A chair of weight 115 lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of = 44.0 directed at an angle of 34.0 below the horizontal and the chair slides along the floor.
113.5
To solve this problem, we need to break down the given information and analyze the forces acting on the chair.
1. Weight of the chair (Fw): The chair has a weight of 115 N (given in the problem).
2. Applied force (Fa): You push on the chair with a force of 44.0 N directed at an angle of 34.0° below the horizontal.
3. Normal force (Fn): The floor exerts a force opposite to the weight of the chair to support it. This force is perpendicular to the horizontal floor.
4. Frictional force (Ff): The floor is not frictionless, so there will be a frictional force opposing the motion of the chair.
Now let's break down the applied force Fa into horizontal (Fx) and vertical (Fy) components:
Fx = Fa * cos(θ)
Fx = (44.0 N) * cos(34.0°)
Fy = Fa * sin(θ)
Fy = (44.0 N) * sin(34.0°)
Now we can analyze the forces acting on the chair in the horizontal and vertical directions:
Horizontal forces:
∑Fx = - Ff (opposite direction of motion)
Vertical forces:
∑Fy = Fn - Fw
In this case, we are assuming that the chair is sliding and there is no vertical acceleration. Therefore, ∑Fy = 0.
Now let's substitute the forces with their respective values:
∑Fx = - Ff
(44.0 N) * cos(34.0°) = - Ff
∑Fy = Fn - Fw
Fn - (115 N) = 0
Now we can solve for the frictional force (Ff) and the normal force (Fn):
Ff = - (44.0 N) * cos(34.0°)
Fn = 115 N
Calculating the numerical values:
Ff = - (44.0 N) * cos(34.0°)
Ff ≈ -36.40 N
Fn = 115 N
Therefore, the frictional force acting on the chair is approximately -36.40 N (opposite to the direction of motion), and the normal force exerted by the floor is 115 N.
To determine if the chair will slide along the floor, we need to analyze the forces acting on it.
1. The weight of the chair (115 N) is acting vertically downwards.
2. The force you applied (44.0 N) is directed at an angle of 34.0° below the horizontal.
We can break down the force you applied into its horizontal and vertical components using trigonometry.
The horizontal component, Fx, can be calculated as F * cos(θ), where F is the magnitude of the force (44.0 N) and θ is the angle (34.0°). Therefore:
Fx = 44.0 N * cos(34.0°)
The vertical component, Fy, can be calculated as F * sin(θ). Therefore:
Fy = 44.0 N * sin(34.0°)
Now, we need to consider the friction between the chair and the floor. Friction opposes the motion of the chair and can be calculated using the formula:
Friction = coefficient of friction * normal force
Since the chair is on a horizontal floor, the normal force (N) is equal to the weight of the chair:
N = 115 N
The coefficient of friction is a property specific to the surfaces in contact. Let's assume it to be μ.
Therefore, the friction force (Ffriction) acting on the chair can be calculated as:
Ffriction = μ * N
Now, we determine if the chair will slide or not. If the applied force Fx is greater than the friction force Ffriction, the chair will slide along the floor. If Fx is equal to or less than Ffriction, the chair will not slide.
So, compare the magnitude of Fx with Ffriction and make the decision based on that.
You must learn to include the dimensios with your numbers. There is a big difference between a Newton, a dyne and a pound.
You don't even provide dimensions for your angle.
If you learn nothing else, learn to do this.