Question
Particle of mass m colides with a second particle of mass m. before the collision the first particle is moving?
in the x direction with a speed 2v and the second particle is at rest. after the collision, the second particle is moving in the direction 45 degrees below the x axis and with a speed square root 2v
a) find the velocity of the first particle after the collision
b)find the total kinetic energy of the 2 particles before and after the collision
c) is the collision elastic or inelastic justify with math
-show all work..step by step please
Explanation / Answer
Given data Mass of the two particles is m Initial velocity of the first particle is, v1i = 2v Final velocity of the second particle is, v2f = 2v [ cos45o (i) - sin 45o (j)] Magnitude of final velocity of second particle is, v2f = 2v [ (1/2 i - 1/2 j ] = 2v (a) From the law of conservation of momentum along x axis, we get mv1ix + m v2ix = m v1fx + m v2fx m (2v) + 0 = m v1fx + m 2v cos45o v1fx = 2v - 2 v (1/2) = v Along y axis, 0 = m v1fy + m v2fy 0 = mv1fy - m2v sin 45o v1fy = 2 v (1/2) = v The velocity of the particle is, v1f = v2 + v2 = 2 v ------------------------------------------------------------------------------------------ (b) Total kinetic energy of the particle before collision is, Ki = 1/2 m (v1i2 + v2i2 ) = 1/2 m (2 v)2 = 2mv2 Total kinetic energy after the collision is, Kf = 1/2 m (v1f2 + v2f2 ) = 1/2 m [(2 v)2 + (2v )2 = 2mv2 ------------------------------------------------------------------------------------------- (c) From part (b), we can conclude that the energy is conserved. So, it is an elastic collision. Total kinetic energy after the collision is, Kf = 1/2 m (v1f2 + v2f2 ) = 1/2 m [(2 v)2 + (2v )2 = 2mv2 ------------------------------------------------------------------------------------------- (c) From part (b), we can conclude that the energy is conserved. So, it is an elastic collision. ------------------------------------------------------------------------------------------- (c) From part (b), we can conclude that the energy is conserved. So, it is an elastic collision.