Unit Dynamics Module The Forces of Friction page 1 of 2 Motion Through a Fluid Drag Force and Terminal Speed The drag force is a frictional force that resists the motion of objects through a 1 fluid For objects in air at moderate speeds Fdrag C Av 2 is a good 2 approximation of the drag force A falling object is not subject to air drag when its velocity is very small and linearly increasing As the velocity of a falling object increases Fdrag increases to a maximum value of 2mg mg When this occurs the object reaches its terminal velocity vT C A The drag force is a frictional force that resists the motion of objects through a fluid Recall that the force of kinetic friction is proportional to the normal force However in a fluid there is no obvious normal force so we must develop an equation for the drag force A good approximation for the drag force on non streamlined objects in air at moderate 1 speeds is Fdrag C Av 2 where is the density of 2 the fluid A is the cross sectional area of the object and v is the relative speed of the air and the object C the drag coefficient is unitless and it depends on the size shape material and texture of the object A parachutist steps out of a stationary helicopter Her velocity just after leaving the helicopter is zero so there is no initial drag force Apply Newton s second law to the parachutist just after she steps out of the helicopter There is just one force her weight acting in the downward direction Her acceleration is the acceleration due to gravity which is a constant You can use the equations of kinematics with constant acceleration to show that the parachutist s velocity increases linearly with time just after she steps out of the helicopter www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1914 doc rev 03 27 2001 Unit Dynamics Module The Forces of Friction page 2 of 2 Motion Through a Fluid Drag Force and Terminal Speed Once the parachutist gathers some speed she feels the force of air drag The air drag will increase with her speed until it is equal to mg At this point the parachutist will reach her terminal velocity and her acceleration will be zero Using Newton s second law you can solve for the terminal velocity 2mg vT C A The graph on the bottom left shows the velocity of the parachutist as a function of time Initially the parachutist s speed increases linearly As the velocity increases the force of air drag approaches the magnitude of the parachutist s weight Similarly the velocity approaches the value of the terminal velocity www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1914 doc rev 03 27 2001
View Full Document
Unlocking...