Answer:
149 N
Step-by-step explanation:
We can start by resolving the forces acting on the chair in the vertical direction:
N - mg = 0
where N is the normal force exerted by the floor on the chair, m is the mass of the chair, and g is the acceleration due to gravity.
Since the chair is not accelerating vertically, we know that the sum of the forces in the vertical direction is zero.
Now, let's resolve the forces acting on the chair in the horizontal direction. We'll use the force you applied and the force of friction between the chair and the floor:
F - f = ma
where a is the acceleration of the chair, and f is the force of friction.
The force of friction can be calculated as:
f = μN
where μ is the coefficient of friction between the chair and the floor.
We don't know the coefficient of friction or the acceleration of the chair, so we can't solve this equation directly. However, we can use the fact that the chair is sliding along the floor, which tells us that the force of friction is equal and opposite to the force you applied:
f = F sinθ = 39.0 N * sin(36.0°) ≈ 23.5 N
Therefore, we can substitute this value for f in the horizontal force equation:
F - f = ma
39.0 N * cos(36.0°) - 23.5 N = ma
Solving for a, we get:
a ≈ 0.34 m/s^2
Now we can go back to the vertical force equation and solve for the normal force:
N - mg = 0
N = mg = (110 N) + (m chair)(a)
We don't know the mass of the chair, but we can use the acceleration we just calculated to find it:
a = F/(m chair)
m chair = F/a ≈ 115 kg
Substituting this value for the mass of the chair, we get:
N = mg = (110 N) + (115 kg)(0.34 m/s^2)
N ≈ 149 N
Therefore, the normal force that the floor exerts on the chair is approximately 149 N.