Given Information and the Problem

Oct 13, 2025 by ludoplayers7.com 138 views

Understanding the Relationship Between Force, Mass, and Acceleration

In physics, the relationship between force, mass, and acceleration is governed by Newton's second law of motion. This law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. Mathematically, this can be expressed as:

F = ma

where F is the net force applied to the object, m is its mass, and a is the acceleration produced.

Given Information and the Problem

We are given a net force of $$8.0 , \text{N}$$ and an acceleration of $$1.1 , \text{m/s}^2$$. Using Newton's second law, we can solve for the mass of the object.

Solving for Mass

Rearranging the equation F = ma to solve for mass, we get:

m = F / a

Substituting the given values, we have:

m = 8.0 N / (1.1 m/s^2)

m = 7.27 kg

Rounding to the Nearest Tenth

Rounding the calculated mass to the nearest tenth, we get:

m ≈ 7.3 kg

Comparing the Answer to the Options

Comparing our calculated mass to the given options, we find that the correct answer is:

B. 7.3 kg

Conclusion

In this problem, we used Newton's second law to solve for the mass of an object given a net force and acceleration. By rearranging the equation F = ma to solve for mass, we were able to calculate the mass of the object and compare it to the given options to find the correct answer.

Key Takeaways

Newton's second law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.
The equation F = ma can be rearranged to solve for mass: m = F / a.
By using this equation, we can solve for the mass of an object given a net force and acceleration.

Additional Practice Problems

A net force of $$4.0 , \text{N}$$ causes an object to accelerate at $$2.5 , \text{m/s}^2$$. What is the mass of the object?
A force of $$10.0 , \text{N}$$ is applied to an object, causing it to accelerate at $$3.0 , \text{m/s}^2$$. What is the mass of the object?
A net force of $$6.0 , \text{N}$$ causes an object to accelerate at $$1.5 , \text{m/s}^2$$. What is the mass of the object?

Answer Key

m ≈ 1.6 kg
m ≈ 3.33 kg
m ≈ 4 kg
Frequently Asked Questions (FAQs) About Mass and Acceleration ================================================================

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

A: The relationship between force, mass, and acceleration is governed by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. Mathematically, this can be expressed as:

F = ma

where F is the net force applied to the object, m is its mass, and a is the acceleration produced.

Q: How can I use Newton's second law to solve for mass?

A: To solve for mass, you can rearrange the equation F = ma to get:

m = F / a

This equation allows you to calculate the mass of an object given a net force and acceleration.

Q: What is the unit of mass in the International System of Units (SI)?

A: The unit of mass in the International System of Units (SI) is the kilogram (kg).

Q: How can I convert between different units of mass?

A: To convert between different units of mass, you can use conversion factors. For example, to convert from grams (g) to kilograms (kg), you can use the conversion factor:

1 kg = 1000 g

Q: What is the difference between mass and weight?

A: Mass and weight are often used interchangeably, but they are not exactly the same thing. Mass is a measure of the amount of matter in an object, while weight is a measure of the force exerted on an object by gravity. On Earth, the weight of an object is equal to its mass multiplied by the acceleration due to gravity (g).

Q: How can I calculate the weight of an object?

A: To calculate the weight of an object, you can use the equation:

W = mg

where W is the weight of the object, m is its mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).

Q: What is the relationship between mass and weight on different planets?

A: The relationship between mass and weight on different planets is governed by the acceleration due to gravity on each planet. On a planet with a stronger gravitational field, the weight of an object will be greater than on a planet with a weaker gravitational field.

Q: How can I calculate the mass of an object on a different planet?

A: To calculate the mass of an object on a different planet, you can use the equation:

m = W / g

where m is the mass of the object, W is its weight, and g is the acceleration due to gravity on the planet.

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 vehicle
Designing roller coasters and other amusement park rides
Understanding the motion of objects in space
Calculating the force required to lift heavy objects

Conclusion

In this article, we have answered some frequently asked questions about mass and acceleration, including the relationship between force, mass, and acceleration, how to use Newton's second law to solve for mass, and the difference between mass and weight. We have also discussed some real-world applications of Newton's second law and provided equations for calculating the mass and weight of objects on different planets.