What is the solution for a pulley system with 200N weight and 40N weight?

[SteliosVas]

Homework Statement

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

Homework Equations

Wa = 200N
V_a0=2m/s
t= 2 seconds
Wb= 40N
μ_K=0.2
g=9.81m/s^2

The Attempt at a Solution

Okay my attempted solution was this:

For block A:

40N + F_n+Tension =m_1a

T - 40N*0.2=40N/9.81

Block 2

200 + F_n + Tension = m_2a

200N + T = 200N/9.81

So lost to be honest!

 

[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 (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

 

[Maharshi Roy]

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

 

[Nathanael]

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

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

 

[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##

 

[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 :(