Relative motion of 2 particles

1. Jan 28, 2010

ilya

Please help. Im starting to think the answer in the back of my book is wrong. Refer to picture below. Question: Find the speed of the elevator if the winches A and B both pull the rope at 5 m/s. Answer is 2.14m/s. How? I have no idea. Im not the kind to just give up.

Thank you very much!

2. Jan 28, 2010

ehild

The length of both ropes changes in a rate -5 m/s. So the sum of the velocities is not zero.

More: notice that xa=xb, xa=xd+xc.

ehild

3. Jan 28, 2010

ilya

Thank you for your reply. In class we set these types of equations as:

Rope 1:

Step one: Xb+Xc+Xd= length(which is just Some constant)
Step two: Differentiate both sides to get velocity since previous equation is length or displacement.

there fore we get Vb+Vc+Vd=0

Step three: we know Vb=Va=5m/s and we can substitute. 5+Vc+Vd=0 -> Vc+Vd= -5m/s

Rope 2:
Step one: Xa+Xa+Xc= length(some constant)
Step two: differentiate both sides to get 2Va+Vc=0
Step three: substitute known. 2(5) + Vc = 0 -> Vc= -10m/s

Finaly
Solving for the last unknown Vc+Vd=-5 -> -10+Vd=-5 -> Vd = 5m/s

Somewhere I am not doing something right because the answer is 2.14m/s (sign is disregarded)
What doesn't make sense is that Vd and Vc are different velocities, and I think they should be the same because how can the elevator go up with a constant velocity. MY GUESS IS THAT I LABELED THE PROBLEM WRONG

4. Jan 28, 2010

ilya

5. Jan 29, 2010

rl.bhat

When the system moves, total changes in each segments of the string must be zero.
In the blue string
change in the 1st segment = Xb - Xc
change in the 2nd segment= Xd - Xc, but Xd = Xb, so
= Xb - Xc
change in the 3rd segment =- Xd - y
So total change in the blue string = (Xb)-2(Xc) - y = 0......(1)
Now in the purple string
change in the 1st segment = Xa - Xf
change in the 2nd segment = y - Xf
change in the 3rd segment = y - Xg
So total change in the purple string = Xa - 3Xf + 2y = 0......(2)
From eq.1 y = (Xb - 2Xc). Substitute it in equation (2). Note that Xf = Xc and Xa = Xb,
Find Xf in terms of Xa. Put Xa = 5m/s and find Xf.