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.