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

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The discussion focuses on calculating the tension in a string connecting two objects, one on an inclined plane and the other on a horizontal surface. The inclined object has a mass of 4 kg at a 34° angle, while the second object weighs 6.4 kg. An external force of 30 N is applied to the object on the ramp, and both objects are accelerating on frictionless surfaces. The participant has set up equations based on Newton's second law but is struggling with negative acceleration results when solving for tension. Assistance is sought to correctly determine the acceleration and the resulting tension in the system.
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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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