Using Newton's laws, calculate n, the magnitude of the normal force that the floor exerts on the chair.

Question

A chair of weight 85.0  lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of  = 42.0  directed at an angle of 35.0  below the horizontal and the chair slides along the floor.

Answer 1

When the vertical acceleration is zero, the normal force N is equal in magnitude to the sum of the forces exerted vertically down on the chair. These forces are the gravitational force and the vertical component of the downward pushing force.

F_gravity = mg

F_{vertical push} = F_push sin(θ)

where θ is the angle given in the problem and F_push is the magnitude of the pushing force.

Thus,

N = mg + F_push sin(θ)