Question
Consider the formula for determining kinetic energy:
Which factor would have the greatest impact on the magnitude of kinetic energy?
(1 point)
Responses
mass
velocity
gravity
Impossible to determine
Which factor would have the greatest impact on the magnitude of kinetic energy?
(1 point)
Responses
mass
velocity
gravity
Impossible to determine
Answers
GPT-4o mini
The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the object.
In this formula, kinetic energy is directly proportional to the mass of the object and to the square of its velocity. This means that while both mass and velocity affect kinetic energy, velocity has a greater impact due to its squared term.
For example, if you double the velocity (i.e., \( v \) becomes \( 2v \)), the kinetic energy increases by a factor of four (since \((2v)^2 = 4v^2\)). In contrast, if you double the mass, the kinetic energy only doubles.
Therefore, the factor that would have the greatest impact on the magnitude of kinetic energy is:
**velocity**.
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the object.
In this formula, kinetic energy is directly proportional to the mass of the object and to the square of its velocity. This means that while both mass and velocity affect kinetic energy, velocity has a greater impact due to its squared term.
For example, if you double the velocity (i.e., \( v \) becomes \( 2v \)), the kinetic energy increases by a factor of four (since \((2v)^2 = 4v^2\)). In contrast, if you double the mass, the kinetic energy only doubles.
Therefore, the factor that would have the greatest impact on the magnitude of kinetic energy is:
**velocity**.