Calculating Stopping Force For An SUV Traveling At 18 M/s

In the realm of physics, understanding the relationship between force, mass, and motion is paramount. Newton's laws of motion provide a fundamental framework for analyzing how objects move and interact. This article delves into a practical application of these principles, exploring the scenario of an SUV traveling at a certain speed and the force required to bring it to a halt within a specific timeframe. We will dissect the problem, applying the concepts of inertia, momentum, and impulse to arrive at a comprehensive solution. This exploration not only reinforces theoretical knowledge but also highlights the real-world relevance of physics in everyday situations, such as vehicle safety and braking systems.

At the heart of this discussion lies the SUV, a vehicle with a mass of 1,550 kg, hurtling down the road at a speed of 18 m/s. The challenge we face is to determine the force necessary to bring this hefty machine to a complete stop in a mere 8 seconds. This seemingly simple question opens a gateway to understanding the intricate interplay of physical forces. To unravel this problem, we will employ the principles of physics, specifically Newton's second law of motion, which establishes a direct relationship between force, mass, and acceleration. Furthermore, we will delve into the concept of impulse, which connects force and time to the change in an object's momentum. By carefully analyzing these concepts and applying the appropriate equations, we can precisely calculate the force required to halt the SUV within the given timeframe. This exercise not only provides a numerical answer but also offers valuable insights into the dynamics of moving objects and the forces that govern their motion. Understanding these principles is crucial for various applications, from designing safer vehicles to analyzing the impact of collisions.

Before we dive into the calculations, let's first grasp the key concepts involved. Force, in its simplest definition, is any interaction that, when unopposed, will change the motion of an object. It can cause an object to accelerate, decelerate, or change direction. Mass is a measure of an object's inertia, its resistance to changes in its state of motion. The more massive an object is, the more force is required to accelerate it. Velocity is the rate of change of an object's position with respect to time, and acceleration is the rate of change of velocity. In this scenario, we are dealing with deceleration, which is simply acceleration in the opposite direction of motion.

Newton's second law of motion is the cornerstone of our analysis. It states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This equation tells us that the greater the force applied to an object, the greater its acceleration will be. Conversely, the greater the mass of an object, the smaller its acceleration will be for a given force. In our SUV problem, we need to determine the force required to produce a specific deceleration, bringing the vehicle to a stop. Another crucial concept is impulse, which is the change in momentum of an object. Momentum is the product of an object's mass and velocity (p = mv), and impulse is the force applied to an object multiplied by the time interval over which it acts (Impulse = FΔt). The impulse-momentum theorem states that the impulse acting on an object is equal to the change in its momentum (FΔt = Δp). This theorem provides an alternative way to calculate the force required to stop the SUV, as we know the change in momentum (from its initial velocity to zero) and the time interval over which the force is applied. By understanding these fundamental concepts and their interrelationships, we can effectively tackle the problem at hand and gain a deeper appreciation for the physics governing the motion of objects.

The first step is to calculate the deceleration required to stop the SUV in 8 seconds. We know the initial velocity ($v_i = 18 m/s$), the final velocity ($v_f = 0 m/s$), and the time interval ($Δt = 8 s$). We can use the following kinematic equation to find the acceleration (a):

$v_f = v_i + aΔt$

Plugging in the values, we get:

$0 m/s = 18 m/s + a (8 s)$

Solving for a, we find:

$a = -18 m/s / 8 s = -2.25 m/s^2$

The negative sign indicates that the acceleration is in the opposite direction of the motion, which is deceleration.

Now that we have the deceleration, we can proceed to the next step in calculating the force required to stop the SUV. The deceleration, -2.25 m/s², represents the rate at which the SUV's velocity decreases over time. This value is crucial because it directly relates to the force needed to bring the vehicle to a halt. A higher deceleration implies a greater force is required to stop the SUV within the same timeframe. The negative sign is essential to remember, as it signifies that the force is acting in the opposite direction of the SUV's initial motion, effectively slowing it down. Understanding the magnitude and direction of the deceleration is paramount for accurately determining the stopping force. This calculated deceleration serves as a bridge between the kinematic description of the SUV's motion and the dynamic forces acting upon it. By combining this value with the SUV's mass, we can utilize Newton's second law of motion to precisely quantify the force needed to achieve the desired deceleration and bring the vehicle to a complete stop within the specified 8-second interval. This step highlights the interconnectedness of different physical concepts and their application in solving real-world problems.

Now that we know the deceleration, we can use Newton's second law of motion ($F = ma$) to calculate the force required. We have the mass of the SUV ($m = 1,550 kg$) and the deceleration ($a = -2.25 m/s^2$). Plugging these values into the equation, we get:

$F = (1,550 kg) * (-2.25 m/s^2) = -3,487.5 N$

The negative sign indicates that the force is acting in the opposite direction of the SUV's motion, which is the braking force.

This calculation provides the magnitude of the force required to stop the SUV within the given timeframe. The force, -3,487.5 N, represents the amount of braking force that must be applied to counteract the SUV's inertia and bring it to a complete stop in 8 seconds. The negative sign is crucial as it indicates the direction of the force, which is opposite to the direction of motion. This force is a significant value, reflecting the substantial mass of the SUV and the relatively short time frame for stopping. Understanding the magnitude of this force is essential for designing effective braking systems and ensuring vehicle safety. A braking system must be capable of generating a force of at least this magnitude to safely stop the SUV under similar conditions. Furthermore, this calculation highlights the relationship between mass, acceleration, and force, as dictated by Newton's second law of motion. A heavier vehicle or a shorter stopping time would necessitate a greater braking force. This principle underscores the importance of maintaining a safe following distance and being aware of road conditions to allow for adequate stopping distance. The calculated force serves as a practical example of how physics principles are applied in real-world scenarios to ensure safety and efficiency in transportation.

Therefore, the force that must be applied to stop the SUV in 8 seconds is -3,487.5 N. This corresponds to option B.

In conclusion, this problem demonstrates the practical application of fundamental physics principles in everyday scenarios. By understanding concepts like force, mass, acceleration, and Newton's laws of motion, we can analyze and solve real-world problems related to motion and braking. The calculated force of -3,487.5 N highlights the significant force required to stop a vehicle of considerable mass within a relatively short time. This underscores the importance of safe driving practices, including maintaining a safe following distance and being aware of road conditions. The negative sign of the force indicates that it acts in the opposite direction of the SUV's motion, representing the braking force. This exercise not only reinforces our understanding of physics concepts but also emphasizes their relevance in ensuring safety and efficiency in transportation. Furthermore, the problem-solving process involved applying kinematic equations to determine deceleration and then utilizing Newton's second law of motion to calculate the force. This step-by-step approach showcases the logical and analytical thinking required to tackle physics problems. By breaking down the problem into smaller, manageable steps, we can effectively apply the appropriate principles and arrive at a comprehensive solution. This approach is valuable not only in physics but also in various other fields requiring problem-solving skills. The successful resolution of this problem demonstrates the power of physics in understanding and predicting the behavior of objects in motion.