1. Draw a Free Body Diagram

Draw a diagram of the box on the ramp. The forces acting on the box are:

* Weight (mg): This acts vertically downward.

* Normal Force (N): This acts perpendicular to the ramp, pushing the box against the ramp.

* Applied Force (F): This acts horizontally.

2. Resolve Forces

* Weight: Break the weight force into components parallel and perpendicular to the ramp:

* *mg* sin(25°) (parallel to the ramp, acting downward)

* *mg* cos(25°) (perpendicular to the ramp)

* Normal Force: The normal force balances the perpendicular component of the weight: *N* = *mg* cos(25°)

3. Apply Newton's Second Law

Since the box moves at constant speed, the net force acting on it is zero. Apply this to the forces parallel to the ramp:

* ΣF_parallel = 0

* F - mg sin(25°) = 0

4. Solve for the Applied Force (F)

* F = mg sin(25°)

* F = (125.0 kg)(9.8 m/s²)(sin 25°)

* F ≈ 519.5 N

Therefore, the magnitude of the applied force F is approximately 519.5 Newtons.