A box sits at rest on an inclined plank. How do the magnitudes of the normal force and the gravitational force exerted on the box compare? (Hints: What is the box's acceleration? Draw a free-body diagram!) A) $\left|\vec{F}_{N}\right|\left|\vec{F}_{g}\right|$ D) $\left|\vec{F}_{N}\right|=0$ ! E) We do not have enough information to answer.

Question

A box sits at rest on an inclined plank. How do the magnitudes of the normal force and the gravitational force exerted on the box compare? (Hints: What is the box's acceleration? Draw a free-body diagram!)
A) $\left|\vec{F}_{N}\right|<\left|\vec{F}_{g}\right|$
B) $\left|\vec{F}_{N}\right|=\left|\vec{F}_{g}\right|$
C) $\left|\vec{F}_{N}\right|>\left|\vec{F}_{g}\right|$
D) $\left|\vec{F}_{N}\right|=0$ !
E) We do not have enough information to answer.

Quizplus · Accepted Answer

The normal force is perpendicular to the surface of the incline, while the gravitational force acts vertically downwards. Since the box is on an incline, part of the gravitational force acts parallel to the incline causing the box to potentially slide down, and part acts perpendicular to the incline, which is balanced by the normal force. Therefore, the magnitude of the normal force is less than the magnitude of the gravitational force because the gravitational force is split into components, and only one of those components (the one perpendicular to the incline) is balanced by the normal force.

A Box Sits at Rest on an Inclined Plank ∣F⃗N∣<∣F⃗g∣\left|\vec{F}_{N}\right|<\left|\vec{F}_{g}\right|​FN​​<​Fg​​ B) ∣F⃗N∣=∣F⃗g∣\left|\vec{F}_{N}\right|=\left|\vec{F}_{g}\right|​FN​​=​Fg​​

A Box Sits at Rest on an Inclined Plank $\left|\vec{F}_{N}\right|<\left|\vec{F}_{g}\right|$ B) $\left|\vec{F}_{N}\right|=\left|\vec{F}_{g}\right|$