Particle 1 with mass m1 encouters elastic collision with particle 2 which has ma
ID: 2061262 • Letter: P
Question
Particle 1 with mass m1 encouters elastic collision with particle 2 which has mass m2 Assume that particle 2 is stationary before collision And movement-direction of particle 1 after collision, is perpendicular to the movement-direction before collision. Let T1 symbolize kinetic-energy of particle 1 before collision And p'1 momentum of particle 1 after collision. Show that the angle between the movement-direction of particle 2 after collision and movement-direction of particle 1 before collision is theta where Show that after collision, length of the momentum-vector of the particle2 isExplanation / Answer
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms. During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute). The conservation of the total momentum demands that the total momentum before the collision is the same as the total momentum after the collision, and is expressed by the equation m1u1 + m2u2 = m1v1 + m2v2 Likewise, the conservation of the total kinetic energy is expressed by the equation m1u1^2/2 + m2u2^2/2 = m1v1^2/2 + m2v2^2/2 These equations may be solved directly to find vi when ui are known or vice versa. However, the algebra can get messy. A cleaner solution is to first change the frame of reference such that one of the known velocities is zero. The unknown velocities in the new frame of reference can then be determined and followed by a conversion back to the original frame of reference to reach the same result. Once one of the unknown velocities is determined, the other can be found by symmetry. Solving these simultaneous equations for vi we get: v1 = u1 * (m1 - m2) + 2m2u2/m1 + m2 and v2 = u2 * (m2 - m1) + 2m1u1/m1 + m2