A chair of weight 150 lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of = 38.0 directed at an angle of 41.0 below the horizontal and the chair slides along the floor.Using Newton's laws, calculate , the magnitude of the normal force that the floor exerts on the chair.

Question

A chair of weight 150  lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of  = 38.0  directed at an angle of 41.0 below the horizontal and the chair slides along the floor.Using Newton's laws, calculate , the magnitude of the normal force that the floor exerts on the chair.

drwls · Accepted Answer

In the vertical direction, the net force is zero, since the velocity component in that direction must remain zero. (It can't go through the floor)

The normal force (Fn) exerted by the floor equals the weight (W) PLUS the downward component of the applied force, 38 sin 41 = 24.9.
Fn = 150 + 24.9 = 174.9

You do not have to assume a friction coefficient to solve this problem.