Determining the Speed of a Cylinder in a Cable and Pulley System

[KillerZ]

Homework Statement

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.

Homework Equations

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

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.

 

[tiny-tim]

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.
…
I don't think its right because I am getting a negative number when it should be positive.
…
This would mean that the cylinder is going down not up.

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 s_c instead of s_b, where s_c is the distance between the two lowest pulleys …

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

 

[KillerZ]

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

 

[tiny-tim]

Yes.

 

[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

 

[tiny-tim]

Hi KillerZ!

Yes, except it's +v_A/3.

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