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.

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41*sin38

To calculate the magnitude of the normal force exerted by the floor on the chair, we need to use Newton's second law, which states that the sum of all forces acting on an object is equal to its mass multiplied by its acceleration.

First, let's break down the forces acting on the chair:

1. Weight (W): The weight of the chair is a force exerted downwards due to gravity. The weight can be calculated using the equation W = m * g, where m is the mass of the chair and g is the acceleration due to gravity. In this case, you've given us the weight of the chair, which is 150 N.

2. Applied Force (Fapplied): You are pushing the chair with a force of 38.0 N at an angle of 41.0° below the horizontal.

3. Normal Force (N): The normal force is the force exerted by the floor perpendicular to the surface of the chair.

Since the chair is sliding along the floor, the applied force and the force of friction are in the same direction. In this case, the force of friction will act opposite to the applied force.

Now, let's calculate the normal force (N):

1. Resolve the applied force into its horizontal and vertical components:
Fx = Fapplied * cosθ
Fy = Fapplied * sinθ
Here, θ is the angle of 41.0° below the horizontal.

Fx = 38.0 N * cos(41.0°)
Fy = 38.0 N * sin(41.0°)

2. Calculate the net force in the horizontal direction:
Fnet_x = Fx - Force of friction
The horizontal component of the net force is responsible for the horizontal acceleration of the chair.

3. Now, apply Newton's second law in the horizontal direction:
Fnet_x = m * ax
Here, m is the mass of the chair, and ax is the horizontal acceleration.

4. Calculate the net force in the vertical direction:
Fnet_y = Normal force - Fy - Weight
The vertical component of the net force is responsible for the vertical acceleration of the chair.

5. Apply Newton's second law in the vertical direction:
Fnet_y = m * ay
Here, ay is the vertical acceleration.

Since the chair is sliding, the frictional force opposes the applied force but does not cause any vertical acceleration. Therefore, the vertical acceleration, ay, is 0. This means the vertical forces are balanced:

Fnet_y = Normal force - Fy - Weight = 0

From this equation, we can solve for the Normal force:

Normal force = Fy + Weight

Substituting the known values:

Normal force = (38.0 N * sin(41.0°)) + 150 N

Now, calculate this value to find the magnitude of the normal force the floor exerts on the chair.