A chair of mass 14.5 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 35.0 N that is directed at an angle of 43.0 ∘ below the horizontal and the chair slides along the floor. find the normal force of chair on floor
35sin43 + 14.5*9.8
Well, let me tell you, the chair is definitely feeling the pressure! Let's figure out the normal force it's experiencing.
To get started, we need to break down the force you applied into components. The force has two components: one parallel to the floor (F_parallel) and one perpendicular to the floor (F_perpendicular).
The force parallel to the floor can be found using the formula F_parallel = F * sin(θ), where θ is the angle below the horizontal. Plugging in the values, we get:
F_parallel = 35.0 N * sin(43.0°)
Calculating that, we find F_parallel ≈ 23.69 N.
Now, the normal force is equal in magnitude but opposite in direction to the perpendicular component of the force. So, the normal force (N) can be calculated using the formula N = F_perpendicular = F * cos(θ). Plugging in the values, we get:
N = 35.0 N * cos(43.0°)
Calculating that, we find N ≈ 25.47 N.
So, the normal force of the chair on the floor is approximately 25.47 newtons. That's quite a balancing act!
To find the normal force of the chair on the floor, we need to consider the forces acting on the chair in the vertical direction.
First, let's resolve the force F into its vertical and horizontal components:
F_horizontal = F * cos(angle)
F_vertical = F * sin(angle)
Given:
mass of the chair, m = 14.5 kg
force, F = 35.0 N
angle, θ = 43.0°
F_horizontal = 35.0 * cos(43°)
F_horizontal ≈ 24.97 N
Now, since the chair is sliding along the floor, the horizontal component of the force exerted by the floor on the chair should be equal in magnitude and opposite in direction to the horizontal component of the applied force.
Therefore, the normal force, N, should be equal and opposite to the horizontal component of the applied force:
N = - F_horizontal
Substituting the value of F_horizontal:
N = - 24.97 N
The normal force of the chair on the floor is approximately -24.97 N. The negative sign indicates that the direction of the normal force is opposite to the applied force.
To find the normal force of the chair on the floor, we need to consider the forces acting on the chair. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the chair is balanced by the normal force of the floor acting in an upward direction.
Let's break down the forces acting on the chair:
1. Weight (W): The weight of the chair can be calculated using the formula W = m * g, where m is the mass and g is the acceleration due to gravity. In this case, the mass of the chair is given as 14.5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, W = 14.5 kg * 9.8 m/s^2.
2. Applied force (F): The force applied to the chair is given as 35.0 N and is directed at an angle of 43.0 degrees below the horizontal. To find the horizontal component of this force, we need to calculate F_x = F * cos(θ), where θ is the angle (43.0 degrees). Similarly, to find the vertical component, we calculate F_y = F * sin(θ).
3. Normal force (N): The normal force is the force exerted by the floor on the chair in an upward direction. It is equal in magnitude but opposite in direction to the weight of the chair (N = -W). It also counteracts the vertical component of the applied force (N = N + F_y).
To find the normal force, we calculate the net vertical force acting on the chair. Summing up all the vertical forces, we have:
Net vertical force = N + F_y - W
Since the chair is sliding along the floor, there is no vertical acceleration, and the net vertical force is zero.
Net vertical force = 0
N + F_y - W = 0
Substituting the values, we can solve for the normal force:
N + (F * sin(θ)) - W = 0
Now, plug in the values for F, θ, m, and g to calculate the normal force.