Minimum possible kinetic energy in an interaction

AI Thread Summary
The discussion focuses on calculating the minimum possible kinetic energy after a collision between two objects with different masses and velocities. The initial momentum of the system is calculated using the formula M1V1o + M2V2o, leading to a combined velocity of 10.89 m/s. The kinetic energy is then computed using the formula KE = 0.5(m)(v^2), resulting in an initial calculation of 1067 J. However, the correct minimum kinetic energy after a completely inelastic collision is identified as 534 J, highlighting the importance of considering momentum as a vector. The user acknowledges a prior misunderstanding regarding the initial conditions of the second object.
Neutrinogun
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Homework Statement


Object A of mass 10 kg moving at 10 m/s [E] interacts with (but does not touch) Object B of mass 8 kg moving at 12 m/s [N]. What is the minimum possible kinetic energy of the system after the collision?


Homework Equations


M1V1o + M2V2o = M1V1f + M2V2f
KE = (.5)(m)(v2)
Kinetic energy is minimized in a completely inelastic collision.


The Attempt at a Solution



10(10) + 8(12) = (10 + 8)v
v = 10.89 m/s
KE = (.5)(10)(10.89)2 + (.5)(8)(10.89)2
KE = 1067 J
Correct answer: 534 J (which is one-half of the answer I got.)

Help please?
Thanks.
 
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Realize that momentum is a vector and must be added as such. (One momentum points east and the other points north. Find their correct vector sum.)
 
Oh...Thanks! Previous problems like this had the second object initially at rest, so I used that way without thinking.
 
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