Calculating the Net Force Required to Stop a Shopping Cart: A Physics Problem

Introduction

Understanding the physical principles involved in motion and force is essential for both theoretical and practical applications. In this piece, we will delve into a specific physics problem involving a 7 kg shopping cart and explore the calculations needed to determine the net force required to stop it within a given time frame.

Problem Statement

The question at hand is: What average net force is required to stop a 7 kg shopping cart in 2 seconds if it is initially traveling at 3.5 m/s?

Calculation Using Momentum Change or Impulse

The concept of impulse is central to answering this question. Impulse is defined as the change in momentum of an object and is given by the product of force and time over which the force acts. Let's break down the calculation step by step.

Step 1: Define the Given Data

Mass of the shopping cart, m 7 kg

Initial velocity of the shopping cart, v_i 3.5 frac{m}{s}

Time to stop the cart, t_s 2 s

Step 2: Apply the Equation of Impulse

Impulse is given by the equation:

-F m frac{dv}{dt}

Integrating both sides:

-F int_0^{t_s} dt m int_{v_i}^0 dv

-Ft_s -mv_i

Thus, the net force required is:

F frac{mv_i}{t_s} frac{7 text{kg} 3.5 frac{text{m}}{text{s}}}{2 text{s}} 12.25 text{N}

The net force is negative, indicating it acts in the opposite direction of the cart's motion.

Verification Using Kinetic Energy and Work

We can also verify our calculation using kinetic energy and work principles. The initial kinetic energy of the cart is:

KE frac{1}{2}mv^2 frac{1}{2} 7 text{kg} (3.5 frac{text{m}}{text{s}})^2 42.875 text{J}

The work done to stop the cart is equal to the initial kinetic energy, and is given by:

W Fd

The stopping distance is:

d frac{v_i^2}{2a} frac{3.5^2}{2 1.75} 3.5 text{m}

Therefore, the net force required is:

F frac{W}{d} frac{42.875 text{J}}{3.5 text{m}} 12.25 text{N}

Conclusion

To summarize, the average net force required to stop a 7 kg shopping cart traveling at 3.5 m/s in 2 seconds is 12.25 N. This calculation demonstrates the application of fundamental physics principles, specifically the concepts of impulse and kinetic energy, in solving real-world problems.

Additional Insights

Understanding these principles can be crucial in various fields, from engineering to sports, where the ability to control and predict motion is essential. Whether it's designing safer vehicle systems or optimizing athletic performance, the principles of force and motion are always at play.