Net Force And Distance Calculation: Physics Problem Solution

Hey guys! Let's break down a classic physics problem involving motion, force, and distance. We'll tackle a scenario with a car accelerating and then briefly touch on a skater's initial motion. So, buckle up, and let's get started!

Determining the Net Force Acting on the Car

First, we need to figure out the net force acting on the car. Remember, net force is the overall force that causes an object to accelerate. In this case, our keywords are net force, acceleration, and mass. To calculate it, we'll be using Newton's Second Law of Motion, which is a fundamental concept in physics. This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This is a crucial relationship to understand in mechanics, guys. So, let’s dive into the details.

Initially, the problem tells us that the car starts from rest, meaning its initial velocity is 0 km/h. After 6 seconds, it reaches a velocity of 72 km/h. We also know the car's mass is 1,200 kg. To use F = ma, we first need to calculate the car's acceleration. Acceleration is the rate of change of velocity over time. The formula for acceleration is: a = (final velocity - initial velocity) / time. But hold on! We've got a slight issue here. Our velocities are in km/h, and we need them in meters per second (m/s) to keep our units consistent (meters, kilograms, and seconds – the MKS system). So, let's convert 72 km/h to m/s. To do this, we multiply 72 km/h by 1000 meters/km and divide by 3600 seconds/hour (since there are 1000 meters in a kilometer and 3600 seconds in an hour). This conversion gives us 72 * (1000/3600) = 20 m/s. Now we're talking!

Now we can calculate the acceleration: a = (20 m/s - 0 m/s) / 6 s = 3.33 m/s². So, the car is accelerating at 3.33 meters per second squared. This means that for every second that passes, the car's velocity increases by 3.33 meters per second. Knowing the acceleration and the mass, we can now find the net force using Newton's Second Law: F = ma. Plugging in the values, we get F = 1200 kg * 3.33 m/s² = 4000 N (approximately). Therefore, the net force acting on the car is approximately 4000 Newtons. This force is what's causing the car to speed up. Remember, guys, the Newton (N) is the standard unit of force in the MKS system. It's defined as the force required to accelerate a 1 kg mass at a rate of 1 m/s².

Understanding net force is crucial in physics as it dictates the motion of objects. The higher the net force, the greater the acceleration, assuming the mass remains constant. Conversely, if the mass increases and the net force remains constant, the acceleration decreases. This interplay between force, mass, and acceleration is fundamental to understanding how objects move in the world around us. Think about pushing a heavy box versus pushing a light one – you need more force to accelerate the heavier box at the same rate. That’s Newton's Second Law in action!

Calculating the Distance Traveled by the Car

Next up, we need to figure out the distance the car travels during those 6 seconds. Our keywords here are distance, initial velocity, time, and acceleration. Since the car is undergoing constant acceleration (we calculated it to be 3.33 m/s²), we can use one of the equations of motion (also known as kinematic equations) to find the distance. The equation that fits our situation best is: d = v₀t + (1/2)at², where d is the distance, v₀ is the initial velocity, t is the time, and a is the acceleration. This equation is a cornerstone of kinematics, allowing us to predict the position of an object moving with constant acceleration.

Let's plug in the values we know: v₀ = 0 m/s (since the car starts from rest), t = 6 s, and a = 3.33 m/s². So, the equation becomes: d = (0 m/s * 6 s) + (1/2 * 3.33 m/s² * (6 s)²). Simplifying this, we get d = 0 + (0.5 * 3.33 * 36) = 60 meters (approximately). Therefore, the car travels approximately 60 meters during the 6 seconds it accelerates. This is a significant distance, and it highlights how quickly an object can cover ground when accelerating. Imagine how far a car traveling at highway speeds can go in just a few seconds!

This equation, d = v₀t + (1/2)at², is incredibly powerful for solving problems involving constant acceleration. It links the distance traveled to the initial velocity, time, and acceleration, allowing us to calculate any one of these quantities if we know the others. The (1/2)at² part of the equation represents the distance covered due to the acceleration, while the v₀t part represents the distance that would have been covered if the object had continued moving at its initial velocity. Since the initial velocity is zero in this case, the entire distance is due to the car's acceleration. Isn't physics cool, guys?

Briefly Addressing the Skater's Initial Motion

The problem also mentions a skater of 50 kg mass starting from rest. While it doesn't give us enough information to calculate specific values like force or distance without knowing the applied force or acceleration, it sets the stage for a similar type of problem. We could, for example, be asked to calculate the force required to accelerate the skater to a certain speed in a given time, or the distance the skater covers under a constant applied force. The principles involved would be the same as those we used for the car problem: Newton's Second Law (F = ma) and the equations of motion. Think of it as a slightly different scenario, but with the same underlying physics principles at play.

To solve a problem about the skater, we'd need additional information, such as the force applied or the acceleration achieved. If we knew the force, we could use F = ma to calculate the acceleration. If we knew the acceleration, we could use the equations of motion to calculate the distance traveled or the final velocity. The key is to identify the knowns and unknowns and then choose the appropriate equation or equations to solve for the unknowns. Physics is like a puzzle, guys, and these equations are the pieces!

Key Takeaways and Practical Applications

So, what have we learned today? We've successfully calculated the net force acting on a car and the distance it traveled while accelerating. We did this by applying Newton's Second Law of Motion (F = ma) and one of the fundamental equations of motion (d = v₀t + (1/2)at²). These are core concepts in physics, and they have wide-ranging applications in the real world. From designing vehicles to understanding the motion of planets, the principles of force, mass, acceleration, and distance are essential.

Understanding these concepts isn't just about solving textbook problems, guys. It's about understanding how the world around us works. Think about the forces involved in driving a car, riding a bike, or even walking. The principles we've discussed here are at play in all of these situations. The ability to analyze these situations using the laws of physics gives us a deeper appreciation for the mechanics of the world.

Furthermore, the process of problem-solving in physics is a valuable skill in itself. Breaking down a problem into smaller, manageable steps, identifying the relevant equations, and applying them correctly is a skill that can be applied in many different areas of life. It's about critical thinking, analytical reasoning, and attention to detail – all qualities that are highly valued in various fields.

In conclusion, guys, this problem illustrates the power of physics to explain and predict the motion of objects. By understanding the relationships between force, mass, acceleration, distance, and time, we can gain valuable insights into the workings of the universe. Keep practicing, keep exploring, and keep asking questions! Physics is an amazing field, and there's always more to learn.