A chair of weight 150 lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of = 36.0 directed at an angle of 40.0 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

Fx= 36cos40 in hor direction

Fy= 36sin40 in vertical downward direction

For equilibrium in vertical direction
Normal Force N=mg+Fy
N=150+36sin40
N=150+23.14
N=173.14

To calculate the magnitude of the normal force that the floor exerts on the chair, we need to consider the forces acting on the chair.

Let's break down the forces acting on the chair:

1. Gravity (Weight): The weight of the chair (150 N) acts vertically downward.

2. Normal Force: This is the force exerted by the floor on the chair and acts perpendicular to the surface of contact. This force prevents the chair from sinking into the floor.

3. Applied Force: This is the force you exert on the chair (36.0 N) at an angle of 40.0 degrees below the horizontal. This force is responsible for causing the chair to start moving horizontally.

4. Friction Force: This is the force opposing the motion of the chair. It acts parallel to the floor's surface and in the opposite direction to the applied force.

Since the chair is sliding along the floor, the applied force overcomes the force of friction. The friction force is given by:

Friction force = Coefficient of friction × Normal force

Newton's second law tells us that the net force acting on an object is equal to the product of its mass and acceleration:

Net force = Mass × Acceleration

In this case, since the chair is moving horizontally, the acceleration is the same as the horizontal component of the applied force divided by the mass of the chair.

Now, let's put all this information together to calculate the normal force:

Step 1: Calculate the horizontal component of the applied force:
Horizontal component = Applied force × cos(angle)
Horizontal component = 36.0 N × cos(40.0°)

Step 2: Determine the coefficient of friction. If it is not given, assume a reasonable value based on the situation. Let's say the coefficient of friction is 0.5.

Step 3: Calculate the friction force:
Friction force = Coefficient of friction × Normal force

Step 4: Write the equation for the net force in the x-direction:
Net force in x-direction = Horizontal component of the applied force - Friction force

Step 5: Solve for the acceleration:
Net force in x-direction = Mass × Acceleration
Acceleration = (Horizontal component of the applied force - Friction force) / Mass

Step 6: Calculate the normal force:
Net vertical forces = Weight - Normal force
Net vertical forces = Mass × gravity - Normal force
Net vertical forces = 150 N - Normal force

Since the chair is not moving vertically, the net vertical forces must be zero:
Net vertical forces = 150 N - Normal force = 0

Solve for the normal force:
Normal force = 150 N

Therefore, the magnitude of the normal force that the floor exerts on the chair is 150 N.