How to Determine Elevator Speed with Winch Mechanics?

In summary, the conversation is discussing a physics problem involving the speed of an elevator being pulled by two ropes. The person asking for help is confused about the solution and is trying to understand the problem better. Another person explains the problem and provides equations and solutions to help clarify the solution. The final conclusion is that the person asking for help may have mislabeled the problem.
  • #1
ilya
3
0
Please help. I am 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. I am not the kind to just give up.

199.png


Thank you very much!
 
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  • #2
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
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
P012810001.jpg
 
  • #5
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.
 

FAQ: How to Determine Elevator Speed with Winch Mechanics?

What is relative motion?

Relative motion is the motion of one object in relation to another object. It describes how the position, velocity, and acceleration of one object changes in relation to the other object.

How is relative motion different from absolute motion?

Absolute motion refers to the motion of an object with respect to a fixed reference point, such as the Earth's surface. Relative motion, on the other hand, takes into account the motion of one object with respect to another object, rather than a fixed reference point.

What factors affect the relative motion of two particles?

The relative motion of two particles can be affected by the distance between the particles, the masses of the particles, and the forces acting upon the particles, such as gravity or friction.

How is relative motion calculated?

Relative motion can be calculated using vector operations, such as addition and subtraction of velocities and accelerations. The relative velocity and acceleration between the two particles can be found by subtracting the velocity and acceleration of one particle from the other.

Why is understanding relative motion important?

Understanding relative motion is important in many fields of science, such as physics, astronomy, and engineering. It allows us to accurately describe and predict the motion of objects in relation to each other, which is crucial in practical applications such as space travel and satellite navigation.

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