Is the Normal Force Larger in a Box-Pushing Scenario?

[hydride]

Homework Statement

A box is being pushed across the floor with a 250 N force directed 20_ο
below the horizontal. Is The normal force is larger than the weight of the box?

True or False.

Explain.

Homework Equations

sin(20) = opp/hyp

The Attempt at a Solution

F_n = 250sin(20^o) + F_g

Please help explain how this problem is done, and why we would add F_g. Thank you.

 

[Precursor]

The force is being applied at an angle below the horizontal. Therefore, the normal force must counteract both the downward component of the applied force and the gravitational force.

 

[hydride]

But how do we know if it is greater than the weight of the object? Shouldn't it be equal?

 

[PhanthomJay]

the normal force is the perpendicular contact force of the floor acting on the box. It's value must be in accord with Newton's 1st law, per Precursor's response, and the equations you noted above in your initial post.

 

[Precursor]

The normal force is greater than the weight because it has to balance both gravitational and applied force.