Calculating Climbing Height Using Work And Force A Physics Problem

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Introduction

In this article, we will delve into a physics problem involving the concepts of work, force, and distance. The problem presented states that a firefighter needs 270 N of force to lift their equipment. If the firefighter performs 5400 J of work while carrying the equipment up a staircase, we need to determine the height the firefighter climbs. This problem provides a practical application of the work-energy principle, which is a fundamental concept in physics.

Understanding the Key Concepts

Before we dive into the solution, let's define the key concepts involved:

  • Work (W): In physics, work is done when a force causes displacement. It is calculated as the product of the force applied and the distance over which the force acts in the direction of displacement. The formula for work is W = Fd, where:
    • W represents work, measured in joules (J).
    • F represents force, measured in newtons (N).
    • d represents distance, measured in meters (m).
  • Force (F): Force is a push or pull that can cause a change in an object's motion. It is a vector quantity, meaning it has both magnitude and direction. In this problem, the force is the effort required to lift the firefighter's equipment against gravity.
  • Distance (d): Distance refers to the length of the path traveled by an object. In this case, the distance is the vertical height the firefighter climbs while carrying the equipment.

Problem Statement

The problem provides us with the following information:

  • Force required to lift the equipment (F) = 270 N
  • Work done by the firefighter (W) = 5400 J

We are asked to find the height (d) the firefighter climbs. This is a classic problem that uses the work-energy theorem, specifically focusing on how work relates to force and displacement.

Applying the Work Formula

To solve this problem, we will use the work formula: W = Fd. We know the values for work (W) and force (F), and we need to find the distance (d). To do this, we can rearrange the formula to solve for d:

d = W / F

Now, we can substitute the given values into the formula:

d = 5400 J / 270 N

Solving for Distance

Performing the division, we get:

d = 20 m

Therefore, the firefighter climbs a height of 20 meters.

Analyzing the Solution

The solution indicates that the firefighter climbs 20 meters while carrying the equipment. This result is consistent with the given values for work and force. The work done (5400 J) is the energy expended to lift the equipment against gravity over the vertical distance. The force (270 N) is the effort exerted to counteract the gravitational force acting on the equipment. This calculation exemplifies how work, force, and displacement are interconnected in physics. Understanding these relationships is crucial for solving a variety of mechanics problems. The correct answer is A. 20 m, which aligns with our calculation.

Why Other Options are Incorrect

Let's analyze why the other options provided are incorrect:

  • B. 200 m: This answer is incorrect because it is an overestimate of the height. If the firefighter climbed 200 meters with a force of 270 N, the work done would be significantly higher than 5400 J. To verify this, we can calculate the work done: W = Fd = 270 N * 200 m = 54000 J. This is ten times the work done in the problem, making this option incorrect.
  • C. 5130 m: This answer is also incorrect and represents an even larger overestimate of the height. Using the work formula, W = Fd = 270 N * 5130 m = 1,385,100 J. This value is far greater than the given work of 5400 J, indicating that this option is not feasible.
  • D. 1,458,000 m: This option represents an extremely high value for the height climbed and is clearly incorrect. If we calculate the work done for this distance, W = Fd = 270 N * 1,458,000 m = 393,660,000 J. This is an astronomical value compared to the given work of 5400 J, making this option entirely unrealistic.

Practical Applications and Importance

Understanding the relationship between work, force, and distance has numerous practical applications in various fields, including:

  • Engineering: Engineers use these principles to design structures, machines, and systems. For example, when designing elevators, it's crucial to calculate the work required to lift the elevator car and its passengers to a certain height. This involves considering the force needed (weight of the elevator and passengers) and the distance (height of the building).
  • Sports Science: In sports, understanding work and energy helps athletes optimize their performance. For example, calculating the work done during a weightlifting exercise can help determine the power output and efficiency of the athlete's movements.
  • Ergonomics: Ergonomics involves designing workplaces and tools to maximize efficiency and safety. Understanding the work required for different tasks can help in designing workstations that minimize strain and prevent injuries.
  • Everyday Life: We encounter these principles in everyday activities such as lifting objects, pushing a lawnmower, or climbing stairs. The amount of work we do depends on the force we exert and the distance we move an object.

By grasping the concepts of work, force, and distance, individuals can better understand the physical world around them and make informed decisions in various situations.

Conclusion

In summary, by applying the work formula (W = Fd) and rearranging it to solve for distance (d = W / F), we determined that the firefighter climbed a height of 20 meters. This problem highlights the practical application of physics principles in real-world scenarios. Understanding the relationship between work, force, and distance is crucial for problem-solving in physics and for various applications in engineering, sports science, ergonomics, and everyday life. The correct answer to the question is A. 20 m.