an important step in science is supporting a theory or idea with data. the questions we ask help determine the type of data we collect. in the warm up, you reviewed the equation to calculate kinetic energy. what question could you ask about kinetic energy which will include the variables that affect it?
LectureNotes said an important step in science is supporting a theory or idea with data. the questions we ask help determine the type of data we collect. in the warm up, you reviewed the equation to calculate kinetic energy. what question could you ask about kinetic energy which will include the variables that affect it?
Answer:
Kinetic energy is a fundamental concept in physics, represented by the equation:
KE = \frac{1}{2}mv^2
Here, ( KE ) stands for kinetic energy, ( m ) is the mass of an object, and ( v ) is the velocity of the object. The kinetic energy of an object depends on both its mass and its velocity.
Given this equation, a pertinent question to ask about kinetic energy that encompasses the variables affecting it would be:
“How does the kinetic energy of an object change when its mass is varied while keeping velocity constant, and when its velocity is varied while keeping mass constant?”
To break it down further:
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Effect of Mass on Kinetic Energy (while keeping velocity constant):
- How does the kinetic energy of an object change if you double the mass while keeping the velocity constant?
- How does the kinetic energy of an object change if you halve the mass while keeping the velocity constant?
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Effect of Velocity on Kinetic Energy (while keeping mass constant):
- How does the kinetic energy of an object change if you double the velocity while keeping the mass constant?
- How does the kinetic energy of an object change if you halve the velocity while keeping the mass constant?
These questions could guide a scientific investigation to collect data. Here’s the concept in practice:
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Effect of Mass:
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Doubling the mass: If the mass of an object is doubled ( (m \rightarrow 2m) ) and the velocity ( v ) is kept constant, the kinetic energy equation becomes:
KE = \frac{1}{2} \cdot 2m \cdot v^2 = 2 \left(\frac{1}{2}mv^2\right) = 2 \cdot KE_{\text{initial}}So, kinetic energy doubles.
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Halving the mass: If the mass of an object is halved ( (m \rightarrow \frac{m}{2}) ) and the velocity ( v ) is kept constant, the kinetic energy equation is:
KE = \frac{1}{2} \cdot \frac{m}{2} \cdot v^2 = \frac{1}{2} \left(\frac{1}{2}mv^2\right) = \frac{KE_{\text{initial}}}{2}So, kinetic energy is halved.
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Effect of Velocity:
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Doubling the velocity: If the velocity of an object is doubled ( (v \rightarrow 2v) ) and the mass ( m ) is kept constant, the kinetic energy equation becomes:
KE = \frac{1}{2}m \cdot (2v)^2 = \frac{1}{2}m \cdot 4v^2 = 4 \left(\frac{1}{2}mv^2\right) = 4 \cdot KE_{\text{initial}}So, kinetic energy quadruples.
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Halving the velocity: If the velocity of an object is halved ( (v \rightarrow \frac{v}{2}) ) and the mass ( m ) is kept constant, the kinetic energy equation is:
KE = \frac{1}{2}m \cdot \left(\frac{v}{2}\right)^2 = \frac{1}{2}m \cdot \frac{v^2}{4} = \frac{1}{4} \left(\frac{1}{2}mv^2\right) = \frac{KE_{\text{initial}}}{4}So, kinetic energy is reduced to one-fourth.
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Final Answer:
The question to ask about kinetic energy that includes the variables that affect it is: “How does the kinetic energy of an object change when its mass is varied while keeping velocity constant, and when its velocity is varied while keeping mass constant?” This question allows you to explore the direct relationship between kinetic energy and the variables of mass and velocity.