Calculating Work Done in a Physics Problem: Pivoting Around Essential Information

When approaching a physics problem like the one mentioned, it is crucial to identify the essential components that contribute to the solution. This article delves into the key elements and techniques needed to effectively calculate work done in the scenario provided. Let's tackle the problem step by step to illustrate the process.

Identifying the Relevant Information

The original question is:

What is the work done if a man pulls a 40 kg crate through 20 m across a leveled floor with a rope which makes 30 degrees with the horizon He exerts a force of 150 N on the rope.

A first glance might reveal some complexities, but as we will show, this problem is simpler than it appears. The mass of the crate, although provided, is not necessary for calculating the work done. Here’s why:

The Role of Force and Motion in Work

Work is defined as the product of force applied in the direction of motion and the distance over which the force acts. The formula for work is given by:

W F * d * cos(θ)

Where:

W is the work done in joules (J) F is the force applied in newtons (N) d is the distance over which the force acts in meters (m) θ is the angle between the force and the direction of motion in degrees

Analyzing the Provided Data

In the given scenario, we have the following information:

Force (F) exerted by the man: 150 N Distance (d) the crate is dragged: 20 m Angle (θ) between the force and the direction of motion: 30°

Using the formula for work, let's calculate the work done:

W F * d * cos(θ)

Substituting the values:

W 150 N * 20 m * cos(30°)

Since cos(30°) √3/2 ≈ 0.866:

W ≈ 150 * 20 * 0.866 ≈ 2598 N·m

Since 1 N·m 1 Joule (J), the work done is approximately 2598 J.

Removing Unnecessary Information

The mass of the crate (40 kg) is provided but is irrelevant to the calculation of work done, as work does not depend on the mass of the object, but rather on the applied force, the distance, and the angle between them.

Conclusion

To summarize, the key to solving this problem effectively lies in recognizing which pieces of information are necessary and which can be disregarded. By focusing on the essential components, such as the force, distance, and angle, you can accurately calculate the work done.

Understanding the relationship between force, distance, and angle in the context of work is fundamental to solving a wide range of physics problems. By mastering the basics, you can tackle more complex scenarios with confidence.

This article aims to provide a clear, step-by-step guide to solving such problems, making it an excellent resource for students, educators, and anyone interested in physics and mechanics.