Physics exam 1

• Fluids


  Any substance that can flow
• Fluids


  • Any gas or liquid
  • Solids made up of tiny particles that sometimes behave as fluids (e.g. flow of sand through an hourglass)
• Density


  mass / volume
• Density depends on temperature. As volume of a body usually increases when heated, density decreases.
• Upthrust is the force that a body feels when submerged in a fluid. It is caused by the fluid pressure.
• Upthrust on an object = weight of the fluid displaced by the object (Archimedes' principle).
• When fully submerged, mass of the fluid displaced = density of the fluid x Volume of the object
• If weight of object > upthrust, the object sinks


  If weight of object < upthrust, the object floats
• Hydrometer


  An instrument used to determine the density of a fluid. It sinks until its weight equals the upthrust, and the reading represents the density compared to water.
• Upthrust is equal to the weight of the fluid displaced, which can be proven by finding the pressure acting at the top and bottom of the object.
• Laminar flow


  Fluid flow where adjacent layers do not cross over one another, with no abrupt changes in speed or direction
• Turbulent flow


  Fluid flow with swirling vortices and eddies, due to abrupt changes in speed or direction
• In low speed or high viscosity fluids, flow tends to be laminar through a pipe, with a parabolic velocity distribution.
• Fluids with velocity that can be explained by the parabolic distribution are called Newtonian fluids.
• Laminar flow over the top of a car

  Turbulent flow at the back of the car
• In turbulent flow, the fluid velocity in any given place changes over time, becoming chaotic with swirling eddies.</b>
• Turbulent flow increases the drag on a vehicle, increasing fuel consumption.
• The air moving over an aerofoil is faster than the air underneath, creating a pressure difference that results in lift.
• Viscosity


  How resistant a fluid is to flowing. A viscous fluid is thick and sticky.
• Coefficient of viscosity


  A numerical value associated with a fluid to indicate how much it resists flow, measured in Pa·s or N·s/m².
• Viscous drag


  The frictional force exerted on objects moving in fluids.
• The rate of flow of a fluid is inversely proportional to its viscosity.
• Liquids have lower viscosity when temperature increases


  Gases have higher viscosity when temperature increases
• Terminal velocity is the velocity reached by a falling body when the forces acting on it (weight, viscous drag and upthrust) are balanced.
• Stokes' Law


  The formula for viscous drag on a sphere moving at low speeds through a fluid
• Deriving the equation for terminal velocity

  1. Equate weight, upthrust and viscous drag forces

  2. Solve for terminal velocity
• The equation for terminal velocity cannot be used unless it is first derived.
• Ball bearing with low density accelerating towards the surface


  • Free body force diagram
  • Force equation
• Ball bearing that has reached terminal velocity while rising

  • Free body force diagram
  • Force equation
• Ball bearing that has reached terminal velocity

  • Free body force diagram
  • Force equation
• Ball bearing that has reached the surface

  • Free body force diagram
  • Force equation
• Terminal velocity equation cannot be used if not derived first
• Viscous drag calculation becomes complex for large, irregularly shaped, fast moving objects as flow becomes turbulent
• Simple slow-moving sphere obeying Stoke's law is not actually common, so calculation of viscous drag is usually more complicated
• Larger objects generally reach a higher terminal velocity
• Tensile force


  An increase in length/stretch/pull causing a positive extension
• Compressive force


  A decrease in length/squash causing a negative extension
• Hooke's law


  The extension/compression of an elastic object is proportional to the force acting on it, up to the object's limit of proportionality
• A stiff spring with spring constant 10Nm^-1 will compress by 2m when a force of 20N is applied
• Elastic limit


  Point beyond which the spring will no longer return to its original shape when the force is removed