The normal force is 165 N
Explanation:
In order to find the normal force on the box, we have to write the equation of the forces along the vertical direction.
We have 3 forces along the vertical direction:
- The weight of the box, downward, of magnitude [tex]mg[/tex]
- The normal reaction on the box, upward, of magnitude [tex]N[/tex]
- The vertical component of the force applied by the student, upward, of magnitude [tex]F sin \theta[/tex]
Since the box is in equilibrium in the vertical direction, the equation of the forces becomes:
[tex]F sin \theta + N - mg = 0[/tex]
where
F = 50 N is the force applied by the student
[tex]\theta = 45^{\circ}[/tex] is the angle at which the force is applied
N is the normal force
m = 20 kg is the mass of the box
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Solving for N, we find the normal force:
[tex]N=mg-F sin \theta = (20)(9.8)-(50)(sin 45)=160.6 N[/tex]
So, the closest answer is 165 N.
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