Download Notes and Hints for AP Physics Summer Assignment

Notes and Hints for AP Physics Summer Assignment
(Note: This is not a complete guide… you will need to use other online
resources to find more information on some of these topics)
Fluids / Buoyancy
A FLUID is any material that can flow and that has no definite shape. Based on
this definition, both liquids AND gases are fluids. In terms of physics, liquids
and gases behave the same way except for one key point: GASES CAN BE
COMPRESSED, WHILE LIQUIDS CAN NOT (liquids have a definite volume). One
key property when dealing with fluids is DENSITY, which is the amount of mass
a substance has per unit of volume. Density is given by the equation:
ρ=m/V
density (in kg/m3) = mass (in kg) / volume (in m3)
Note that the first symbol is the Greek letter rho, which stands for density.
Remember that VOLUME is the amount of 3-dimensional space that an object or
a material takes up. The unit of volume will always be cubed because it is 3dimensional (the standard unit is m3).
Fluids exert BUOYANT FORCE on objects that are submerged in them. This
buoyant force points upward, and it is what causes objects to float. The
amount of buoyant force on an object is given by ARCHIMEDES’ PRINCIPLE:
*The amount of buoyant force on an object is equal to the weight of the fluid
displaced by the object.
The equation for this is:
FB = mfg
Buoyant Force (in N) = Mass of Fluid (in kg) * gravity (9.8 m/s2)
Because mass = density * volume, this can also be written as:
FB = ρfVfg
Buoyant Force = Density of fluid (in kg/m3) * volume of fluid (in m3) * gravity
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*Whether an object floats or sinks depends on whether the buoyant force is
enough to overcome its weight.
If you draw a free-body diagram for an object submerged in a fluid (either
partially or completely), there will be only 2 forces: the object’s weight pulling
down, and the buoyant force pushing up. The NET FORCE on an object in a fluid
is equal to the difference between these 2 forces:
Fnet = FB – Fg
Net force = Buoyant force – Weight (all units in N)
Substituting in density and volume for mass, this becomes
Fnet = ρfVfg – ρoVog or Fnet = (ρfVf – ρoVo)g
The subscript f refers to the density and volume of fluid, while the subscript o
refers to the density and volume of the object.
When you place an object in a fluid, there are 3 possible situations:
*If the object is FLOATING ON THE SURFACE, this means that the BUOYANT
FORCE MUST EQUAL THE WEIGHT. The object ends up being in equilibrium:
FB = Fg or ρfVfg = ρoVog or ρfVf = ρoVo
*If the object is COMPLETELY SUBMERGED BUT LESS DENSE THAN THE FLUID, it
should float, so the BUOYANT FORCE WILL BE GREATER THAN THE WEIGHT and
the object will rise toward the surface.
*If the object is COMPLETELY SUBMERGED AND MORE DENSE THAN THE FLUID, it
should sink, so the WEIGHT WILL BE GREATER THAN THE BUOYANT FORCE and it
will sink towards the bottom.
For objects in this third situation, even though they sink, the buoyant force
cancels out some of their weight and makes them appear lighter than they
really are. This is why astronauts have used underwater training to simulate
low-gravity environments.
*If you hook a scale up to a completely submerged object, the scale will read
the object’s APPARENT WEIGHT, which is less because of the buoyant force
pushing up:
Apparent Weight = Fg – FB = ρoVog - ρfVfg
Keep in mind that in cases where the object is completely submerged, the
volumes Vf and Vo will be equal. In this case, you can rearrange the equation
to get:
Fg / FB = ρo / ρf
This equation can be used to solve for unknown densities in certain problem
types.
Pressure / Hydraulics
Fluids exert pressure on the surfaces and containers around them. PRESSURE
refers to a force spread out over an area. It is given by:
P=F/A
Pressure (in Pa or N/m2) = Force (in N) / Area (in m2)
Note that the unit of pressure in physics is the PASCAL (Pa). One Pascal is
equal to 1 N/m2, so the units stay standard and everything works out.
An alternate unit for measuring pressure is the atmosphere (atm). 1 atm is the
normal atmospheric pressure at sea level. The conversion for atm to Pa is:
1 atm = 1.01 x 105 Pa
Fluids all follow PASCAL’S PRINCIPLE, which states that pressure applied to a
fluid in a closed container is transferred equally throughout the fluid. This
principle is the reason that HYDRAULIC systems (like a car jack) work. Force is
applied to one piston, and the pressure generated is transferred to the other
piston, raising the car.
Because of Pascal’s principle, the pressure on both pistons must be the same
(If the areas are different, then the forces will be different, but the pressure is
the same):
P1 = P2
F1 / A1 = F2 / A2
Where force is in N and area is in m2. You may have to use geometry formulas
(area of a circle, area of a square) to find A so you can plug it into the
equation.
(continued ------à)
Continuity
Fluids must follow the conservation of mass (mass can’t be created or
destroyed), so the CONTINUITY EQUATION states that all mass that flows into a
pipe must flow out of the pipe. The amount of mass flowing is based on the
area of the pipe and the speed of flow, so at any 2 points:
A1v1 = A2v2
Where A is area (in m2) and v is velocity (in m/s). Once again, you may have to
use geometry equations to find the area.
If the amount of mass flowing must stay the same, the general idea is this:
*Fluid will move SLOWER in a LARGER section of the pipe
*Fluid will move FASTER in a SMALLER section of the pipe
This is how a nozzle on a hose works: it forces the same mass through a much
smaller opening, so the fluid must travel much faster.