Plane Curvilinear Motion - Constrained & Dependent Motion - Example Problem 3.7-3

 

If the end of rope A is pulled down with a speed of 1 m/s, determine the speed at which block B rises.

 

 

Given: v_A = 1 m/s

 

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) Choose and draw your datum(s) on the figure in the book. Click on the figure to see the results.

 

Step 2) Draw your position coordinates. Measure the distance to every moving object. Click on the figure to see the results.

 

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

 

L₁ = s_A + s_B + s_C + Constant

 

 

 

 

L₂ = s_A + s_B + s_C + Constant

 

 

 

 

Step 4) Take the time derivative of both length equations and determine the relationship between v_A and v_B.

 

v_A = v_B

 

 

 

 

v_B = m/s

 

 

 

 

Is block B traveling upward or downward?

 

  

 

 

 

Step 5) Verify that the solution makes sense.