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.
In the vertical direction, the net force is zero, since the velocity component in that direction must remain zero. (It can't go through the floor)
The normal force (Fn) exerted by the floor equals the weight (W) PLUS the downward component of the applied force, 38 sin 41 = 24.9.
Fn = 150 + 24.9 = 174.9
You do not have to assume a friction coefficient to solve this problem.
Well, if there's one thing I know for sure, it's that the normal force is anything but normal. It's kind of like that one friend who always has your back, no matter how weird or uncomfortable the situation is.
Anyway, let's tackle this problem with a touch of humor. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, that object is our lovely chair.
So, the normal force is basically the floor's way of saying, "Hey chair, you're too heavy, I need to push back to keep you balanced." It's all about maintaining equilibrium, my friend.
Now, using Newton's laws of motion, we can analyze this situation. Since the chair is sliding along the floor, we know that there's some friction involved. And let me tell you, friction can be a real party pooper sometimes.
The force of friction acts in the opposite direction to the chair's motion, trying to slow it down. It's like a mischievous kid putting a banana peel in front of your chair just to watch you stumble.
To calculate the normal force, we need to take into account the vertical and horizontal components of the applied force. Now, the vertical component of the force is responsible for countering the weight of the chair, so it definitely plays a role in determining the normal force.
However, the horizontal component of the applied force is what's causing the chair to slide. It's like a gentle push in the back, telling the chair to get moving. But beware, this push also increases the force of friction, making it harder for the chair to slide smoothly.
In this case, we have an applied force of 38.0 units directed at an angle of 41.0 below the horizontal. That means the vertical component of the force is 38.0 times the cosine of 41.0 degrees. And the horizontal component is 38.0 times the sine of 41.0 degrees.
Now, let's take a moment to appreciate what the floor has to endure. It has to support the weight of the chair, counteract the vertical component of the applied force, and balance the horizontal component of the force to allow for motion. It's like juggling flaming bowling pins while riding a unicycle. Talk about multitasking!
So, the magnitude of the normal force can be calculated by adding the weight of the chair to the vertical component of the applied force. In other words, the normal force equals the weight plus the vertical push.
I know you've been eagerly waiting for the numbers, so here they are. The weight of the chair is 150 units, and the vertical component of the applied force is 38.0 times the cosine of 41.0 degrees.
Put all those numbers together, crunch them with some calculations, and voila! You've got yourself the magnitude of the normal force.
Just remember that the normal force is like that loyal friend who's always there when you need support. And in this case, it's supporting the chair against the forces of gravity, friction, and your mischievous shenanigans.
I hope that answers your question with a touch of humor! If you have any more inquiries or need a good pun, feel free to ask!
To determine the magnitude of the normal force exerted by the floor on the chair, we need to analyze the forces acting on the chair.
1. The weight of the chair: The weight of the chair, given as 150 , acts vertically downward. We can calculate the magnitude of this force using the formula:
Weight (W) = mass (m) * gravitational acceleration (g)
Given that the mass of the chair is not provided, we need to know the gravitational acceleration, which is typically 9.8 . Assuming this value, we can calculate the weight:
Weight (W) = 150 * 9.8
W ≈ 1470
2. The force applied by pushing: The force applied by pushing the chair is given as 38.0 at an angle of 41.0 below the horizontal. We can break down this force into horizontal and vertical components.
Horizontal component of the applied force:
F_horizontal = F * cos(θ)
F_horizontal = 38.0 * cos(41.0)
F_horizontal ≈ 28.74
Vertical component of the applied force:
F_vertical = F * sin(θ)
F_vertical = 38.0 * sin(41.0)
F_vertical ≈ 24.32
3. The normal force: The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, it counteracts the weight of the chair.
Since the chair is sliding, the horizontal component of the applied force is equal to the force of friction opposing its motion. The normal force and the applied vertical force balance out to counteract the weight of the chair.
Therefore, the magnitude of the normal force can be calculated as:
Normal force + F_vertical = W
Normal force = W - F_vertical
Normal force = 1470 - 24.32
Normal force ≈ 1445.68
Therefore, the magnitude of the normal force that the floor exerts on the chair is approximately 1445.68 .
To calculate the magnitude of the normal force that the floor exerts on the chair, we can use Newton's laws.
Step 1: Resolve the force into horizontal and vertical components.
Given:
Pushing force, F = 38.0 N
Angle, θ = 41.0° (below the horizontal)
The horizontal component of the force can be calculated as:
F_horizontal = F * cos(θ)
= 38.0 N * cos(41.0°)
The vertical component of the force can be calculated as:
F_vertical = F * sin(θ)
= 38.0 N * sin(41.0°)
Step 2: Calculate the net force acting on the chair.
Since the chair is sliding along the floor, we know that the net force acting on it is equal to the force of friction.
The force of friction, F_friction, can be represented as:
F_friction = μ * N
Where:
μ is the coefficient of friction between the chair and the floor.
N is the normal force exerted by the floor on the chair (which we want to calculate).
Step 3: Equate the horizontal component of the force to the force of friction.
F_horizontal = F_friction
Step 4: Solve for the normal force, N.
N = F_friction / μ
Now we have all the information we need to calculate the magnitude of the normal force.
Note: The coefficient of friction between the chair and the floor is not given in the problem statement. Without that information, we cannot determine the exact magnitude of the normal force. The value of the coefficient of friction must be provided for an accurate calculation.
Once you have the coefficient of friction, substitute it into the equation and solve for N.