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INCLINED PLANES
1. The system below is in equilibrium.
   
     
    Frictional forces can be neglected.
a) Given that m2=0.2kg, calculate m1.
  b) Calculate the gravitational potential energy gained by m1 if m2 is pushed down 0.3m.
  c) If m1 is removed and replaced by an object of mass 2m1, calculate the acceleration of the system.
  d) Calculate the total kinetic energy of the system after 2s of acceleration (with the mass 2m1 in place and assuming that vo=0).
2.   A body rests, without slipping, on a plane which is inclined at 30 to the horizontal.
  a) Draw a diagram showing the forces acting on the body.
  b) If the body has a mass of 2kg, calculate the magnitude of the force of friction acting on it.
     
3.   An object of mass m=5kg is being pulled up an inclined plane which is at 40 to the horizontal.
    The object is pulled at a constant speed of 0.8ms-1 by a force which acts parallel to the inclined plane.
    The coefficient of friction between the object and the plane is 0.2
  a) Draw a diagram showing the forces acting on the object.
b) Calculate the magnitude of the force of friction acting on the object.
  c) Calculate the gain in gravitational potential energy when the object has moved 0.5m (measured parallel to the slope).
d) Calculate the total work done in pulling the block 0.5m (measured along the slope).
     
4.   A piece of metal is given an initial kinetic energy, K, near the bottom of a plane inclined at θ degrees to the horizontal.
    The coefficient of dynamic friction between the metal and the inclined plane is μ.
     
   
     
    The centre of gravity of the piece of metal moves through a vertical distance, h, before coming to rest.
    Using the principle of conservation of energy, show that the relation between h and K is
   
 
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