How Is Tension Calculated in a Two-Object System on an Inclined Plane?

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SUMMARY

The discussion focuses on calculating the tension in a string connecting two objects in a two-object system on an inclined plane. The first object has a mass of 4 kg and is on a 34° incline, while the second object has a mass of 6.4 kg on a horizontal surface. An external force of 30 N is applied to the first object, and the system is assumed to be frictionless. The equations of motion derived from the forces acting on both objects lead to a negative acceleration, indicating an error in the setup or calculations that needs to be addressed to find the correct tension in the string.

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Homework Statement


An object on an inclined ramp of mass 4 kg forms an angle of 34° with the horizontal. The object on the ramp is connected to a second object of mass 6.4 kg on a horizontal surface below an overhang that is formed by the inclined surface. An external force of 30 N is exerted on the object on the ramp. Both objects are accelerating. Assume that the surfaces and the pulley are frictionless, and the connecting string and the pulley are massless, what is the tension in the string connecting the two objects?

Homework Equations



F = ma
m1g - T = m1a
T - m2g = m2a

The Attempt at a Solution



I drew out the FBD for the object on the incline

The force of gravity of the object must be broken into component parts:

(4)(9.8) = 39.2 N
x component: 39.2 sin34 = 21.9 N
y component: 39.2 cos34

The x component is counteracting the exerted force of 30 N, so 30-21.9 = 8.1 N

object 2 is not on an incline so: (6.4)(9.8) = 62.7 N is the force applied on it

8.1 - T = 4a
T - 62.7 = 6.4a

From here I am lost because if the above equations are solved for a - it turns out to be negative.

Any help in finding acceleration and then tension would be greatly appreciated
Thanks
 
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