To understand how the mass and speed of an object affect its kinetic energy, we need to analyze the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]
Here, [tex]\( m \)[/tex] is the mass of the object, and [tex]\( v \)[/tex] is its speed. Let's examine how changes in mass and speed impact the kinetic energy separately.
### Effect of Mass on Kinetic Energy
If we double the mass [tex]\( m \)[/tex] while keeping the speed [tex]\( v \)[/tex] constant:
1. Initial kinetic energy with mass [tex]\( m \)[/tex]:
[tex]\[ KE_{initial} = \frac{1}{2} mv^2 \][/tex]
2. Kinetic energy with doubled mass [tex]\( 2m \)[/tex]:
[tex]\[ KE_{doubled \ mass} = \frac{1}{2} (2m)v^2 = mv^2 \][/tex]
By doubling the mass, the kinetic energy doubles.
### Effect of Speed on Kinetic Energy
If we double the speed [tex]\( v \)[/tex] while keeping the mass [tex]\( m \)[/tex] constant:
1. Initial kinetic energy with speed [tex]\( v \)[/tex]:
[tex]\[ KE_{initial} = \frac{1}{2} mv^2 \][/tex]
2. Kinetic energy with doubled speed [tex]\( 2v \)[/tex]:
[tex]\[ KE_{doubled \ speed} = \frac{1}{2} m (2v)^2 = \frac{1}{2} m (4v^2) = 2mv^2 \][/tex]
By doubling the speed, the kinetic energy quadruples.
### Conclusion
From the above observations:
- Doubling the mass results in the kinetic energy doubling.
- Doubling the speed results in the kinetic energy quadrupling.
Therefore, speed has a greater effect on kinetic energy than mass. Specifically, doubling the speed results in four times the kinetic energy, whereas doubling the mass only results in twice the kinetic energy.
Thus, the correct answer is:
[tex]\[ \boxed{C. \text{Speed has a greater effect than mass on kinetic energy.}} \][/tex]
