Answer :
To find the force needed to accelerate the ball, we can use the formula [tex]\( F = ma \)[/tex], where:
- [tex]\( F \)[/tex] is the force in newtons (N),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s²).
Here’s how to solve the problem step-by-step:
1. Convert the Mass from Grams to Kilograms:
- The mass of the ball is given as 140 grams.
- Since there are 1000 grams in a kilogram, convert the mass to kilograms:
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the Given Acceleration:
- The problem states that the acceleration [tex]\( a \)[/tex] is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
3. Use the Formula to Calculate the Force:
- Apply the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
- [tex]\( F \)[/tex] is the force in newtons (N),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s²).
Here’s how to solve the problem step-by-step:
1. Convert the Mass from Grams to Kilograms:
- The mass of the ball is given as 140 grams.
- Since there are 1000 grams in a kilogram, convert the mass to kilograms:
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the Given Acceleration:
- The problem states that the acceleration [tex]\( a \)[/tex] is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
3. Use the Formula to Calculate the Force:
- Apply the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
