Answer :
To find the force needed to accelerate a ball with a mass of 140 grams at 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.
Step 1: Convert the mass from grams to kilograms.
The mass of the ball is given as 140 grams. To work with the formula, we need to convert this mass to kilograms since the standard unit of mass in physics is kilograms.
[tex]\[ 1 \text{ kg} = 1000 \text{ g} \][/tex]
So, to convert grams to kilograms, we divide by 1000:
[tex]\[ 140 \text{ g} = \frac{140}{1000} = 0.14 \text{ kg} \][/tex]
Step 2: Use the formula to calculate the force.
Now, we can plug the mass in kilograms and the given acceleration into the formula:
[tex]\[ F = ma = 0.14 \text{ kg} \times 25 \text{ m/s}^2 \][/tex]
[tex]\[ F = 3.5 \text{ N} \][/tex]
Therefore, the force needed to accelerate the ball at 25 m/s² is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Step 1: Convert the mass from grams to kilograms.
The mass of the ball is given as 140 grams. To work with the formula, we need to convert this mass to kilograms since the standard unit of mass in physics is kilograms.
[tex]\[ 1 \text{ kg} = 1000 \text{ g} \][/tex]
So, to convert grams to kilograms, we divide by 1000:
[tex]\[ 140 \text{ g} = \frac{140}{1000} = 0.14 \text{ kg} \][/tex]
Step 2: Use the formula to calculate the force.
Now, we can plug the mass in kilograms and the given acceleration into the formula:
[tex]\[ F = ma = 0.14 \text{ kg} \times 25 \text{ m/s}^2 \][/tex]
[tex]\[ F = 3.5 \text{ N} \][/tex]
Therefore, the force needed to accelerate the ball at 25 m/s² is 3.5 N.
