Question

a box of mass ( m ) is on a frictionless incline that makes an angle ( \theta ) with the horizontal. a force ( f ) is applied to the box parallel to the incline, as modeled below: what is the magnitude of the net force on the box?

Explanation:

Step1: Resolve the gravitational force

The gravitational force acting on the box is \(mg\). The component of the gravitational force along the incline is \(mg\sin\theta\).

Step2: Apply Newton's second law

The net force \(F_{net}\) along the incline is the sum of the applied force \(F\) and the component of the gravitational force. Since the incline is frictionless, there is no frictional force.

$$F_{net}=F - mg\sin\theta$$

Answer:

\(F - mg\sin\theta\)