Investigate the factors which affect the terminal velocity of a falling object.

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AS Physics Coursework                Page  of

Hannan Shah

AS Physics Coursework

HANNAN SHAH

Aim

To investigate the factors which affect the terminal velocity of a falling object.

Background Knowledge

  • Velocity is defined as the rate of change of displacement of an object, with respect to time.  It is the vector quantity corresponding to speed.  Displacement is the distance moved by an object in a particular direction.
  • Velocity = Displacement

                            Time

  • An object falling freely under gravity freely under gravity has a constant acceleration, provided the gravitational field strength is constant.  Fluid resistance (liquid or gas, such as air) reduces acceleration.  When fluid resistance equals the object's weight the resultant force is zero as opposing forces are balanced.  When this is the case the velocity becomes and there is no acceleration.  This is the terminal velocity of the object.
  • Viscosity is an internal property of a fluid that offers resistance to flow.  An object falling through a viscous medium will reach a terminal velocity when the force of drag acting upwards upon the object equals the force of gravity.  
  • The terminal velocity of an object depends on the object's size, shape and weight.
  • According to Stoke's law, the terminal velocity of a sphere falling through a fluid can be found by the following formula:

4/3πr3g (ρ-σ) = 6πrηvt

OR

vt = 2r2 (ρ-σ) g                η = 2r2 (ρ-σ) g

      9η                                  9vt

        Where r is radius of the sphere (m), g is acceleration due to gravity (ms-2), η is         viscosity (Ns m-2), σ is fluid density (kg m-3), ρ is sphere density (kg m-3) and vt is         terminal velocity (ms-1).

Prediction

  • I predict that when a ball bearing is dropped in oil it will initially accelerate but this acceleration will reduce gradually until it reaches 0ms-2 and the ball moves with a constant velocity  (it's terminal velocity).
  • A ball bearing of a greater radius will fall with a greater velocity and will take longer to reach its terminal velocity.
  • A ball bearing of a smaller radius will fall with a smaller velocity and will take less time to reach its terminal velocity.
  • The terminal velocity of a ball bearing is inversely proportional to the viscosity of the fluid.

This is a predicted shape for the results graph showing the variation of velocity with respect to time.  This velocity-time graph shows the ball bearing initially accelerating from rest but the acceleration is gradually dropping until it reaches 0ms-2.  This is when the object reaches its terminal velocity.

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Hypothesis

  • When an object is released from rest the frictional force (F) is 0 and the resultant force is equal to the weight (W=mg) of the object.  When F is less than W the object's velocity increases i.e. there is acceleration.  When an object gains velocity a frictional force opposes the weight of the object and this force grows as velocity increases.  When F=W the resultant force is 0 and there is no acceleration.  The terminal velocity has been reached.
  • A ball bearing with a greater radius than another ball bearing should have a greater terminal velocity ...

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