Multiple Choice
Which formula correctly represents the calculation of mechanical energy in a system?
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9. Work & Energy
Intro to Energy & Kinetic Energy
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A particle with mass m and velocity v has kinetic energy K. What is the kinetic energy of a particle with mass m/2 and velocity 2v?
A
K/4
B
K/2
C
K
D
4K
E
2K
Verified step by step guidance1
Start by recalling the formula for kinetic energy: \( K = \frac{1}{2}mv^2 \). This formula tells us that kinetic energy depends on both the mass and the square of the velocity of the particle.
For the original particle with mass \( m \) and velocity \( v \), the kinetic energy is given as \( K = \frac{1}{2}mv^2 \).
Now, consider the new particle with mass \( \frac{m}{2} \) and velocity \( 2v \). Substitute these values into the kinetic energy formula: \( K' = \frac{1}{2} \left(\frac{m}{2}\right)(2v)^2 \).
Simplify the expression for the new kinetic energy: \( K' = \frac{1}{2} \times \frac{m}{2} \times 4v^2 = \frac{1}{2} \times 2m \times v^2 = mv^2 \).
Compare the new kinetic energy \( K' = mv^2 \) with the original kinetic energy \( K = \frac{1}{2}mv^2 \). Notice that \( K' = 2K \), which means the new kinetic energy is twice the original kinetic energy.
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