Answer:
The total kinetic energy must be greater than the momentum of either ball
Step-by-step explanation:
In order to solve this problem, we must clarify the following conditions, the balls are in motion that is, there is kinetic energy, the kinetic energy is a scalar magnitude, therefore this energy is greater than zero.
But however momentum is equal to zero, momentum is a vector quantity, that is, these velocities have a direction, momentum is defined as the product of mass by Velocity.
P = m*v (momentum lineal)
where:
P = lineal momentum [kg*m/s]
m = mass [kg]
v = velocity [m/s]
Since the masses of the balls are equal, we have:
m1 = m2
therefore:
m1*v1 + (m2*v2) = 0 (total momentum)
For the sum to be equal to zero, besides the equivalation of the masses, the velocities must also be equal, but the velocities must be of opposite sign, to meet equality to zero.
m1*v1 - m2*v2 = 0
And the kinetic energy of a body is defined by means of the following equation
Ek = 0.5*m*v²
Since the magnitude of the velocities is greater than zero, so that there is movement, we can say that the kinetic energy is much greater than zero, as well as greater than the total linear momentum