- #1

baseballfan_ny

- 92

- 23

- Homework Statement
- Block 1 and block 2, with masses m1 and m2, are connected by a system of massless,

inextensible ropes and massless pulleys as shown above.

Solve for the acceleration of block 2 in terms of m1, m2 and g. Assume that ”down” is

positive. Express your answer in terms of some or all of the following: g, m1, and m2.

- Relevant Equations
- F = ma

2nd derivative of length of inextensible string = 0

**FBD Block 1**

**FBD Block 2**

**FBD Pulley B**

I'm mainly concerned with the coordinate system direction in this problem, but just to show my attempt, here are the equations I got from the system.

##-T_A + m_1g = m_1a_1##

##T_B - m_2g = m_2a_2##

##T_A - 2T_B = 0##

Using the fact that the lengths of rope A (wrapped around pulley A) and rope B (wrapped around pulley B), are constant...

##l_A = y_1(t) + y_B(t) + Constants##

##l_A'' = a_1 + a_B =0##

##a_1 = -a_B##

##l_B = y_2(t) -2y_B(t) + Constants##

##l_B'' = a_2 -2a_B =0##

##a_B = \frac {a_2} {2}##

With 5 equations and 5 unknowns, I solved for ##a_2## and got $$a_2 = \frac {-g(2m_1 + 4m_2)} {4m_2 + m_1}$$

My main concern is with the coordinate direction in Blocks 1 and 2. The problem says to take "down" as positive, which I did for Block 1. However, for Block 2, I assumed that the positive direction would be upwards, because if block 1 were to move a bit down, Block 2 (and Pulley B) would move up. Is this the correct way of thinking about it? In an online solution of the problem, the downwards direction was chosen as positive in both Blocks 1 and 2. Appreciate your help!

Thanks in advance! (Also thought I should mention I'm new to PhysicsForums).