# Dynamics involving dependent motion

1. Jan 26, 2006

### kc2974

If cylinder B has a downward velocity in feet per second given by
vB = t2/2 + t3/6 , where t is in seconds. Calculate the acceleration of A
when t = 2 seconds.

How does the velocities of A & B relate...Seems to be at C but I am not clear how to state it.

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2. Jan 28, 2006

### jamesrc

If you just look at A and C, you should see that vA=-vC. In other words, A and C move at the same speed and when A moves down, C moves up (and vice versa).

You might be able to see the relationship between B and see, but let's try it a little more analytically: Let's call yC the position of C and yB the position of B. Now let's write yB as a function of yC:

$$y_B=y_c - x$$

where x is a variable I just made up to represent the length of rope between the pulley and weight B. But the length of the rope (let's call it L) is constant and equal to L=yC-x

Plug this into the equation for yB:

$$y_B=y_C - (L - y_C)$$
$$y_B = 2y_C - L$$

Take the derivative to find the relationship between velocities (remember L is constant):

$$v_B=2v_C$$

with

$$v_C=-v_A$$

so

$$v_B=-2v_A$$

3. Jan 28, 2006

### kc2974

Thanks, I finally arrived at this answer Thursday.