A 10 kg ball moving due west at 2m/sec collided with a 4kg ball that is moving due east at 3m/sec. you determine that immediately after the collision the 10 kg ball is moving due west at .57 m/sec.
a) this probably is a totally elastic collision
b) this definitely is NOT a totally inelastic collision
c) more info is needed
we are to show all of our work.
To determine if the collision is elastic, inelastic, or if more information is needed, we can analyze the conservation of momentum and kinetic energy before and after the collision.
Let's first calculate the initial momentum and kinetic energy of both balls:
Initial momentum of the 10 kg ball moving due west:
P1 = m1 * v1 = 10 kg * (-2 m/s) = -20 kg*m/s
Initial momentum of the 4 kg ball moving due east:
P2 = m2 * v2 = 4 kg * (3 m/s) = 12 kg*m/s
Total initial momentum of the system:
P_total_initial = P1 + P2 = -20 kg*m/s + 12 kg*m/s = -8 kg*m/s
Initial kinetic energy of the 10 kg ball:
KE1 = (1/2) * m1 * v1^2 = (1/2) * 10 kg * (2 m/s)^2 = 20 J
Initial kinetic energy of the 4 kg ball:
KE2 = (1/2) * m2 * v2^2 = (1/2) * 4 kg * (3 m/s)^2 = 18 J
Total initial kinetic energy of the system:
KE_total_initial = KE1 + KE2 = 20 J + 18 J = 38 J
Now, let's calculate the final momentum and kinetic energy of the 10 kg ball:
Final momentum of the 10 kg ball moving due west:
P1_final = m1 * v1_final = 10 kg * (-0.57 m/s) = -5.7 kg*m/s
Final kinetic energy of the 10 kg ball:
KE1_final = (1/2) * m1 * v1_final^2 = (1/2) * 10 kg * (-0.57 m/s)^2 = 1.6285 J
Now, let's analyze the situation based on the conservation of momentum and kinetic energy:
Conservation of momentum:
P_total_initial = P_total_final
-8 kg*m/s = -5.7 kg*m/s + P2_final
To determine P2_final, we need to find the final velocity of the 4 kg ball. Therefore, more information is needed to calculate P_total_final and determine whether it is conserved.
Conservation of kinetic energy:
KE_total_initial = KE_total_final
38 J = 1.6285 J + KE2_final
Again, we cannot determine KE_total_final or whether kinetic energy is conserved without the final velocity of the 4 kg ball.
Therefore, based on the given information, more information is needed to determine whether the collision is totally elastic, totally inelastic, or something else.