We all know the effects of gravity? Right??? http://www.youtube.com/watch?v=cIwTYL1fwJk http://www.youtube.com/watch?v=F-pX1X2cUv4youtube http://www.youtube.com/watch?v=lLmJ1Mm13IQ
What does it mean to be in Free Fall? Occurs when an object is being acted upon by the force of gravity. If gravity is the only force acting on an object, the object will accelerate at 9.8 m/s 2. That is a constant on Earth! All objects fall at the same rate!
Acceleration due to Gravity Constant Acceleration… 9.8 m/s/s You can use the kinematic equations!! Sometimes seen as ‘g’ rather than ‘a’ in equations Usually given a negative symbol representing a downward direction. g = 9.8 m/s/s, downward
Kinematic Review V = Vo + at X = Xo + Vot + ½ at 2 V 2 = Vo 2 + 2 a (X-Xo) a = -g (gravitational constant. –9.8 m/s 2 )
You keep speeding up as you fall! Time (s) Velocity (m/s) V = Vo + -at 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0
Until You Hit ‘Terminal Velocity’ Happens around 10 seconds after YOU fall Air resistance counters gravity causing no more acceleration to occur Continue at a constant velocity to ground Downward Gravity = Upward Air Resistance
The first 10 seconds, you are in constant acceleration. You can use your beloved kinematics! After 10 seconds, you have reached terminal velocity (no longer accelerate), Net force = 0 (Mechanical Equilibrium) You can use your beloved constant Velocity equation!! V= displacement/time Until you pull the parachute at about 30 seconds…
Sample Problem A Sky diver jumps out of a plane at an elevation of 5000 meters. He reaches terminal velocity at 10 seconds. A. What is his velocity at 10 seconds? B. How far did he fall in the first 10 seconds? C. How far did he fall in the first 16 seconds?
Part A: What is his Velocity at 10s? Vo = 0 T = 10 sec A = -9.8 m/s2 Vf =? Vf = Vo + at Vf = 0 + (-9.8)(10) Vf = -98 m/s In the first ten seconds, the skydiver accelerated to a terminal velocity of 98 m/s in the downward direction
Part B: How far did he fall in the first 10 s? Vo = 0 T = 10 sec A = -9.8 m/s2 Vf =-98 m/s Δ x = ?? Δ x = Vot + 1/2 at 2 Δ x = 0 + ½ (-9.8)(10) 2 Δ x = - 490 meters In the first ten seconds, the skydiver fell a total of 490 meters towards the Earth
Part C: How far did he fall in the first 16s? For the first 10s, Δ x = - 490 meters For the next 6s, he travels at a constant speed V = -98m/s T = 6 seconds Δ x = ??? Constant Velocity = Δ x / time -98 m/s = Δ x / 6 seconds -98 * 6 = Δ x -588 m = Δ x In the next 6 seconds, the skydiver fell a total of 588 meters towards the Earth -490 + -588 = -1078 meters or 1078 meters down
Rising Objects Now consider an object thrown straight up: It moves upward for a while. At the highest point, when the object is changing its direction from upward to downward, its instantaneous speed is zero. It then falls downward as if it had been dropped from rest at that height. 4.5 Free Fall: How Fast
During the upward part of this motion, the object slows from its initial upward velocity to zero velocity. The object is accelerating because its velocity is changing. How much does its speed decrease each second? 4.5 Free Fall: How Fast
The speed decreases at the same rate it increases when moving downward—at 9.8 meters per second each second. The instantaneous speed at points of equal elevation in the path is the same whether the object is moving upward or downward. The velocities are different because they are in opposite directions. During each second, the speed or the velocity changes by 9.8 m/s downward. 4.5 Free Fall: How Fast
The change in speed each second is the same whether the ball is going upward or downward. 4.5 Free Fall: How Fast
Change in Displacement The distance which a free-falling object has fallen from a position of rest is also dependent upon the time of fall. ∆X =Vot + 1/2at 2 At t = 1 s ∆X = (0.5) * (-9.8 m/s 2 ) * (1 s) 2 = -4.9 m At t = 2 s ∆X = (0.5) * (-9.8 m/s 2 ) * (2 s) 2 = -19.6 m
Will an elephant and a mouse fall at the same rate?
Neglecting Air resistance… ALL OBJECTS FALL AT THE SAME RATE!! 9.8m/s/s An elephant and a mouse will hit the ground at the same time!!