OK. as drawn, ignoring mass and accelerations, the force $F_p$ will appear as a torque on your ball screw.
However, the total force on the ball screw, and hence the torque, depends on the mass of the thing you're moving with the ball screw interacting with gravity (if it's being moved in anything other than a horizontal plane), and on whether or not the whole assembly -- frame and load -- is moving at anything other than a steady velocity.
On a bad day, your mass-spring-damper system will have an overall resonance that interacts with your control system, making oscillations happen where you never expected them.
Edit bei questioner: The point where you get stucked, is that torque is a form of energy while force is a potential. Applying Newton's third law, as suggested, $F_p$ is affecting the bearing with 100% - but $F_p$ is also moving the the mass/screw by $x$ and therefore introducing the energy $F_p \cdot x$, which is transformed into the torque $T_p$ ~ $F_p \cdot x$, which finally brakes the motor.