To determine which ball accelerates faster given that both Hafiz and Saturn apply the same amount of force to their respective balls, we can use Newton's second law of motion. Newton's second law states that the acceleration (a) of an object is directly proportional to the force (F) applied to it and inversely proportional to its mass (m). The mathematical representation of this law is:
[tex]\[ a = \frac{F}{m} \][/tex]
1. Identify the Masses:
- The mass of Hafiz's ball is 15 kg.
- The mass of Saturn's ball is 0.5 kg.
2. Identify the Applied Force:
- Both Hafiz and Saturn apply the same amount of force to their balls. Let's assume this force is [tex]\( F = 10 \)[/tex] Newtons (N).
3. Calculate the Acceleration for Hafiz's Ball:
- For Hafiz's ball:
[tex]\[ a_{Hafiz} = \frac{F}{m_{Hafiz}} \][/tex]
[tex]\[ a_{Hafiz} = \frac{10 \, \text{N}}{15 \, \text{kg}} \][/tex]
[tex]\[ a_{Hafiz} = 0.6667 \, \text{m/s}^2 \][/tex]
4. Calculate the Acceleration for Saturn's Ball:
- For Saturn's ball:
[tex]\[ a_{Saturn} = \frac{F}{m_{Saturn}} \][/tex]
[tex]\[ a_{Saturn} = \frac{10 \, \text{N}}{0.5 \, \text{kg}} \][/tex]
[tex]\[ a_{Saturn} = 20 \, \text{m/s}^2 \][/tex]
5. Comparison and Conclusion:
- The acceleration of Hafiz's ball is [tex]\( 0.6667 \, \text{m/s}^2 \)[/tex].
- The acceleration of Saturn's ball is [tex]\( 20 \, \text{m/s}^2 \)[/tex].
Since [tex]\( 20 \, \text{m/s}^2 \)[/tex] is significantly greater than [tex]\( 0.6667 \, \text{m/s}^2 \)[/tex], we can conclude that Saturn's ball accelerates faster than Hafiz's ball when the same amount of force is applied to both.
Justification:
Saturn's ball accelerates faster because it has a smaller mass compared to Hafiz's ball. According to Newton's second law, for a given force, the acceleration is inversely proportional to the mass. This means that a smaller mass will result in a greater acceleration when the same force is applied.
