the upper rope.

Express your answer in terms of some or all of the variables M1, M2, a, and g.

Answer 1

It's often useful to draw free body diagrams like the ones below for masses M₁ and M₂. M₂ only has two forces: tension (T₂) and gravitational (M₂ g), so it's easy to determine T₂ in terms of M₂, a, and g. M₁ has three forces: two are tension (T₁ and T₂) and the third is gravitational (M₁ g).

A: T₂ – M₂ g = 0, so

T₂ = M₂ g

B: T₁ – M₁ g – T₂ = 0, so T₁ = M₁ g + T₂

Since T₂ = M₂ g, T₁ = M₁ g + M₂ g

T₁ = (M₁ + M₂)g

C: T₂ – M₂ g = M₂ a, so T₂ = M₂ g + M₂ a

T₂ = M₂(g + a)

D: T₁ – M₁ g – T₂ = M₁ a, so T₁ = M₁ g + T₂ + M₁ a

Since T₂ = M₂ g + M₂ a, T₁ = M₁ g + M₂ g + M₂ a + M₁ a = (M₁ + M₂)(g + a)

T₁ = (M₁ + M₂)(g + a)