Answer :
To determine the force needed to accelerate the ball, we can use the formula for force:
[tex]\[ F = m \times a \][/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 the mass from grams to kilograms:
The mass of the ball is given as 140 grams. To use the standard units in physics, we need to convert this to kilograms.
[tex]\[ 1 \, \text{gram} = 0.001 \, \text{kilograms} \][/tex]
So,
[tex]\[ 140 \, \text{g} = 140 \times 0.001 \, \text{kg} = 0.14 \, \text{kg} \][/tex]
2. Use the formula [tex]\( F = m \times a \)[/tex]:
Now that we have the mass in kilograms, we can plug it into the formula along with the given acceleration.
Given:
- Mass ([tex]\( m \)[/tex]) = 0.14 kg
- Acceleration ([tex]\( a \)[/tex]) = 25 m/s²
Calculate the force:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
[tex]\[ F = m \times a \][/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 the mass from grams to kilograms:
The mass of the ball is given as 140 grams. To use the standard units in physics, we need to convert this to kilograms.
[tex]\[ 1 \, \text{gram} = 0.001 \, \text{kilograms} \][/tex]
So,
[tex]\[ 140 \, \text{g} = 140 \times 0.001 \, \text{kg} = 0.14 \, \text{kg} \][/tex]
2. Use the formula [tex]\( F = m \times a \)[/tex]:
Now that we have the mass in kilograms, we can plug it into the formula along with the given acceleration.
Given:
- Mass ([tex]\( m \)[/tex]) = 0.14 kg
- Acceleration ([tex]\( a \)[/tex]) = 25 m/s²
Calculate the force:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
