A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with a speed v each in mutually perpendicular directions. The total energy released in the process of explosion is.....?

3. Consider the following two types of completely inelastic collisions between Турe A two identical masses, m. Type A: a m m particle of mass m and velocity v strikes V a stationary target consisting of an identical particle of mass m. Type B: Туре В each particle has a mass m and a speed m m v/(22) – in this case they collide head v/2/2 V/22 on. Ignore gravity, and express your answers in terms of m and v. A. What is the speed of the center of mass for type A, and for type B collisions (before the collision occurs)? What the center of mass speed after the collision for each type of collision. Justify your answers. В. ( What is the change in the total kinetic energy for type A and type B ?

The carbon isotope 14C is used for carbon dating of objects.  A  14C nucleus can change into a different kind of element, a neighbor on the periodic table with lower mass, by emitting a beta particle – an electron or positron – plus a neutrino or an anti-neutrino.  Consider the scenario where 14C ( mass of 2.34 x 10 -26) decays by emitting an electron and anti neutrino.  The electron has a mass of 9.11x 10-31 kg and a speed of 5.5 x107  m/s.  While the anti neutrino has  a momentum of 8.5x10-24 kg-m/s.  If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.

As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed  (0.516)v  after passing through the target. The collision is inelastic and during the collision, the amount of kinetic energy lost by the bullet and paper is equal to [(0.333)Kb BC] , that is, 0.333 of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V =____v M = ___m