Question

wo particles move perpendicular to each other unM they collide Particle 1 has mass m and momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p Suppose that after the collision, the particles trade' thee momenta, as shown in the figure That is. partido 1 now has magnitude of momentum p. and particle 2 has magnitude of momontum 2p. furthermore, each particle is now moving m the direction m which the other had been moving How much kinetic energy. h\M. is lost in the collision? Express your answer In terms of m and p. Consider an alternative situation: This time the particles collide completely inelastically. How much kinetic energy K_lost is lost in this case? Express your answer in terms of m and p.

Answer 1

In the collision where the particles trade momentum, 4mp^2 of kinetic energy is lost. In a completely inelastic collision, 6mp^2 of kinetic energy is lost.

Step-by-step explanation:

In the given scenario, the particles collide and trade momentum so that particle 1 has momentum of magnitude p and particle 2 has momentum of magnitude 2p. The question asks how much kinetic energy is lost in the collision. To find the kinetic energy lost, we need to compare the initial kinetic energy before the collision with the final kinetic energy after the collision.

Before the collision, the kinetic energy is given by 0.5 * m * (2p)^2 + 0.5 * 2m * p^2 = 6mp^2. After the collision, the kinetic energy is given by 0.5 * m * p^2 + 0.5 * 2m * (2p)^2 = 10mp^2. Therefore, the kinetic energy lost in the collision is 10mp^2 - 6mp^2 = 4mp^2.

In the case of a completely inelastic collision, the two particles stick together after the collision. In this case, all of the initial kinetic energy is lost. So, the kinetic energy lost is 6mp^2.

Answer 2

In the first scenario, the kinetic energy lost in the collision is mp^2(2 - m). In the second scenario, the kinetic energy lost in the completely inelastic collision is -1/2mp^2.

Step-by-step explanation:

In the given scenario, when the two particles collide and trade momentum, there is a loss of kinetic energy. To calculate the loss of kinetic energy, we need to compare the initial kinetic energy before the collision with the final kinetic energy after the collision.

For the first scenario where the particles trade momenta, the kinetic energy lost can be calculated as K_lost = K_initial - K_final = (1/2)m(2p)^2 - (1/2)m(p)^2 = 2mp^2 - m^2p^2 = mp^2(2 - m).

For the second scenario where the particles collide completely inelastically, the kinetic energy lost can be calculated as K_lost = K_initial - K_final = m(2p)^2 - (1/2)m(3p)^2 = 4mp^2 - 9/2mp^2 = (8mp^2 - 9mp^2)/2 = -1/2mp^2.