Acceleration of Gravity Gravity and Projectiles Distance velocity time of upward moving object Velocity at position on the way up is the same as velocity in the same position on the way down neglecting air resistance Velocity reaches zero object begins to fall Then is falling under the influence of gravity Roll the Ball Loses speed for each interval of time it rises on an upward throw Gains at same rate on its downward path Upward motion Acted upon by gravity just like a falling object Goes up slower and slower until upward velocity reaches zero Goes shorter and shorter distances in same time interval Slows at 10 m s2 the acceleration of gravity Types of Motion Linear in a straight line Non linear curved path Projectiles have curved path called parabola Parabolic curves are parabolas Photo of ball falling Projectiles Move both horizontally and vertically Vertical motion influenced by gravity Horizontal motion not influenced by gravity Are NOT dependent upon one another Path of Ball from Side Ball Rolling off table Freely falling object ho riz ont al Has acceleration downward Pushed away from table Has velocity outward Combines to have a parabolic path http galileo rice edu lib student work experiment95 paraintr html 1 Front View the ball Front View Top View of the ball Projectile motion Each component acts separately Same horizontal distance in each time increment Vertical distance increases for each time increment that passes Top View Series2 distance from table What if Cannonball without gravity What if you dropped a cannon ball off the cliff at exactly the instant a cannon was fired in the horizontal direction Which cannon ball would hit the ground first There is gravity This is the outside force acting on the object to change its course http www physicsclassroom com Class vectors U3L2a html Components of cannonball motion Cannonball with gravity Airplane and Package Flying straight and level at 45 m above ground level at a speed of 40 m s Drops package which falls to the ground Where will package land neglect air resistance http www physicsclassroom com Class vectors u3l2b html http www physicsclassroom com mmedia vectors hlp gif http www physicsclassroom com mmedia vectors pap gif 2 Airplane and Package Airplane and Package 300 Flying straight and level at 45 m above ground level at a speed of 40 m s Drops package which falls to the ground Where will package land neglect air resistance Vertical height 250 200 150 100 50 0 http www physicsclassroom com mmedia vectors pap gif 0 50 100 150 200 250 300 350 Horizontal distance Banana without gravity Faster Cannonball Cannonball with gravity Banana with gravity 350 300 250 200 150 100 50 0 0 50 100 150 200 250 300 Distance http www physicsclassroom com mmedia vectors mzg gif 350 http www physicsclassroom com mmedia vectors mzng gif Cannonball with Gravity Slower banana Cannon Ball Trajectory with no Gravity 350 90 80 300 V ertical H e ig h t 70 250 Vertical height a b c d Flying straight and level at 45 m above ground level at a speed of 40 m s Drops package which falls to the ground Where will package land neglect air resistance Straight down from where it was dropped Underneath plane 80 m behind plane More than 120 m behind plane H eig h t Cannon Ball Trajectory Cannonball without gravity with no Gravity 350 200 150 60 50 40 30 20 100 10 50 0 0 0 0 50 100 150 200 250 Horizontal distance http www physicsclassroom com mmedia vectors mzs html 300 350 10 20 30 40 50 60 70 80 90 Horizontal Distance Cannonball with gravity 3 Vectors of projectile motion Steeper trajectory Acceleration of Cannonball What is the acceleration in a horizontal direction What is the acceleration in a vertical direction Cannonball 90 80 70 V e r tic a l 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 Horizontal Projectile Range Steeper Cannonball 350 Cannonball Trajectories 300 Vertical 250 200 150 100 50 0 0 50 100 150 200 250 300 350 Horizontal Cannonball trajectories http www physicsclassroom com mmedia vectors mr gif With air resistance Calculations of distance speed and acceleration Projectile will fall from maximum height in same amount of time it took to rise Because the acceleration of gravity slows it at the same rate it increases the speed on the way down How fast was this ball thrown 4 How fast was ball thrown dvert gt2 dvert 5 m g 10 m s2 Want to find dhorz t We can calculate t dvert gt2 We know dhorz dvert g How fast was ball thrown How fast was ball thrown Want to find v v dhorz t We calculated t 1s Distance 20 m v 20 m 1 s v 20 m s How fast was ball thrown v 20m 1s 20 m s Solve for how long to fall d t2 1 2 gt 2 5m 1 10m 2 s2 5m t 1 10m 2 t 2 s2 5m 1s 1 10m 2 2 s Object thrown horizontally Falls the same distance in the same time no matter the speed of the throw 72 5 mi h 20m 60 s 60 min 1km 0 62mi 44 6mi h s min 1000m 1km h Satellite as projectile Satellite as projectile No gravity No gravity 6000 m s http www physicsclassroom com mmedia vectors tp gif 6000 m s Satellite as projectile 8000 m s http www physicsclassroom com mmedia vectors 6kms gif 8000 m s http www physicsclassroom com mmedia vectors co gif 5 Object thrown horizontally Falls the same distance in the same time no matter the speed of the throw Earth s surface is 5 meters lower for every 8000 meters horizontal distance Acceleration of Gravity Free fall of object Time elapsed Speed increases seconds 10 m s for every second of fall 0 10 m s 10m 1 s s2 2 Speed meters second 0 10 20 3 30 4 40 Freely falling object Velocity is a function of how long it has been falling Distance is also a function of how long it has been falling because And average velocity is sum of two velocities divided by 2 gt v vt d v2 v1 2 Earth s surface is 5 meters lower for every 8000 meters horizontal distance If it is thrown 8000m s it will never reach the surface Because it falls just as fast as the surface departs from a horizontal path Speed and distance of falling objects Remember that velocity is defined as distance time Average velocity can be determined over time intervals average velocity v2 v1 2 Time Speed elapsed meters second secon ds 0 0 1 10 2 20 3 30 4 40 Freely falling objects We will use this equation And substitute average velocity calculated from two velocities Which will be calculated from vt d vaverage v2 v1 2 gt v If it is thrown 8000m s it will never reach the surface nearly 18 000 mi h Because it falls as fast as the …
View Full Document
Unlocking...