Answer :
To solve this problem, we need to find the force required to accelerate a ball with a mass of 140 grams at an acceleration of 25 meters per second squared. We can use the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-step Solution:
1. Convert Mass to Kilograms:
Since the mass is given in grams, we need to convert it to kilograms because the standard unit of mass in physics is kilograms.
[tex]\[
140 \text{ g} = 140 \div 1000 = 0.14 \text{ kg}
\][/tex]
2. Apply the Formula:
Now, use the formula [tex]\( F = ma \)[/tex] where:
- [tex]\( m = 0.14 \)[/tex] kg (the mass in kilograms)
- [tex]\( a = 25 \)[/tex] m/s² (the given acceleration)
Plug the values into the formula:
[tex]\[
F = 0.14 \times 25
\][/tex]
3. Calculate the Force:
Perform the multiplication to find the force:
[tex]\[
F = 3.5 \text{ N}
\][/tex]
Thus, the force needed to accelerate the ball at [tex]\( 25 \text{ m/s}^2 \)[/tex] is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-step Solution:
1. Convert Mass to Kilograms:
Since the mass is given in grams, we need to convert it to kilograms because the standard unit of mass in physics is kilograms.
[tex]\[
140 \text{ g} = 140 \div 1000 = 0.14 \text{ kg}
\][/tex]
2. Apply the Formula:
Now, use the formula [tex]\( F = ma \)[/tex] where:
- [tex]\( m = 0.14 \)[/tex] kg (the mass in kilograms)
- [tex]\( a = 25 \)[/tex] m/s² (the given acceleration)
Plug the values into the formula:
[tex]\[
F = 0.14 \times 25
\][/tex]
3. Calculate the Force:
Perform the multiplication to find the force:
[tex]\[
F = 3.5 \text{ N}
\][/tex]
Thus, the force needed to accelerate the ball at [tex]\( 25 \text{ m/s}^2 \)[/tex] is 3.5 N.
