2 blocks with an angled force problem

[SkyRequiem]

Homework Statement

block 1 of mass m1 = 2.4 kg and block 2 of mass m2 = 1.4 kg are connected by a string of negligible mass. Block 2 is pushed by force of magnitude 23 N and angle θ = 40°. The coefficient of kinetic friction between each block and the horizontal surface is 0.18. What is the tension in the string?

Homework Equations

F=ma fs=uFn

The Attempt at a Solution

for m1 i got 2.4*9.8*0.18= 4.2336 for its force of friction
and the T-fs=m*a

for m2 becuase the additional force, (m)(g)+force(sinθ)=Fn which is 28.504 N
and times 0.18 to have 5.13 N of force of friction.

and the force that is push block 2 in the x-axis is force(cosθ) = 17.619 N

and finally, T- fs of block 2 =mass of block 2 *a
but by slove the system equation, my answer is still wrong, is my thinking incorrect?

 

[anathema]

Thank you for your post. It seems like you have a good understanding of the problem and have correctly identified the relevant equations. However, your approach may be missing a few key steps.

First, when solving for the tension in the string, it is important to consider the forces acting on both blocks separately. In this case, you have correctly identified the forces acting on block 1 (gravity and friction) and on block 2 (gravity, the applied force, and friction). However, you also need to consider the tension in the string as a force acting on both blocks. This means that, for block 1, the equation should be T - fs = m1a, and for block 2, the equation should be fs - T = m2a. This accounts for the fact that the string is pulling on both blocks, and the direction of the tension force changes for each block.

Next, when solving for the force of friction, it is important to consider the direction of motion. In this case, block 1 is sliding to the left, so the force of friction should be in the opposite direction (to the right). However, for block 2, the force of friction should be in the same direction as the applied force, as it is sliding to the right. This means that the force of friction for block 2 should be 0.18 * (m2g + Fsinθ).

Lastly, when solving for the tension, you can use the fact that the acceleration of both blocks must be the same (since they are connected by a string). This means that you can set the two equations for acceleration equal to each other and solve for T.

I hope this helps you to arrive at the correct solution. Keep up the good work!