Particle leaving a surface

A particle on a surface (horizontal, inclined, or curved) attached to an elastic string leaves the surface when normal reaction becomes zero, requiring energy and force analysis.

2 questions · Standard +0.6

Sort by: Default | Easiest first | Hardest first
CAIE M2 2015 November Q5
8 marks Standard +0.8
A particle \(P\) of mass \(0.2\text{ kg}\) is attached to one end of a light elastic string of natural length \(0.75\text{ m}\) and modulus of elasticity \(21\text{ N}\). The other end of the string is attached to a fixed point \(A\) which is \(0.8\text{ m}\) vertically above a smooth horizontal surface. \(P\) rests in equilibrium on the surface.
  1. Find the magnitude of the force exerted on \(P\) by the surface. [2]
\(P\) is now projected horizontally along the surface with speed \(3\text{ m s}^{-1}\).
  1. Calculate the extension of the string at the instant when \(P\) leaves the surface. [3]
  2. Hence find the speed of \(P\) at the instant when it leaves the surface. [3]
CAIE M2 2015 November Q5
8 marks Standard +0.3
A particle \(P\) of mass \(0.2\,\text{kg}\) is attached to one end of a light elastic string of natural length \(0.75\,\text{m}\) and modulus of elasticity \(21\,\text{N}\). The other end of the string is attached to a fixed point \(A\) which is \(0.8\,\text{m}\) vertically above a smooth horizontal surface. \(P\) rests in equilibrium on the surface.
  1. Find the magnitude of the force exerted on \(P\) by the surface. [2]
\(P\) is now projected horizontally along the surface with speed \(3\,\text{m s}^{-1}\).
  1. Calculate the extension of the string at the instant when \(P\) leaves the surface. [3]
  2. Hence find the speed of \(P\) at the instant when it leaves the surface. [3]