Calculating the Force Needed to Accelerate the Ball

Oct 13, 2025 by pynkocean.com 70 views

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 $$F = ma$$, 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 Formula: $$F = ma$$

The formula $$F = ma$$ is a direct application of 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. This formula is a fundamental concept in physics and is used to describe the motion of objects in a wide range of situations.

Calculating the Force Needed to Accelerate the Ball

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

First, 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 g to kilograms as follows:

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

Next, we can plug in the values for mass and acceleration into the formula $$F = ma$$:

F = ma = (0.14 \, \text{kg})(25 \, \text{m/s}^2)

To calculate the force, we can multiply the mass and acceleration:

F = (0.14 \, \text{kg})(25 \, \text{m/s}^2) = 3.5 \, \text{N}

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

Comparing the Answer to the Options

Now that we have calculated the force needed to accelerate the ball, we can compare our answer to the options provided:

A. 3.5 N B. 115 N C. 165 N D. 4.5 N

Our calculated answer of 3.5 N matches option A.

Conclusion

In this problem, we used the formula $$F = ma$$ to calculate the force needed to accelerate a ball with a mass of 140 g at $$25 , \text{m/s}^2$$. We converted the mass from grams to kilograms, plugged in the values for mass and acceleration into the formula, and calculated the force. Our calculated answer of 3.5 N matches option A.

Understanding the Significance of the Formula

The formula $$F = ma$$ is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. This formula is used to describe the motion of objects in a wide range of situations and is a crucial tool in understanding the behavior of objects in the physical world.

Real-World Applications of the Formula

The formula $$F = ma$$ has a wide range of real-world applications. For example, it is used in the design of roller coasters, where the force needed to accelerate a car at a certain rate is calculated using this formula. It is also used in the design of aircraft, where the force needed to accelerate a plane at a certain rate is calculated using this formula.

Common Misconceptions About the Formula

There are several common misconceptions about the formula $$F = ma$$. One common misconception is that the formula is only used to describe the motion of objects in a straight line. However, this formula can be used to describe the motion of objects in any direction, as long as the force and acceleration are in the same direction.

Another common misconception is that the formula is only used to describe the motion of objects that are moving at a constant velocity. However, this formula can be used to describe the motion of objects that are accelerating, as long as the force and acceleration are in the same direction.

Conclusion

Q: What is the formula $$F = ma$$ used for?

A: The formula $$F = ma$$ is used to describe the relationship between force, mass, and acceleration. It is a fundamental concept in physics that is used to describe the motion of objects in a wide range of situations.

Q: What is the difference between force and mass?

A: Force is a push or pull that causes an object to change its motion, while mass is a measure of the amount of matter in an object. The formula $$F = ma$$ shows that force is equal to mass multiplied by acceleration.

Q: What is acceleration?

A: Acceleration is the rate of change of velocity. It is a measure of how quickly an object's velocity changes. In the formula $$F = ma$$, acceleration is represented by the variable $$a$$.

Q: How do I use the formula $$F = ma$$ to solve a problem?

A: To use the formula $$F = ma$$ to solve a problem, you need to know the mass of the object and the acceleration it is experiencing. You can then plug these values into the formula and solve for the force.

Q: What are some real-world applications of the formula $$F = ma$$?

A: The formula $$F = ma$$ has a wide range of real-world applications. For example, it is used in the design of roller coasters, where the force needed to accelerate a car at a certain rate is calculated using this formula. It is also used in the design of aircraft, where the force needed to accelerate a plane at a certain rate is calculated using this formula.

Q: Can I use the formula $$F = ma$$ to describe the motion of objects in any direction?

A: Yes, you can use the formula $$F = ma$$ to describe the motion of objects in any direction, as long as the force and acceleration are in the same direction.

Q: Can I use the formula $$F = ma$$ to describe the motion of objects that are moving at a constant velocity?

A: Yes, you can use the formula $$F = ma$$ to describe the motion of objects that are moving at a constant velocity, as long as the force and acceleration are in the same direction.

Q: What are some common misconceptions about the formula $$F = ma$$?

A: There are several common misconceptions about the formula $$F = ma$$. One common misconception is that the formula is only used to describe the motion of objects in a straight line. However, this formula can be used to describe the motion of objects in any direction, as long as the force and acceleration are in the same direction.

Q: How do I convert units in the formula $$F = ma$$?

A: To convert units in the formula $$F = ma$$, you need to make sure that the units of force, mass, and acceleration are consistent. For example, if you are using kilograms for mass and meters per second squared for acceleration, you need to use newtons for force.

Q: Can I use the formula $$F = ma$$ to solve problems that involve friction?

A: Yes, you can use the formula $$F = ma$$ to solve problems that involve friction. However, you need to take into account the force of friction, which is a force that opposes the motion of an object.

Q: Can I use the formula $$F = ma$$ to solve problems that involve gravity?

A: Yes, you can use the formula $$F = ma$$ to solve problems that involve gravity. However, you need to take into account the force of gravity, which is a force that attracts objects towards each other.

Conclusion

In conclusion, the formula $$F = ma$$ is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. It is a crucial tool in understanding the behavior of objects in the physical world and has a wide range of real-world applications.