Inclined Blocks Connected By a String

[efekwulsemmay]

Homework Statement

The mass of block a or M_a is equal to 3.00 kg and the mass of block b or M_b is equal to 1.50 kg. The two blocks are connected by a string and are sitting on an incline of 38^$$\circ$$ with block b being the higher on the incline than block a. The string between them is taut. I need to find the acceleration of the system of the two blocks and the tension in the connecting string.

Homework Equations

$$F_{net}=m\cdot a$$
$$F_{w}=m\cdot g$$
$$F_{N}=-F_{w}$$
$$F_{x}=m\cdot g\cos\theta$$
$$F_{y}=m\cdot g\sin\theta$$

The Attempt at a Solution

Ok so I am thinking that because the x compoent of force on Block b is less than Block a the acceleration of the system would just be the x component of the vector for Block a over the mass of Block a minus the mass of Block b:
$$a=\frac{m_{a}\cdot g\cos\theta}{m_{a}-m_{b}}$$
I think subtracting the masses is correct because Block b is preventing Block a from achieving its full potential acceleration because they are connected via the string. I also think that this is the formula for the acceleration of the system because if the x component of the force for Block b were higher than that of Block a then the string would slacken because Block b would be accelerating faster than Block a.

If there is any flaws to my logic please point them out.

Also for the tension of the string I am not sure what to start with to solve the problem. I think something like:
$$T_{s}=m_{a}\cdot g\cos\theta - m_{b}$$
would be it but I don't know.

Please help. Thanks.

 

[AvroArrow]

The correct equations and solution are as follows:a=\frac{m_{a}\cdot g\sin\theta-m_{b}\cdot g\sin\theta}{m_{a}+m_{b}}T_{s}=m_{a}\cdot g\cos\theta + m_{b}\cdot g\cos\theta

 

[tomcue]

Your initial approach for finding the acceleration of the system seems to be on the right track. However, I would suggest using the net force equation, Fnet = ma, to solve for the acceleration instead of just looking at the x component of the force. This way, you can take into account the forces acting on both blocks, including the tension in the string.

For the tension in the string, you can use the equation Fnet = ma again, but this time for the y direction. The net force in the y direction is equal to the weight of block a minus the normal force, which is equal to the tension in the string. So you can set up the equation as follows:

Fnet,y = ma,y
T - m_a*g*sin(theta) = m_a*a

Solving for T, you should get T = m_a*(a + g*sin(theta)). This will give you the tension in the string.

Also, keep in mind that the acceleration of the system will be the same for both blocks, since they are connected by the same string. So once you have calculated the acceleration, you can use it to find the tension for both blocks.

I hope this helps. Good luck with your problem!