Plane Curvilinear Motion - Constrained & Dependent Motion - Example Problem 3.7-4

 

If collar A moves with a constant speed v_A, determine the speed of collar B as a function of the position and velocity of A and the distance h.

 

 

Given: v_A, s_A, h, L

 

Find: v_B

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

Step 1) Locate the datums on the figure in your book.

 

Step 2) Locate the position coordinates on the figure in your book.

 

Step 3) What is the length of the rope in terms of the position coordinates?

 

L = (s_A² + s_B²)^1/2 + (s_A² + h²)^1/2
L = 2s_A + s_B + h
L = 2s_A² + s_B² + h²

 

 

 

Step 4) Take the time derivative of the length equations and determine v_B.

 

v_B = -s_Av_A/ s_B(s_A² + h²)^1/2
v_B = -s_AL/ s_B(s_A² + h²)^1/2
v_B = -s_Av_AL/ s_B(s_A² + h²)^1/2

 

 

 

Step 5) Verify that the solution makes sense.