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Mechanics, EXT2 M1 2022 HSC 12c

A particle with mass 1 kg is moving along the -axis. Initially, the particle is at the origin and has speed m s-1 to the right. The particle experiences a resistive force of magnitude    newtons, where m s-1 is the speed of the particle after seconds. The particle is never at rest.

  1. Show that    (1 mark)

  2. Hence, or otherwise, find as a function of .  (2 marks)

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Mechanics, EXT2 M1 2021 HSC 14b

An object of mass 5 kg is on a slope that is inclined at an angle of 60° to the horizontal. The acceleration due to gravity is   and the velocity of the object down the slope is .

As well as the force due to gravity, the object is acted on by two forces, one of magnitude newtons and one of magnitude newtons, both acting up the slope.

  1. Show that the resultant force down the slope is    newtons.  (2 marks)

  2. There is one value of such that the object will slide down the slope at a constant speed.
  3. Find this value of in , correct to 1 decimal place, given that  .  (2 marks)

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Mechanics, EXT2 M1 2020 HSC 12a

A 50-kilogram box is initially at rest. The box is pulled along the ground with a force of 200 newtons at an angle of 30° to the horizontal. The box experiences a resistive force of    newtons, where is the normal force, as shown in the diagram.
 
Take the acceleration due to gravity to be 10m/s2.
 

  1. By resolving the forces vertically, show that  .   (2 marks)

  2. Show that the net force horizontally is approximately 53.2 newtons.  (2 marks)

  3. Find the velocity of the box after the first three seconds.  (2 marks)

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Mechanics, EXT2 M1 EQ-Bank 2

A particle with mass moves horizontally against a resistance force , equal to    where is the particle's velocity.

Initially, the particle is travelling in a positive direction from the origin at velocity .

  1. Show that the particle's displacement from the origin, , can be expressed as
     
           (2 marks)

     

  2. Show that the time, , when the particle is travelling at velocity , is given by
     
           (4 marks)

     

  3. Express as a function of , and hence find the limiting values of and .  (2 marks)

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Mechanics, EXT2 M1 2014 HSC 14c

A high speed train of mass starts from rest and moves along a straight track. At time hours, the distance travelled by the train from its starting point is km, and its velocity is km/h.

The train is driven by a constant force    in the forward direction. The resistive force in the opposite direction is  , where    is a positive constant. The terminal velocity of the train is 300 km/h.

  1. Show that the equation of motion for the train is
     
         .  (2 marks)

  2. Find, in terms of    and  , the time it takes the train to reach a velocity of 200 km/h.  (4 marks)

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