X and y components of the force that the axle exerts on the pulley?

[azila]

Homework Statement

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00- kgweight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 2.50 kg and diameter 0.440m .

What are the x and y components of the force that the axle exerts on the pulley?

Homework Equations

Ok, so I found the tension in the Horizontal Wire to be 32.2
Ok, then I found the tension in the Vertical Wire to be 35.6
The acceleration of the box when it goes down is 2.68 m/s^2

The Attempt at a Solution

So, I asked the teacher and the teacher told us that the x component is the tension in the horizontal wire and the y component is the vertical tension plus the weight of the block that is accelerating downwards. So, I did that. The x component would be 32.2 and the y component woud be 35.6 + mg which is 84.6. I tried that but that is not the answer. I think that the x component is right but I am messing up somewhere on the y component. Can anyone help me with this one. Thanks in advance.

 

[bel]

The acceleration would also be the angular acceleration of the pulley times its diameter, and that times its mass would be the force on the pulley, I think. So calculate the vertical and horizontal components of the acceleration vector on the pulley, remembering all the while that only the tensions would act on the pulley because all forces on the pulley are transmitted through the wires.

 

[m2003]

I would first clarify the question by asking for more information. Are we assuming that the pulley is at rest or in motion? Is the axle attached to the pulley or just supporting it? This information would affect the answer.

Assuming that the pulley is at rest and the axle is attached to it, the x component of the force that the axle exerts on the pulley would be equal to the tension in the horizontal wire, which is 32.2 N. This is because the pulley is not moving in the horizontal direction, so the net force in that direction must be zero.

The y component of the force that the axle exerts on the pulley would be equal to the sum of the vertical tension in the wire and the weight of the block, which is accelerating downwards. The vertical tension in the wire can be found using the equation T = ma, where T is the tension, m is the mass of the block, and a is the acceleration. So, the vertical tension would be 12 kg * 2.68 m/s^2 = 32.16 N. Therefore, the y component of the force would be 32.16 N + (12 kg * 9.8 m/s^2) = 140.56 N.

It's important to note that the y component of the force includes the weight of the block because the block is accelerating downwards, so there must be a net force acting on it in the y direction. The axle, being attached to the pulley, is also exerting a force on the pulley in the y direction to support the weight of the block.

In summary, the x component of the force that the axle exerts on the pulley is 32.2 N and the y component is 140.56 N. However, as I mentioned before, the answer could differ depending on the assumptions made about the situation. It's always important to clarify any uncertainties and assumptions when solving physics problems.