HSC Physics Atwood's Machine

/

Atwood’s machine, the name given to two blocks connected by a light inelastic string passing over a smooth pulley, is used in many mechanics experiments.

  1. A single Atwood's machine is suspended from the roof of an elevator. Masses of of m1 and m2 are connected by a light inelastic string that passes over the smooth pulley. Find the acceleration of the elevator if m1 and m2 are at rest relative to the elevator.
  2. A double Atwood’s machine consists of a fixed pulley with a string connected to a mass m1 passing over it, with another Atwood’s machine connected to the other end of the string passing over the first pulley. On the second Atwood’s machine there are masses of m2 and m3 connected by a light inelastic string. We neglect the mass of each pulley.Show that the acceleration of the second pulley is given by a = g(4 m2 m3 - m1(m2+ m3))/(4 m2 m3 + m1(m2 + m3))

HSC Physics Elastic Collision

/

A sheet of harder mechanics questions appears below.

An elastic collision occurs between an alpha partice of mass m moving at a speed u and a stationary nucleus of mass M. After collision the alpha particle moves at speed v at an angle 𝜃 to its initial direction and the nucleus moves at speed V at an angle ϕ to the initial direction of the alpha particle.

  1. Show that v = u sinϕ/sin(ϕ + 𝜃).
  2. Show that V = m u sin𝜃/( M sin(ϕ + 𝜃)).
  3. Show that m/M = sin(2ϕ + 𝜃)/sin𝜃.