Answer:
Step-by-step explanation:
The 25.0 kg mass has momentum before the collision of
p = 25.0(3.0) = 75 kg•m/s
If all this momentum gets transferred into a 5.0 kg mass, the velocity of the 25.0 kg mass will be zero and the velocity of the 5.0 kg mass will be
75 / 5.0 = 15.0 m/s
Getting this to occur will require an addition of a significant amount of energy via an internal explosion or release of spring potential energy. This can be shown by looking at kinetic energies.
Initial system kinetic energy is ½(25.0)3.0² = 112.5 Joules
After the collision, system kinetic energy is ½(5.0)25² = 1,562.5 Joules
so 1562.5 - 112.5 = 1450 Joules of energy must be released during the collision to complete this scenario.
The most efficient energy transfer without energy release is an ideal elastic collision. Had these two masses been in such a collision with the given initial conditions, the 5 kg mass would have moved away at 5.0 m/s taking with it 5(5) = 25 kg•m/s of momentum leaving the 25 kg mass with 75 - 25 = 50 kg•m/s of momentum and a velocity of 50/25 = 2.0 m/s. Both masses are now traveling in the same direction as the original velocity, but at different speeds. Notice kinetic energy is conserved in elastic collisions
½(25)2² + ½(5.0)5² = 112.5 Joules.
The only time one mass can transfer its entire momentum to another mass without additional energy addition or subtraction is when the two colliding masses are identical in magnitude. Think pool balls colliding on a table.