Lecture 3: 26/02
Resistive forces
Newtons first law: an object if in motion will continue at constant speed
When moving through a fluid the medium will exert a resistive drag force on the object
The magnitude is determined by the medium
Its always opposite to the direction of the motion
3 states of matter
Gas: a substance that flows to take up the shape of its container and fill its volume
Liquid: a substance that flows to take up the shape of its container but does not fill the volume
Solid: a substance with its own shape a volume.
Fluids are gases and liquids
Fluids exert a force on their container but only normal to the surface and can’t support shear stress.
For small, smooth, symmetrical and slow objects, r is proportional to v
If its large irregular and fast, r is proportional to v^2
Resisted force expression
R=bv
B depends on the medium, and the on the shape and dimensions of the object.
Analyzing motion in the vertical direction
Mg-bv=ma=m(dv/dt)
Mg-bv-m(dv/dt)=0
A=dv/dt=g-(b/m)v
To find the terminal velocity
There is an asymptote relationship
For objects moving at high speeds through air the magnitude of the resistive force is approximately
equal to the square of the speed.
R=1/2 DpAv^2
D is the drag coefficient
P is the density of the fluid
A is the cross-sectional area of the object
V is the speed of the object
P=m/V (V in this case is volume)
Particle trajectory now accounts for air drag causing graphs to lose their parabolic nature
R=1/2 DpAv^2
Balances of forces at different points are important I need to think about newtons second law