A Ball Has A Mass Of 140 G. What Is The Force Needed To Accelerate The Ball At $25 , \text{m/s}^2$? (Formula: $F = M \cdot A$)A. 3.5 N B. 115 N C. 165 N D. 4.5 N

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In physics, the relationship between force, mass, and acceleration is a fundamental concept that is often used to describe the motion of objects. The formula $F = m \cdot a$, where $F$ is the force applied to an object, $m$ is the mass of the object, and $a$ is the acceleration produced, is a crucial tool in understanding this relationship.

The Given Problem

In this problem, we are given a ball with a mass of 140 g and asked to find the force needed to accelerate it at a rate of $25 , \text{m/s}^2$. To solve this problem, we will use the formula $F = m \cdot a$ and plug in the given values.

Converting Mass from Grams to Kilograms

Before we can use the formula, we need to convert the mass of the ball from grams to kilograms. Since 1 kilogram is equal to 1000 grams, we can convert 140 grams to kilograms by dividing by 1000.

140 g=1401000 kg=0.14 kg140 \, \text{g} = \frac{140}{1000} \, \text{kg} = 0.14 \, \text{kg}

Plugging in the Values

Now that we have the mass in kilograms, we can plug in the values into the formula $F = m \cdot a$.

F=0.14 kg⋅25 m/s2F = 0.14 \, \text{kg} \cdot 25 \, \text{m/s}^2

Solving for Force

To solve for force, we can multiply the mass and acceleration together.

F=0.14 kg⋅25 m/s2=3.5 NF = 0.14 \, \text{kg} \cdot 25 \, \text{m/s}^2 = 3.5 \, \text{N}

Conclusion

Therefore, the force needed to accelerate the ball at a rate of $25 , \text{m/s}^2$ is 3.5 N.

Why is This Problem Important?

This problem is important because it illustrates the relationship between force, mass, and acceleration. Understanding this relationship is crucial in many real-world applications, such as designing roller coasters, calculating the force of a car's brakes, and determining the thrust of a rocket engine.

Real-World Applications

The concept of force, mass, and acceleration is used in many real-world applications, including:

  • Roller Coasters: The force of gravity and the mass of the roller coaster car determine the acceleration of the car as it moves along the track.
  • Car Brakes: The force of the brakes and the mass of the car determine the acceleration of the car as it slows down.
  • Rocket Engines: The thrust of the rocket engine and the mass of the rocket determine the acceleration of the rocket as it lifts off the launchpad.

Common Misconceptions

There are several common misconceptions about the relationship between force, mass, and acceleration. Some of these misconceptions include:

  • Force is equal to mass: This is not true. Force is equal to mass times acceleration.
  • Acceleration is equal to force: This is not true. Acceleration is equal to force divided by mass.
  • Mass is equal to force: This is not true. Mass is a measure of the amount of matter in an object, while force is a measure of the push or pull on an object.

Conclusion

In conclusion, the relationship between force, mass, and acceleration is a fundamental concept in physics that is used to describe the motion of objects. The formula $F = m \cdot a$ is a crucial tool in understanding this relationship, and it has many real-world applications. By understanding this concept, we can design safer and more efficient systems, such as roller coasters and car brakes, and determine the thrust of a rocket engine.

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._

Additional Resources

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

A: The relationship between force, mass, and acceleration is described by the formula $F = m \cdot a$, where $F$ is the force applied to an object, $m$ is the mass of the object, and $a$ is the acceleration produced.

Q: What is the mass of the ball in kilograms?

A: The mass of the ball is 140 g, which is equal to 0.14 kg.

Q: What is the acceleration of the ball?

A: The acceleration of the ball is $25 , \text{m/s}^2$.

Q: What is the force needed to accelerate the ball at $25 , \text{m/s}^2$?

A: To find the force needed to accelerate the ball, we can use the formula $F = m \cdot a$. Plugging in the values, we get:

F=0.14 kg⋅25 m/s2=3.5 NF = 0.14 \, \text{kg} \cdot 25 \, \text{m/s}^2 = 3.5 \, \text{N}

Q: Why is this problem important?

A: This problem is important because it illustrates the relationship between force, mass, and acceleration. Understanding this relationship is crucial in many real-world applications, such as designing roller coasters, calculating the force of a car's brakes, and determining the thrust of a rocket engine.

Q: What are some common misconceptions about the relationship between force, mass, and acceleration?

A: Some common misconceptions about the relationship between force, mass, and acceleration include:

  • Force is equal to mass: This is not true. Force is equal to mass times acceleration.
  • Acceleration is equal to force: This is not true. Acceleration is equal to force divided by mass.
  • Mass is equal to force: This is not true. Mass is a measure of the amount of matter in an object, while force is a measure of the push or pull on an object.

Q: What are some real-world applications of the concept of force, mass, and acceleration?

A: Some real-world applications of the concept of force, mass, and acceleration include:

  • Roller Coasters: The force of gravity and the mass of the roller coaster car determine the acceleration of the car as it moves along the track.
  • Car Brakes: The force of the brakes and the mass of the car determine the acceleration of the car as it slows down.
  • Rocket Engines: The thrust of the rocket engine and the mass of the rocket determine the acceleration of the rocket as it lifts off the launchpad.

Q: How can I use the formula $F = m \cdot a$ to solve problems involving force, mass, and acceleration?

A: To use the formula $F = m \cdot a$ to solve problems involving force, mass, and acceleration, simply plug in the values for mass and acceleration, and solve for force.

Q: What are some additional resources for learning about force, mass, and acceleration?

A: Some additional resources for learning about force, mass, and acceleration include:

Conclusion

In conclusion, the relationship between force, mass, and acceleration is a fundamental concept in physics that is used to describe the motion of objects. The formula $F = m \cdot a$ is a crucial tool in understanding this relationship, and it has many real-world applications. By understanding this concept, we can design safer and more efficient systems, such as roller coasters and car brakes, and determine the thrust of a rocket engine.