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Answer :
To find the force needed to accelerate a ball with a mass of 140 g at an acceleration of 25 m/s², we can use the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Let's break it down step by step:
1. Convert the mass to kilograms:
- The mass of the ball is given as 140 grams. To use the mass in the formula, we need to convert it into kilograms because the standard unit for mass in the formula is kilograms.
- Since 1 kilogram = 1000 grams, convert 140 grams to kilograms:
[tex]\[
m = \frac{140 \, \text{grams}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula [tex]\( F = ma \)[/tex]:
- Plug the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}²
\][/tex]
3. Calculate the force:
- Multiply the mass by the acceleration:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is 3.5 Newtons.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Let's break it down step by step:
1. Convert the mass to kilograms:
- The mass of the ball is given as 140 grams. To use the mass in the formula, we need to convert it into kilograms because the standard unit for mass in the formula is kilograms.
- Since 1 kilogram = 1000 grams, convert 140 grams to kilograms:
[tex]\[
m = \frac{140 \, \text{grams}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula [tex]\( F = ma \)[/tex]:
- Plug the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}²
\][/tex]
3. Calculate the force:
- Multiply the mass by the acceleration:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is 3.5 Newtons.
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