Unit Kinematics Module One Dimensional Motion with Constant Acceleration page 1 of 2 Free Falling Objects Objects fall to the ground with uniform acceleration agrav g 9 8 m s2 If air friction is present it may change the acceleration of a falling object Free fall acceleration occurs when an object is subject only to the force of gravity The master equations of kinematics with uniform acceleration hold for free falling objects Be sure to choose a consistent coordinate system when solving free fall problems A heavy object and a light object simultaneously dropped to the ground from the same height will land at exactly the same instant Both objects experience free fall acceleration which is the acceleration due to gravity and is constant near the m Earth s surface agrav g 9 8 2 Galileo Galliei s performed the first experiments on the speed of falling objects from the top of the Leaning Tower of Pisa in about 1590 Objects that experience a lot of air friction will fall to the ground more slowly than objects that do not experience much air friction For example if a feather and a coin are dropped the coin will land first because it experiences much less air friction than a feather The acceleration due to gravity is always constant The air is removed from the tube containing the feather and the coin minimizing the effects of air drag Now when the two objects are dropped they fall to the bottom at the same instant www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1808 doc rev 03 27 2001 Unit Kinematics Module One Dimensional Motion with Constant Acceleration page 2 of 2 Free Falling Objects Because objects in free fall have constant acceleration the master equations of kinematics can be used to describe their motion You should be careful to define a coordinate system before solving free fall problems A ball is tossed upwards How would you calculate its final velocity using the first equation of kinematics If you choose a coordinate system where up is positive as in the example on the left the initial velocity would be positive and the free fall m acceleration would be 9 8 2 If you choose a s coordinate system where down is positive as in the example on the right vi would be negative and m agrav 9 8 2 s Prof Pollock and two colleagues find a deep pit They throw a stone in the pit and it takes 3 s to hit the bottom How deep is the pit The stone is in free fall as it drops to the bottom of the pit so you can use the equations of kinematics to determine the distance to the bottom Choose the third equation since it allows you to solve for xf Set up a coordinate system that is positive in the downwards direction The top of the pit xi is at 0 m The stone was at rest before it was dropped so m v i 0 The time required for the stone to hit the s bottom t is 3 s Since the coordinate system is positive in the downwards direction m m agrav 9 8 2 10 2 You can calculate that the s s pit is about 50 m deep www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1808 doc rev 03 27 2001
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