# Dynamics of a Box attached to a pully

1. Mar 11, 2016

### ciubba

1. The problem statement, all variables and given/known data
Body A in Fig. 6-33 weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are μs 0.56 and μk 0.25. Angle θ is 40. Let the positive direction of an x axis be up the incline. In unit-vector notation, what is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down
the incline?

Free body diagram: http://postimg.org/image/fh6livrer/

See attached picture (problem 27)
http://postimg.org/image/5svunp27z/

2. Relevant equations
Fnet=ma

3. The attempt at a solution

Clearly the answer to part a is 0-- I'm stuck on part b.

For B, $$F_{Net, y}= -m_B a_y = F_T -m_B g \rightarrow F_T = m_B g - m a_y$$

For A, $$F_{Net, x}=ma_x = - \mu _k m_A g cos(40) +F_T - m_A g sin(40)$$

Plugging in the information,

$$102 a= -0.25*102*cos(40)+32-32a -102sin(40) \rightarrow a=-.39$$

However, the book lists the correct answer as -3.9, so I'm off by a power of ten. Where did I go wrong?

2. Mar 11, 2016

### TSny

Be sure to distinguish between mass and weight.

3. Mar 11, 2016

### ciubba

D'oh! It should be

$$\frac {102}{9.8} a= -0.25*102*cos(40)+32- \frac {32}{9.8}a -102sin(40) \rightarrow a=-3.82$$

Thanks!

4. Mar 11, 2016

### TSny

Good.
(I get -3.88 m/s2, but close enough).