6. Consider the following head-on elastic collision. Particle 1 has a mass of 2m

Question

6. Consider the following head-on elastic collision. Particle 1 has a mass of 2mo and particle 2 has a mass of mo. Before the collision, particle 1 moves toward particle 2, which is initially at rest, with a speed u (=0.6c). After the collision each particle moves in the forward direction with speeds of u1 and u2 for particles 1 and 2, respectively. (a) Find u1 and u2 in terms of mo and c. (b) Calculate the initial and final kinetic energies and show that kinetic energy is indeed conserved in this elastic collision.

Explanation / Answer

b.. You should know the intial velocities of the 2 masses (well B has zero velocity) hence you can apply the equation KE = 1/2mv^2 to find out the kinetic energy before impact where v is the initial velocity: Total KE before impact = (KE of A) + (KE of B). Since B has zero velocity, it's KE value is zero, Now from B you should have found the final velocities after collision yes? Well again use KE = 1/2mv^2 to find the kinetic energy of each object where v is the final velocity: Total KE after impact = (KE of A) + (KE of B) Now to see if mechanical energy is conserved: Total KE before impact - total KE after impact = 0. If it does not equal zero, then it is not conserved (since it is inelastic collision it shouldn't!), and this 'loss' of energy is transferred to the surroundings as heat.

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