Final answer:
The total kinetic energy of the clay after a head-on inelastic collision, where a 1.0 kg ball of clay with a velocity of 3 m/s collides with a 1.5 kg ball with a velocity of 2 m/s in the opposite direction and they stick together, is 0 joules.
Step-by-step explanation:
The question is about calculating the total kinetic energy after a head-on inelastic collision between two balls of clay. In an inelastic collision where the objects stick together, momentum is conserved, but kinetic energy is not. To find the final kinetic energy, we first find the final velocity of the combined masses using conservation of momentum. The initial momentum of the system is given by the sum of the momenta of each ball:
m1v1 + m2v2 = (1.0 kg)(3 m/s) + (1.5 kg)(-2 m/s) = 3 kg·m/s - 3 kg·m/s = 0 kg·m/s.
Since the combined mass after the collision is 1.0 kg + 1.5 kg = 2.5 kg and the momentum is conserved at 0 kg·m/s, the final velocity (vf) of the combined mass is:
(2.5 kg)(vf) = 0 kg·m/s
vf = 0 m/s.
Because the final velocity is 0 m/s, the final kinetic energy (KEf) of the system will be:
KEf = (1/2)(m1 + m2)(vf)2 = (1/2)(2.5 kg)(0 m/s)2 = 0 J.
The total kinetic energy of the clay after the collision is 0 joules, as the balls come to rest when they stick together.