Introduction

When analyzing physical scenarios involving forces and motion, one must consider various factors such as the mass of an object, the frictional forces opposing its motion, and the applied forces required to achieve a given acceleration. This article will take a detailed look at a problem where a box with a mass of 5 kg is pushed along a floor with a given acceleration and frictional resistance. We will explore the physics behind the problem and derive the correct applied force required to achieve the specified acceleration.

Underlying Physics and Key Concepts

The fundamental principles of Newton's laws of motion are crucial in solving such problems. Newton's second law states that the net force acting on an object is equal to the product of its mass and its acceleration, i.e., F ma. Here, F represents the net force, m is the mass, and a is the acceleration.

The Problem: Box with Friction

Consider a 5 kg box that is being pushed along a floor with a frictional force of 10 N. The box accelerates at 1 m/s2. The question is: what is the magnitude of the applied force required to achieve this acceleration?

Assumptions and Correct Approach

Important to note is that in such problems, it is often assumed that the applied force is horizontal unless otherwise specified. Let's assume the applied force is indeed horizontal. The first step is to identify the forces acting on the box:

Fapplied: The force applied to move the box. Ffriction: The frictional force opposing the motion (10 N). Fnet: The net force causing the acceleration.

The net force causing the acceleration is given by:

Fnet Fapplied - Ffriction ma

Calculations

Given:

Mass, m 5 kg Acceleration, a 1 m/s2 Frictional force, Ffriction 10 N

To find the applied force, we use the equation:

Fapplied Fnet Ffriction

First, we calculate the net force:

Fnet ma 5 × 1 5 N

Then, adding the frictional force:

Fapplied 5 10 15 N

Discussion on Variable Friction

It's important to note that in many practical scenarios, the frictional force may not be constant. For example, frictional forces can vary with the square of the velocity. However, in the context of this problem, we are operating under the assumption of a constant frictional force. Therefore, any variation in friction would modify the frictional force, not the basic solution provided.

Conclusion

The magnitude of the applied force required to move the 5 kg box with an acceleration of 1 m/s2, considering a frictional force of 10 N, is 15 N. This calculation is based on the principle of Newton's second law and assumes a constant frictional force. Any deviation from these assumptions (such as time-varying frictional force) would require more complex models to accurately determine the applied force.