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Answer :
To find the force required to accelerate a ball with a mass of 140 grams at an acceleration of [tex]\(25 \, \text{m/s}^2\)[/tex], follow these steps:
1. Convert the mass: The mass of the ball is given in grams, but we need it in kilograms to use the formula correctly. Since there are 1000 grams in a kilogram, convert the mass as follows:
[tex]\[
\text{mass\_kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the acceleration: The problem states the acceleration is [tex]\(25 \, \text{m/s}^2\)[/tex].
3. Use the formula for force: The formula to find the force is:
[tex]\[
F = ma
\][/tex]
where [tex]\(F\)[/tex] is the force, [tex]\(m\)[/tex] is the mass in kilograms, and [tex]\(a\)[/tex] is the acceleration in meters per second squared.
4. Calculate the force: Substitute the values you have into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex].
1. Convert the mass: The mass of the ball is given in grams, but we need it in kilograms to use the formula correctly. Since there are 1000 grams in a kilogram, convert the mass as follows:
[tex]\[
\text{mass\_kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the acceleration: The problem states the acceleration is [tex]\(25 \, \text{m/s}^2\)[/tex].
3. Use the formula for force: The formula to find the force is:
[tex]\[
F = ma
\][/tex]
where [tex]\(F\)[/tex] is the force, [tex]\(m\)[/tex] is the mass in kilograms, and [tex]\(a\)[/tex] is the acceleration in meters per second squared.
4. Calculate the force: Substitute the values you have into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex].
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