A Cart Is Sliding Across A Horizontal Floor With A Mass Of 25 Kg And A Force Of 250 N. Using Newton's Second Law, $a = \frac{F}{m}$, What Is The Acceleration Of The Cart?A. $0.1 \, \text{m/s}^2$ B. $5 \, \text{m/s}^2$ C.

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Introduction

Newton's second law of motion is a fundamental concept in physics that describes the relationship between a force applied to an object and its resulting acceleration. The law states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. In this article, we will explore how to use Newton's second law to calculate the acceleration of a cart sliding across a horizontal floor.

Newton's Second Law

Newton's second law is often expressed mathematically as:

a=Fma = \frac{F}{m}

where:

  • aa is the acceleration of the object
  • FF is the net force applied to the object
  • mm is the mass of the object

Calculating Acceleration

To calculate the acceleration of the cart, we need to know the force applied to it and its mass. In this case, the force applied to the cart is 250 N, and its mass is 25 kg. We can plug these values into the equation for Newton's second law to find the acceleration.

# Import necessary modules
import math

# Define variables
force = 250  # N
mass = 25  # kg

# Calculate acceleration using Newton's second law
acceleration = force / mass

print("The acceleration of the cart is:", acceleration, "m/s^2")

Solving for Acceleration

Using the equation for Newton's second law, we can solve for the acceleration of the cart:

a=Fm=250 N25 kg=10 m/s2a = \frac{F}{m} = \frac{250 \, \text{N}}{25 \, \text{kg}} = 10 \, \text{m/s}^2

Therefore, the acceleration of the cart is 10 m/s^2.

Conclusion

In this article, we used Newton's second law to calculate the acceleration of a cart sliding across a horizontal floor. We found that the acceleration of the cart is 10 m/s^2, which is the correct answer. This demonstrates the importance of understanding Newton's second law and how to apply it to real-world problems.

Discussion

The discussion category for this article is physics. The article covers the topic of Newton's second law and its application to calculating acceleration.

Related Topics

  • Newton's first law of motion
  • Newton's third law of motion
  • Force and motion
  • Acceleration and velocity

References

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Frequently Asked Questions

  • Q: What is Newton's second law of motion? A: Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass.
  • Q: How do I calculate the acceleration of an object using Newton's second law? A: To calculate the acceleration of an object using Newton's second law, you need to know the force applied to the object and its mass. You can then plug these values into the equation for Newton's second law to find the acceleration.
  • Q: What is the unit of acceleration? A: The unit of acceleration is m/s^2.
    A Cart is Sliding Across a Horizontal Floor: Q&A =====================================================

Introduction

In our previous article, we explored how to use Newton's second law to calculate the acceleration of a cart sliding across a horizontal floor. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is Newton's second law of motion?

A: Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. Mathematically, it is expressed as:

a=Fma = \frac{F}{m}

where:

  • aa is the acceleration of the object
  • FF is the net force applied to the object
  • mm is the mass of the object

Q: How do I calculate the acceleration of an object using Newton's second law?

A: To calculate the acceleration of an object using Newton's second law, you need to know the force applied to the object and its mass. You can then plug these values into the equation for Newton's second law to find the acceleration.

# Import necessary modules
import math

# Define variables
force = 250  # N
mass = 25  # kg

# Calculate acceleration using Newton's second law
acceleration = force / mass

print("The acceleration of the object is:", acceleration, "m/s^2")

Q: What is the unit of acceleration?

A: The unit of acceleration is m/s^2.

Q: What is the difference between force and acceleration?

A: Force is a push or pull that causes an object to change its motion, while acceleration is the rate of change of velocity of an object.

Q: Can I use Newton's second law to calculate the force applied to an object?

A: Yes, you can use Newton's second law to calculate the force applied to an object if you know its acceleration and mass. The equation for Newton's second law can be rearranged to solve for force:

F=maF = ma

Q: What is the relationship between force, mass, and acceleration?

A: The relationship between force, mass, and acceleration is described by Newton's second law:

a=Fma = \frac{F}{m}

This equation shows that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass.

Q: Can I use Newton's second law to calculate the mass of an object?

A: Yes, you can use Newton's second law to calculate the mass of an object if you know its acceleration and the force applied to it. The equation for Newton's second law can be rearranged to solve for mass:

m=Fam = \frac{F}{a}

Q: What are some real-world applications of Newton's second law?

A: Newton's second law has many real-world applications, including:

  • Calculating the force required to accelerate a car from 0 to 60 mph
  • Determining the force required to lift an object
  • Calculating the acceleration of a projectile
  • Understanding the motion of objects in different environments, such as on a frictionless surface or in a gravitational field.

Conclusion

In this article, we answered some frequently asked questions related to Newton's second law and its application to calculating acceleration. We hope that this article has provided you with a better understanding of this important concept in physics.

Discussion

The discussion category for this article is physics. The article covers the topic of Newton's second law and its application to calculating acceleration.

Related Topics

  • Newton's first law of motion
  • Newton's third law of motion
  • Force and motion
  • Acceleration and velocity

References

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Frequently Asked Questions

  • Q: What is Newton's second law of motion? A: Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass.
  • Q: How do I calculate the acceleration of an object using Newton's second law? A: To calculate the acceleration of an object using Newton's second law, you need to know the force applied to the object and its mass. You can then plug these values into the equation for Newton's second law to find the acceleration.
  • Q: What is the unit of acceleration? A: The unit of acceleration is m/s^2.