Answer :
To calculate the force needed to accelerate a ball with a mass of 140 grams at an acceleration of 25 [tex]\(m/s^2\)[/tex], we 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.
Here's a step-by-step solution:
1. Convert Mass to Kilograms:
The mass of the ball is given in grams, but we need to use kilograms in our calculations because the standard unit of mass in the formula is kilograms (kg).
[tex]\[ 1 \text{ kg} = 1000 \text{ grams} \][/tex]
So, convert 140 grams to kilograms:
[tex]\[ 140 \text{ grams} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \][/tex]
2. Apply the Formula:
Now that we have the mass ([tex]\(m\)[/tex]) in kilograms, we can multiply it by the acceleration ([tex]\(a\)[/tex]) to find the force:
[tex]\[ F = m \times a \][/tex]
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 \][/tex]
3. Calculate the Force:
[tex]\[ F = 3.5 \text{ N} \][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \text{ N} \)[/tex].
Among the given options, the correct answer is:
[tex]\[ 3.5 \text{ N} \][/tex]
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Here's a step-by-step solution:
1. Convert Mass to Kilograms:
The mass of the ball is given in grams, but we need to use kilograms in our calculations because the standard unit of mass in the formula is kilograms (kg).
[tex]\[ 1 \text{ kg} = 1000 \text{ grams} \][/tex]
So, convert 140 grams to kilograms:
[tex]\[ 140 \text{ grams} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \][/tex]
2. Apply the Formula:
Now that we have the mass ([tex]\(m\)[/tex]) in kilograms, we can multiply it by the acceleration ([tex]\(a\)[/tex]) to find the force:
[tex]\[ F = m \times a \][/tex]
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 \][/tex]
3. Calculate the Force:
[tex]\[ F = 3.5 \text{ N} \][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \text{ N} \)[/tex].
Among the given options, the correct answer is:
[tex]\[ 3.5 \text{ N} \][/tex]
