# Pulleys what is going on!

1. Aug 24, 2014

### SteliosVas

1. The problem statement, all variables and given/known data

Pulley system, attachment below. Would be impossible to explain without a diagram.

2. Relevant equations

Wa = 200N
Va0=2m/s
t= 2 seconds
Wb= 40N
μK=0.2
g=9.81m/s^2

3. The attempt at a solution

For block A:

40N + Fn+Tension =m1a

T - 40N*0.2=40N/9.81

Block 2

200 + Fn + Tension = m2a

200N + T = 200N/9.81

So lost to be honest!

#### Attached Files:

• ###### Screen Shot 2014-08-25 at 2.32.45 pm.png
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2. Aug 25, 2014

### Nathanael

Recheck the forces on each of the blocks (I didn't see you include the force of friction anywhere??)

Also, please use the correct names of the blocks ("A" and "B") to avoid confusion :tongue: (you said "Block A" and "Block 2")

Edit:
Hint: (in case I go to sleep before you reply) it only takes 3 equations to solve this problem:
The "equation of forces" on block A
The "equation of forces" on block B
And an equation which relates the acceleration of block A to the acceleration of block B

Last edited: Aug 25, 2014
3. Aug 25, 2014

### Maharshi Roy

Ans:
final velocity= v(initial) + g(Wa-2μWb)/(4Wb+Wa)t

4. Aug 25, 2014

### Nathanael

That is correct, but Stelios already knows the answer. He doesn't just want the answer, he wants to understand it.

5. Aug 25, 2014

### andrewkirk

The downward force on block A is its weight minus twice the frictional force on B (twice because of the mechanical advantage of the two-fold pulley). This will be constant because (IIRC) sliding frictional force does not vary with speed.

That is $F_A=W_A-2\mu_k W_B$

The mass of A is $m_A=W_A/g$

The mass of B is $m_B=W_B/g$

The acceleration of A is $a_A=F_A/(m_A+2m_B)$ The coefficient of 2 for $m_B$ is there because of the reverse mechanical advantage of the pulley: a downward force on the pulley translates to half that force on the single rope leading to B.

The speed at time $t$ will be $v_{A0}+a_At$

Last edited: Aug 25, 2014
6. Aug 25, 2014

### SteliosVas

Thanks Andrew, I forgot to include note the fact that their is mechanical advantage as a result of two pulleys in the system.

And as for block a and block 2 I think it was just a typo :(