Pulley dynamics problem 12-205 Hibbeler

[issacnewton]

Homework Statement

I have posted the snapshot.

Homework Equations

I have written the distances from the datum line. Since we have two threads, I got two
equations.
$$2S_A +S_C=L_1$$

$$(S_B -S_C)+(h-S_C)=L_2$$

where L₁ and L₂ are the lengths of the strings excluding the
parts which remain constant in time.

The Attempt at a Solution

I can now relate B and A as

$$\dot{S_A}=-\frac{\dot{S_B}}{4}$$

$$\ddot{S_A}=-\frac{\ddot{S_B}}{4}$$

So I get $\dot{S_A} =-1$ , which means the block A is going upwards.
Now the problem says that the speed of the cable being pulled at B is decreasing
at the rate of 2 ft/s². So that means $\ddot{S_B}=-2 ft/s^2$.
So I get $\ddot{S_A}= 0.5$. I got the first answer right. I have question about
the interpretation of the second answer. Since $\ddot{S_A}$ is positive, does
it mean the speed of block A is increasing ?. My second numerical answer is correct
though.

 

[tiny-tim]

hi IssacNewton!

… So I get $\dot{S_A} =-1$ , which means the block A is going upwards.

Now the problem says that the speed of the cable being pulled at B is decreasing
at the rate of 2 ft/s². So that means $\ddot{S_B}=-2 ft/s^2$.
So I get $\ddot{S_A}= 0.5$ …

Since $\ddot{S_A}$ is positive, does it mean the speed of block A is increasing ?

A's velocity is -1 downward, ie 1 upward.

A's acceleration is positive downward, ie negative upward, so the speed of 1 upward is decreasing.

 

[issacnewton]

tim, makes perfect sense. these pulley problems sometime throw me...