In an elastic collision of particles, one particle is stationary and another one is moving to the particle at speed u. After colliding, particle 1 and 2 moves at two different velocity, say v1 and v2. Why is the angle between v1 and v2 must be 90 degrees if the resulting particles and the initial particles all have the same mass?

The figure below shows a system of three identical particles A, B and C each with mass M. Particles B and C are fixed in place on the x – axis at the same distance D from the origin. Particle A is held in place on the y – axis at a distance v3D from the origin. If particle A is released and allowed to move freely, with what speed will it pass through the origin? В C D -D-

A 40-ton rail car and an 80-ton rail car, initially at rest, are connected together with a giant but massless compressed spring between them. When released, the 40-ton car is pushed away at a speed of 3.0 m/s relative to the 80-ton car. What is the speed of the 40-ton car relative to the ground?

A puck of mass m, moving at a speed of ₁ collides with an identical mass stationary puck. After the collision, one puck moves off at an angle ₁ with a speed of V₁, and the other puck moves off at an angle 9₂ with a speed of V₂'. a) What are the speeds ₁ and ₂ if ₁ + ₂ = 90°? Express your answers in terms of V₁ and ₁. b) Is the collision inelastic or (totally) elastic? Support your answer with a calculation.

Three asteroids coated with cosmic slime are moving in the same plane when they collide and stick together. Initially, asteroid A has a mass of 2*107 kg and is moving to the right at a speed of 150 m/s, asteroid B has a mass of 3*107 kg and is moving at 50 m/s towards the lower left at an angle of 60 degrees with respect to asteroid A, while asteroid C has a mass of 5*107 kg and is moving with an unknown speed and angle. After the collision, the resulting single asteroid is moving toward the right at a speed of 50 m/s. Determine the speed and angle of asteroid C prior to the collision.

The diagram shows four identical particles (labeled 1, 2, 3, and 4) that are moving in the x-y plane. The mass of each particle is 0.31 kg and they all move at the same speed of 33.3 m/s. Particle 1 is at (-4 m, 2 m) and is moving in the positive x direction. Particle 2 is at (4 m, 3 m) and traveling in the negative x direction. Particle 3 is at (0 m, -3 m) and moving in the positive y direction. Particle 4 is at (5 m, -3 m) and its velocity makes an angle of 45 degrees with the coordinate axes. a) What is the magnitude of the angular momentum of particle 1 about the origin? Express your answer in units of kg⋅m2/s.  b) What is the magnitude of the angular momentum of particle 3 about the origin? Express your answer in units of kg⋅m2/s.  c) What is the magnitude of the angular momentum of particle 4 about the origin? Express your answer in units of kg⋅m2/s.

A railroad car of mass M moving at a speed v_1 collides and couples with two coupled railroad cars, each of the same mass M and moving in the same direction at a speed v_2. (a) What is the speed v_f of the three coupled cars after the collision in terms of v_1 and v_2? (b) How much kinetic energy is lost in the collision? Answer in terms of M, v_1, andv_2 .

The carbon isotope 14C is used for carbon dating of archaeological artefacts. 14C decays to 14N by a process known as beta decay, in which the nucleus emits an electron (also known as a beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted in opposite directions to each other. The electron has a speed of 5 x 10 m/s and the neutrino has a momentum of 5 x 1024 kg m/s. n as What is the recoil speed of the resulting 14N nucleus? (Take the mass of the carbon-14 and nitrogen-14 nuclei to be 2.34 x 10 26 kg and the mass of the electron to be 9.11 x 1031 kg. If you were aware of such things and concerned, please ignore relativistic effects.)

The carbon isotope 14C is used for carbon dating of archaeological artefacts. 14C decays to 14N by a process known as beta decay, in which the nucleus emits an electron (also known as a beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted in opposite directions to each other. The electron has a speed of 4 x 107 m/s and the neutrino has a momentum of 8 × 10-24 kg m/s. What is the recoil speed (in m/s) of the resulting 14N nucleus? (Take the mass of the carbon-14 and nitrogen-14 nuclei to be 2.34 x 10-26 kg and the mass of the electron to be 9.11 x 1031 kg. If you were aware of such things and concerned, please ignore relativistic effects.)

The following question concerns a collision in outer space, far enough from any planets so that the external forces can be considered as negligible. An unmanned spacecraft, having mass 1,500,000 kg and speed 25,000 km/hr collides with a small meteor, having mass 3,000 kg and speed 2,100 km/hr, in the Kuiper belt. a. Prior to the collision, what are the total kinetic energy and total momentum? b. Assuming a head-on collision, in which the meteor becomes lodged into the spacecraft’s body and the two objects move off together, what are the total kinetic energy and momentum after the collision? c. If instead of getting lodged into the spacecraft, the meteor bounced off, would the change in the space craft’s momentum be larger or smaller, or is there not enough information to tell? Explain.