Hey guys! Let's dive into the fascinating world of physics with a classic problem: a metal bolt falling freely for 5 seconds. This is a perfect example of free fall, where the only force acting on the object is gravity. We're going to break down this problem step by step, making sure we understand the concepts behind each calculation. So, grab your thinking caps, and let's get started!
What is Free Fall?
Before we jump into the calculations, let's make sure we're all on the same page about what free fall really means. In physics, free fall is when an object is falling solely under the influence of gravity. This means we're ignoring air resistance, which can be a significant factor in real-world scenarios (think of a feather falling versus a bowling ball). However, for this problem, we're simplifying things to focus on the core principles. When an object is in free fall near the Earth's surface, it experiences a constant acceleration due to gravity. This acceleration is approximately 9.8 meters per second squared (m/s²), often rounded to 10 m/s² for easier calculations. This means that for every second an object falls, its speed increases by 9.8 meters per second. This constant acceleration is a crucial piece of information for solving our problem. Understanding free fall also involves recognizing that the object's initial velocity might not always be zero. In our case, the bolt falls freely, implying it starts from rest. However, if the bolt were thrown downwards, it would have an initial velocity, affecting our calculations later on. The key takeaway here is that gravity is the sole actor in this scenario, dictating how the bolt's speed changes over time and the distance it covers.
a) What is its Acceleration?
Our first question is straightforward but fundamental: What is the acceleration of the metal bolt? Remember our discussion about free fall? The acceleration due to gravity is the key here. On Earth, the acceleration due to gravity is approximately 9.8 m/s². This value is often represented by the symbol 'g'. For simplicity in calculations, we sometimes round it to 10 m/s², which is what we'll do for this example. So, the answer to our first question is: the acceleration of the metal bolt is 10 m/s² downwards. This means that for every second the bolt falls, its downward velocity increases by 10 meters per second. It's important to note that acceleration is a vector quantity, meaning it has both magnitude (the numerical value) and direction. In this case, the magnitude is 10 m/s², and the direction is downwards, towards the Earth's center. Understanding the direction of acceleration is crucial for correctly applying kinematic equations, which we'll use in the following steps. This constant downward acceleration is what governs the entire motion of the bolt during its free fall. It's the driving force behind the increasing speed and the distance the bolt covers as it falls.
b) What is its Speed after 5 Seconds?
Now, let's figure out the bolt's speed after 5 seconds of falling. This is where our understanding of acceleration comes into play. We know the bolt starts from rest (initial velocity = 0 m/s) and accelerates at 10 m/s² downwards. To find the final speed, we can use a simple kinematic equation: final velocity (v) = initial velocity (u) + (acceleration (a) * time (t)). In our case: * u = 0 m/s (starts from rest) * a = 10 m/s² (acceleration due to gravity) * t = 5 s (time of fall) Plugging these values into our equation, we get: v = 0 m/s + (10 m/s² * 5 s) v = 50 m/s So, the speed of the metal bolt after 5 seconds is 50 meters per second. That's pretty fast! This calculation highlights the direct relationship between acceleration, time, and velocity in free fall. The longer the bolt falls, the faster it goes, thanks to the constant acceleration due to gravity. It's essential to remember the units in our calculations to ensure we get the correct answer and understand the physical meaning of the result. In this case, meters per second (m/s) is the standard unit for speed.
c) What is its Average Speed?
Next, we need to calculate the average speed of the bolt during its 5-second fall. The average speed isn't simply the final speed we calculated in the previous step. Instead, it's the total distance traveled divided by the total time taken. However, there's a handy shortcut we can use when the acceleration is constant, like in our free fall scenario. The average speed is simply the average of the initial and final speeds. We already know: * Initial speed (u) = 0 m/s * Final speed (v) = 50 m/s To find the average speed, we use the formula: average speed = (initial speed + final speed) / 2 Plugging in our values: average speed = (0 m/s + 50 m/s) / 2 average speed = 25 m/s Therefore, the average speed of the metal bolt during its 5-second fall is 25 meters per second. This value represents the constant speed the bolt would need to travel to cover the same distance in the same amount of time. It's a useful concept for understanding the overall motion of the bolt, even though its instantaneous speed is constantly increasing due to gravity. The average speed gives us a holistic view of the bolt's journey through free fall.
d) What Height has it Fallen?
Finally, let's determine the height the bolt has fallen after 5 seconds. This involves calculating the distance traveled during free fall. We can use another kinematic equation that relates distance, initial velocity, acceleration, and time: distance (s) = (initial velocity (u) * time (t)) + (0.5 * acceleration (a) * time (t)²). We have all the values we need: * u = 0 m/s (starts from rest) * t = 5 s (time of fall) * a = 10 m/s² (acceleration due to gravity) Plugging these values into the equation, we get: s = (0 m/s * 5 s) + (0.5 * 10 m/s² * (5 s)²) s = 0 + (0.5 * 10 m/s² * 25 s²) s = 125 meters So, the metal bolt has fallen a height of 125 meters after 5 seconds. This calculation shows how the distance covered during free fall increases rapidly with time due to the constant acceleration of gravity. The bolt covers significantly more distance in the later seconds of its fall compared to the initial seconds. This is a direct consequence of its increasing speed. This final calculation provides a complete picture of the bolt's free fall, telling us how far it traveled in the given time.
Conclusion
So, there you have it! We've successfully calculated the acceleration, speed, average speed, and distance fallen for our metal bolt in free fall. By breaking down the problem step-by-step and using the appropriate kinematic equations, we've gained a deeper understanding of how objects move under the influence of gravity. Remember, these principles apply to all objects in free fall, regardless of their mass or shape (assuming we ignore air resistance). Physics can be fun, especially when we apply it to real-world scenarios like this. Keep exploring, keep questioning, and keep learning!