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Kinetic Energy From Momentum Formula:
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Kinetic energy calculated from momentum provides an alternative way to determine the energy of a moving object using its momentum and mass rather than velocity. This relationship is derived from the fundamental definitions of kinetic energy and momentum in classical mechanics.
The calculator uses the kinetic energy from momentum formula:
Where:
Explanation: This formula is derived by substituting velocity from the momentum equation \( p = mv \) into the standard kinetic energy formula \( KE = \frac{1}{2}mv^2 \).
Details: Calculating kinetic energy from momentum is particularly useful in collision problems, conservation of energy analyses, and situations where momentum is known but velocity is not directly measured.
Tips: Enter momentum in kg·m/s and mass in kg. Both values must be positive numbers. The calculator will compute the kinetic energy in joules.
Q1: Why calculate kinetic energy from momentum instead of velocity?
A: This approach is useful when momentum is known or conserved (as in collisions) but velocity measurements are unavailable or impractical.
Q2: What are typical units for momentum and kinetic energy?
A: Momentum is measured in kg·m/s, while kinetic energy is measured in joules (1 J = 1 kg·m²/s²).
Q3: Can this formula be used for relativistic speeds?
A: No, this formula is for classical mechanics only. For relativistic speeds, the relativistic kinetic energy formula must be used.
Q4: How is this related to conservation laws?
A: In elastic collisions, both momentum and kinetic energy are conserved, making this relationship particularly important.
Q5: What if I only have velocity instead of momentum?
A: You can calculate momentum first using \( p = mv \), then use this formula, or directly use \( KE = \frac{1}{2}mv^2 \).