Question

A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 37.fJ' below the horizontal and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair.

Answer 1

(a)


(b)
We can break the applied force into its components parallel and perpendicular to the floor:

$F_{\parallel} = F\sin37^\circ = 23.8$ N

$F_{\perp} = F\cos37^\circ = 30.6$ N

The only forces acting on the chair are the force of gravity, $F_g = mg$, and the normal force, $F_n$, from the floor. Since the chair is not accelerating vertically, the normal force must be equal in magnitude and opposite in direction to the force of gravity:

$F_n = F_g = mg = 12.0\text{ kg}\cdot9.81\text{ m/s}^2 = 117.7\text{ N}$

In the horizontal direction, the applied force is the only force, so we can use Newton's second law:

$F_{\parallel} = ma$

$23.8\text{ N} = 12\text{ kg}\cdot a$

$a = 1.98\text{ m/s}^2$

Therefore, the normal force exerted by the floor on the chair is 117.7 N.