# Absolute Dependent Motion

1. Oct 3, 2009

### KillerZ

1. The problem statement, all variables and given/known data

The cylinder C is being lifted using the cable and pulley system shown. If point A on the cable is being drawn toward the drum with a speed of 2 m/s, determine the speed of the cylinder.

2. Relevant equations

$$2s_{A} + s_{b} = l$$

3. The attempt at a solution

I set my points to this:

I don't think its right because I am getting a negative number when it should be positive.

$$2s_{A} + s_{b} = l$$

$$2v_{A} + v_{b} = 0$$

$$v_{b} = -2(2m/s) = -4 m/s$$ This would mean that the cylinder is going down not up.

2. Oct 3, 2009

### tiny-tim

Hi KillerZ!

I think the cylinder does go down when the cable is drawn up.

But I don't think it's 2:1.

Try using sc instead of sb, where sc is the distance between the two lowest pulleys …

and use the fact that the total length of the string is constant.

3. Oct 3, 2009

### KillerZ

So sc would be like this the difference between s1 and s2?

4. Oct 3, 2009

Yes.

5. Oct 3, 2009

### KillerZ

I got it:

$$s_{B} + (s_{b} - h) + (s_{B} - h - s_{A}) = l$$

$$3s_{B} - s_{A} - 2h = l$$

$$3v_{B} - v_{A} - 0 = 0$$

$$v_{B} = -v_{A}/3 = -0.667m/s = 0.667m/s$$ up

6. Oct 3, 2009

### tiny-tim

Hi KillerZ!

Yes, except it's +vA/3.

(ignore what I said originally … I misread the diagram … the cylinder does go up! )