If two different masses have the same kinetic energy, their momenta are:
1. inversely proportional to their masses
2. inversely proportional to the square roots of their masses
3. proportional to the squares of their masses
4. proportional to their masses
5. proportional to the square roots of their masses
Would the correct answer be 4. proportional to their masses ?
Yes, the correct answer is 4. proportional to their masses.
To understand why, we need to recall the formula for kinetic energy and momentum, and how they are related to mass.
Kinetic energy (KE) is given by the equation KE = (1/2)mv^2, where m represents mass and v represents velocity.
Momentum (p) is given by the equation p = mv, where m represents mass and v represents velocity.
When two masses have the same kinetic energy:
KE1 = KE2
Therefore, (1/2)m1v1^2 = (1/2)m2v2^2
Since v1 and v2 are squared, we can ignore them for this comparison.
Therefore, we have m1 = m2, which means that the momenta of the two masses are proportional to their masses.
In other words, if two different masses have the same kinetic energy, their momenta are proportional to their masses.