Answer :
To find the force needed to give a 0.25 kg arrow an acceleration of [tex]\( 196 \, \text{m/s}^2 \)[/tex], we can use Newton's second law of motion. Newton's second law states that force is equal to mass multiplied by acceleration, which is expressed as the formula:
[tex]\[ F = m \times a \][/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:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 0.25 kg
- Acceleration ([tex]\( a \)[/tex]) = [tex]\( 196 \, \text{m/s}^2 \)[/tex]
2. Plug the values into the formula:
[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]
3. Calculate the force:
[tex]\[ F = 49 \, \text{N} \][/tex]
Therefore, the force needed to give the arrow the specified acceleration is [tex]\( 49 \, \text{N} \)[/tex].
[tex]\[ F = m \times a \][/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:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 0.25 kg
- Acceleration ([tex]\( a \)[/tex]) = [tex]\( 196 \, \text{m/s}^2 \)[/tex]
2. Plug the values into the formula:
[tex]\[ F = 0.25 \, \text{kg} \times 196 \, \text{m/s}^2 \][/tex]
3. Calculate the force:
[tex]\[ F = 49 \, \text{N} \][/tex]
Therefore, the force needed to give the arrow the specified acceleration is [tex]\( 49 \, \text{N} \)[/tex].
