A Toy Is Moving At A Rate Of $2.5 \, \text{m/s}^2$. The Mass Of The Toy Is $3.9 \, \text{kg}$. What Is The Amount Of Force Used To Move The Toy?

Feb 27, 2025 by ADMIN 145 views

**Understanding the Relationship Between Force, Mass, and Acceleration**

In physics, the relationship between force, mass, and acceleration is a fundamental concept that is often used to describe the motion of objects. The force applied to an object is directly proportional to its mass and the acceleration it experiences. This relationship is described by Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

Newton's Second Law of Motion

Newton's second law of motion is often expressed mathematically as:

F = ma

Where:

F is the force applied to the object in newtons (N)
m is the mass of the object in kilograms (kg)
a is the acceleration of the object in meters per second squared (m/s^2)

Calculating the Force Used to Move the Toy

Given that the toy is moving at a rate of $2.5 \, \text{m/s}^2$ and has a mass of $3.9 \, \text{kg}$ , we can use Newton's second law of motion to calculate the amount of force used to move the toy.

Step 1: Identify the Given Values

Mass of the toy: $m = 3.9 \, \text{kg}$
Acceleration of the toy: $a = 2.5 \, \text{m/s}^2$

Step 2: Plug in the Values into the Equation

Using the equation F = ma, we can plug in the given values to calculate the force:

F = (3.9 kg) * (2.5 m/s^2)

Step 3: Calculate the Force

Performing the calculation, we get:

F = 9.75 N

Therefore, the amount of force used to move the toy is 9.75 N.

Understanding the Significance of the Result

The result of 9.75 N represents the amount of force required to accelerate the toy at a rate of $2.5 \, \text{m/s}^2$ . This means that if a force of 9.75 N is applied to the toy, it will accelerate at a rate of $2.5 \, \text{m/s}^2$ . This is a fundamental concept in physics and is used to describe the motion of objects in a wide range of situations.

Real-World Applications of Newton's Second Law of Motion

Newton's second law of motion has a wide range of real-world applications, including:

Designing vehicles: Understanding the relationship between force, mass, and acceleration is crucial in designing vehicles that can accelerate and decelerate safely.
Developing safety systems: Knowing the amount of force required to stop an object in motion is essential in developing safety systems, such as airbags and anti-lock braking systems.
Analyzing the motion of objects: Newton's second law of motion is used to analyze the motion of objects in a wide range of situations, including the motion of projectiles, the motion of objects on inclined planes, and the motion of objects in circular motion.

Conclusion

In conclusion, the amount of force used to move the toy is 9.75 N. This result is based on the application of Newton's second law of motion, which describes the relationship between force, mass, and acceleration. Understanding this relationship is essential in a wide range of situations, including designing vehicles, developing safety systems, and analyzing the motion of objects.
A Toy is Moving at a Rate of $2.5 \, \text{m/s}^2$ . The Mass of the Toy is $3.9 \, \text{kg}$ . What is the Amount of Force Used to Move the Toy? (Q&A)

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

A: Newton's second law of motion is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. It states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

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

A: The equation for Newton's second law of motion is F = ma, where:

F is the force applied to the object in newtons (N)
m is the mass of the object in kilograms (kg)
a is the acceleration of the object in meters per second squared (m/s^2)

Q: How do I calculate the force used to move an object?

A: To calculate the force used to move an object, you need to know the mass of the object and its acceleration. You can use the equation F = ma to calculate the force.

Q: What is the mass of the toy in the problem?

A: The mass of the toy is $3.9 \, \text{kg}$ .

Q: What is the acceleration of the toy in the problem?

A: The acceleration of the toy is $2.5 \, \text{m/s}^2$ .

Q: How do I plug in the values into the equation?

A: To plug in the values into the equation, you need to multiply the mass of the toy by its acceleration. In this case, you would multiply $3.9 \, \text{kg}$ by $2.5 \, \text{m/s}^2$ .

Q: What is the result of the calculation?

A: The result of the calculation is 9.75 N, which is the amount of force used to move the toy.

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

A: Some real-world applications of Newton's second law of motion include:

Designing vehicles: Understanding the relationship between force, mass, and acceleration is crucial in designing vehicles that can accelerate and decelerate safely.
Developing safety systems: Knowing the amount of force required to stop an object in motion is essential in developing safety systems, such as airbags and anti-lock braking systems.
Analyzing the motion of objects: Newton's second law of motion is used to analyze the motion of objects in a wide range of situations, including the motion of projectiles, the motion of objects on inclined planes, and the motion of objects in circular motion.

Q: Why is it important to understand Newton's second law of motion?

A: Understanding Newton's second law of motion is essential in a wide range of situations, including designing vehicles, developing safety systems, and analyzing the motion of objects. It is a fundamental concept in physics that helps us understand the relationship between force, mass, and acceleration.

Q: Can I use Newton's second law of motion to calculate the force used to move any object?

A: Yes, you can use Newton's second law of motion to calculate the force used to move any object, provided you know the mass of the object and its acceleration.

Q: What are some common mistakes to avoid when using Newton's second law of motion?

A: Some common mistakes to avoid when using Newton's second law of motion include:

Not using the correct units: Make sure to use the correct units for force, mass, and acceleration.
Not plugging in the values correctly: Make sure to multiply the mass of the object by its acceleration.
Not checking the result: Make sure to check the result of the calculation to ensure it is reasonable.

By understanding Newton's second law of motion and avoiding common mistakes, you can use this fundamental concept in physics to calculate the force used to move any object.