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Answer :
To solve this problem, we want to find the force needed to accelerate a ball with a mass of 140 grams at an acceleration of [tex]\(25 \, \text{m/s}^2\)[/tex].
Here’s a step-by-step solution:
1. Understand the Formula:
The formula to calculate force is given by:
[tex]\[
F = ma
\][/tex]
where [tex]\(F\)[/tex] is the force in newtons, [tex]\(m\)[/tex] is the mass in kilograms, and [tex]\(a\)[/tex] is the acceleration in meters per second squared.
2. Convert Mass to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this to kilograms because the standard unit of mass in physics equations is kilograms.
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
[tex]\[
\text{mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Apply the Formula:
Now, substitute the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
4. Calculate the Force:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex].
Therefore, the correct answer is 3.5 N.
Here’s a step-by-step solution:
1. Understand the Formula:
The formula to calculate force is given by:
[tex]\[
F = ma
\][/tex]
where [tex]\(F\)[/tex] is the force in newtons, [tex]\(m\)[/tex] is the mass in kilograms, and [tex]\(a\)[/tex] is the acceleration in meters per second squared.
2. Convert Mass to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this to kilograms because the standard unit of mass in physics equations is kilograms.
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
[tex]\[
\text{mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Apply the Formula:
Now, substitute the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
4. Calculate the Force:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex].
Therefore, the correct answer is 3.5 N.
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