Unlocking Friction: The Case Of The Stationary Book

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Unlocking Friction: The Case of the Stationary Book

Hey guys, let's dive into a classic physics problem that's all about friction! We've got a scenario involving a book, a table, and some applied force. The core question revolves around figuring out the coefficient of static friction. So, grab your notebooks, and let's break this down together. This is going to be fun, and I promise you will be an expert on friction at the end of this!

Understanding the Problem: Friction's Role

Alright, so the deal is this: a 0.50 kg book is chilling on a table, and we're going to give it a nudge. The interesting part? The book doesn't budge until we hit a force of 3.25 N. That critical point, just before the book starts to slide, is where static friction reaches its maximum value. Remember, static friction is the force that prevents an object from moving when it's at rest. It's the reason why things don't slide away at the slightest push. The question now becomes, how do we use this information to calculate the coefficient of static friction? This is where physics concepts such as the normal force, the weight of the book, and the relationship between the applied force and the static friction force come into play. We are going to find out the normal force of the book and the maximum static friction so that we can find the coefficient. It may sound complex but it is not!

To solve this, we will use a few key principles. First, Newton's First Law tells us that an object at rest stays at rest unless acted upon by a net force. In our case, the book wants to stay put, and friction is the force opposing the applied force. The applied force is what we want to find. Second, the coefficient of static friction (μs) is a dimensionless number that describes the relative roughness between two surfaces. A higher coefficient means a greater force is required to initiate movement. Finally, the force of static friction (Fs) is directly proportional to the normal force (Fn), which is the force exerted by the table on the book. This normal force is equal to the weight of the book in this case, and it acts perpendicular to the surface. So, basically, we need to understand the forces at play and how they interact to solve this problem. Ready to make some calculations? Then let's do it!

The Forces at Play: Weight, Normal Force, and Friction

Okay, before we get to the calculations, let's talk about the forces. The book is experiencing a few key forces:

  1. Weight (W): This is the force due to gravity, pulling the book downwards. We calculate it using the formula W = mg, where 'm' is the mass (0.50 kg) and 'g' is the acceleration due to gravity (approximately 9.8 m/s²). Let us calculate this, this is the first step of the process.
  2. Normal Force (Fn): This is the force exerted by the table on the book, pushing upwards. In this scenario, the normal force is equal in magnitude and opposite in direction to the weight of the book. Remember Newton's Third Law, which states that for every action, there is an equal and opposite reaction!
  3. Applied Force (Fa): This is the force you're applying to the book to try and move it.
  4. Static Friction (Fs): This is the force that opposes the applied force, preventing the book from moving. It increases in response to the applied force until it reaches its maximum value. At the point where the book just starts to move, the static friction has reached its maximum, and that is what we are going to use here.

Now, let's put these forces into action. When you push the book, the static friction counteracts your push, keeping the book stationary. The static friction force increases in response to your push until it can't handle it anymore. At that point, the book starts to move, and we know that the applied force is equal to the maximum static friction force. So, when the applied force reaches 3.25 N, the static friction is at its maximum, meaning the book is on the verge of movement. Once we understand the forces, the rest is fairly straightforward, so let us move on!

Calculating the Coefficient of Static Friction

Alright, it's calculation time! Here's how we find the coefficient of static friction (μs):

  1. Calculate the Weight (W): Using the formula W = mg, we get: W = 0.50 kg * 9.8 m/s² = 4.9 N. This is how we are going to do it. Easy! The mass is in kg, and the gravitational acceleration is 9.8m/s2 so the result is in Newtons.
  2. Determine the Normal Force (Fn): The normal force is equal in magnitude to the weight, so Fn = 4.9 N. We got this by the force that the table is exerting on the book. And we know that there is no movement in the y direction, so the sum of the forces must be 0, which means the normal force and the weight have the same magnitude, but opposite direction!
  3. Identify the Maximum Static Friction (Fs_max): The problem tells us that the book starts to move when the applied force reaches 3.25 N. This is the maximum static friction, so Fs_max = 3.25 N. This means that if we apply more than 3.25N, the book will start moving!
  4. Use the Formula: The relationship between these forces is given by the formula: Fs_max = μs * Fn. So we can rearrange this formula to solve for μs: μs = Fs_max / Fn. Then, put in the numbers we got before, and we can find the coefficient!
  5. Calculate the Coefficient: μs = 3.25 N / 4.9 N ≈ 0.66. Now, that's it! We have the answer, and it is 0.66!

The Significance of the Result

So, what does this coefficient of static friction of 0.66 actually mean? Well, it tells us something about the surfaces in contact (the book and the table). A coefficient of 0.66 indicates a moderate level of friction. This means that the surfaces have a decent amount of