# Dynamics pulley problem

1. Mar 13, 2008

### mwelly007

Here is the problem;

The 40-lb block is moving downward with a speed of 3 ft/s at t=0 when constant forces P and 2P are applied through the ropes. Knowing that the block is moving upward with a speed of 2 ft/s when t=4 s, determine (a) the magnitude of P. (b) the time at which the speed is 0 ft/s. Neglect all friction.

**The picture is attached as a pdf, which consists of 4 pulleys.

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Last edited: Mar 13, 2008
2. Mar 13, 2008

### Staff: Mentor

Show your work and point out where you got stuck.

3. Mar 13, 2008

### mwelly007

difficulties

I am having difficulties setting it up and getting the ball rolling. There are no examples of pulley problems in this chapter. Thus far, I have figured the length of the ropes to be from left to right:

L1=y1+3*y2
L2=y2+y3

where,
y1=length to P
y2=pulley to pulley/box
y3=length to 2P

From this we no that dL/dt=0 so
v1=y1'+3*y2'
v2=y2+y3

Then I can apply the Principle of Impulse:
mv1+Imp(1-->2)=mv2

I don't think I am setting it up correctly, but once I do, I think I could continue on the right track.

4. Mar 13, 2008

### mwelly007

Any help or assistance would be greatly appreciated. Thank you.

5. Mar 14, 2008

### kamerling

The only thing you really need to know about a pully, is that the tension in the ropes on both sides of the wheel is equal. The tension in the rope through the fixed end of the pully is then twice that value.
If you use this then it's easy to find the total upward force of all the ropes on the block.

6. Mar 14, 2008

### Staff: Mentor

Although in many pulley problems you do have to worry about such constraints in order to solve for the tensions, in this particular problem they give you the tensions. So just follow kamerling's advice and find the net force on the block.

You could use this principle, or you could just use Newton's 2nd law. (What's the acceleration?)

7. Mar 27, 2008

### mwelly007

So, to clarify, my tensions from left to right are... P/4 (for all 4) and P for the last 2... correct? And the acceleration, using v=v0+at, is 5/4 ft/s^2 upward. Then, all the tensions forces are up, mg is down, and F=ma is up, and solve for P? Seems i'm missing something.

8. Mar 27, 2008

### Staff: Mentor

No. The rope on the left is being pulled with a force P, so the tension in all its segments is P; similarly, the rope on the right has a tension of 2P.
That's all there is to it.

9. Mar 27, 2008

### mwelly007

Makes sense, because otherwise adding pulleys would have no benefit. So then the equation is 5P+ma-mg=0, where mg=40 and m=40/32.3? Sorry, but for some reason, this problem is difficult for me to grasp.

10. Mar 27, 2008

### Staff: Mentor

I'd write it as: 5P - mg = ma

11. Sep 18, 2010