Simple Mechanics Problem -- Block connected to a wall by a rope

[domingoleung]

Homework Statement

Block A (5 kg) is connected to the wall with a cord of tension T, and initially at rest on top of block B (10 kg) on a rough floor. If there is an applied force 54 N acting on block B, block B could move to the right while block A is still at rest due to the connecting cord. Assume the coefficient of kinetic friction between blocks A and B and between block B and the ground is μk = 0.3.

(i) Draw free body diagrams of blocks A and B.
(ii) Find the tension T of the cord and the acceleration of block B.

Relevant Equations

F = ma

(So this is the system given)

The following is my analysis:
(i)

(ii)

Well, my problem is - I got a negative acceleration and its quite impossible to have block B moving to the left. So I am wondering if there are any mistakes I've made.

 

[PeroK]

Can you write out the equations for all the forces on both blocks? Horizontal and vertical. In particular, can you check the calculation of $T$. How did you get that?

 

[PeroK]

Can you write out the equations for all the forces on both blocks? Horizontal and vertical. In particular, can you check the calculation of $T$. How did you get that?

Okay, $T$ is correct.

I think I agree with you. You need a force of slightly more than $54N$ to get this system moving.

Increasing $g$ to $10 m/s^2$ makes things worse, of course.

You can check once more, but unless we've made the same mistake, I think the problem might be wrong. It's a bit suspicious, as $54N$ is approximately the force needed.

 

[kuruman]

Equation 2 is incorrect. $f_{k1}=\mu_k F_{N1}$ and $F_{N1}$ is given by equation 1.

 

[PeroK]

$f_{k1}=\mu_k F_{N1}$ and $F_{N1}$ is given by equation 1.

That's true, but considering horizontal forces on block $A$ also gives:

$f_{k1} = T\cos \theta$

 

[kuruman]

Ah yes. I forgot A is not accelerating. I agree that the 54 N force is not enough to provide an acceleration to the right. A negative acceleration could be compatible with the situation in which block B is already moving and then block A is dropped on it to slow it down, but that's not what the problem says.