Can two bodies, whose velocity moduli differ by a factor of three, have the same kinetic energy?
Can two bodies, whose velocity moduli differ by a factor of three, have the same kinetic energy? If so, under what conditions?
(m1 * v1 ^ 2) / 2 – kinetic energy of the first body
(m2 * v2 ^ 2) / 2 – kinetic energy of the second body
since the kinetic energies of the bodies are equal, we make up the equality:
(m1 * v1 ^ 2) / 2 = (m2 * v2 ^ 2) / 2
m1 * v1 ^ 2 = m2 * v2 ^ 2
knowing that the speed of one body is three times greater than that of another, i.e. v1 = 3 * v2, we get:
m1 * v1 ^ 2 = m2 * (3 * v1) ^ 2
m1 * v1 ^ 2 = 9 * m2 * v1 ^ 2
m1 = 9 * m2 * v1 ^ 2 / v1 ^ 2
m1 = 9 * m2
The kinetic energies of bodies, one of which moves three times faster, will be equal if:
A slower body will have a mass 9 times that of a faster body.
Answer: They can, provided that the slow body has a mass 9 times greater than the fast body.