March 23, 2015

March 23, 2015

Free fall - motion of an object which is only subject to gravitational force (no friction / air resistance considered)

acceleration due to Earth's gravitational pull:

g = 9.80 m/s2

sign convention:

axis of reference is y-axis pointing upwards --> falling object is subject to acceleration of -9.80 m/s2 and has a negative velocity:

y

a = -9.8 m/s2v < 0

v > 0

same equations as for other accelerated motions hold true:

March 23, 2015

y = (-9,8 m/s2) t212

--> inverted half-parabula as position / time graph

--> in the second second of movement object is 9.8 m/s faster than in first second and so on.

--> mass of object does not appear in formula - what does that mean?

Strobe phtograph of a falling ballhttps://www.youtube.com/watch?v=xQ4znShlK5A

https://www.youtube.com/watch?v=AV-qyDnZx0A

March 23, 2015

Do heavy and light objects fall with the same speed?

http://video.mit.edu/watch/feather-and-coin-in-a-vacuum-6407/

compare styrofoam and rubber ball, feather and ball

March 23, 2015

motion of a ball thrown into the air:

- ascend and descend take the same amount of time

- final velocity same magnitude as initial velocity (but opposite sign)

March 23, 2015

Example:

From a hight of 15m an object is thrown into the air with a velocity of 10 m/s. What is the objects flight time and what will its final velocity be?

(vf2 = vi2 + 2a y)

15 m

y = yfinal - yinitial = 0m - 15m = -15m

March 23, 2015

March 23, 2015

March 23, 2015

A  car  travels  at  a  velocity  of  5  m/s  for  five  seconds  and  then  accelerates  to  a  velocity  of  10  m/s  within  5  sec.  What  is  the  average  velocity  over  the  course  of  this  movement?

March 23, 2015

Isaac's  house  lies  at  a  distance  of  1500  m  from  school.  Kyle  lives  on  the  same  street  as  Isaac  but  750  m  further  from  school.  On  Friday  morning  they  both  head  out  the  door  at  the  same  time.  Isaacs  strolls  to  school  at  a  velocity  of  1  m/s.  Kyle  however  has  an  urgent  question  to  ask  his  math  teacher  before  his  quiz  and  therefore  hurries  to  school  at  a  velocity  of  2  m/s.  At  what  point  in  time  after  leaving  the  house  does  Kyle  overtake  Isaac?

March 23, 2015

Air resistance increases with velocity

March 23, 2015

"Real" fall and terminal velocity

initially:

not much air resistance --> skydiver accelerates

later:

the greater the velocity, the greater the air resistance --> drag created by air resistance becomes equal to acceleration due to gravity --> terminal velocity reached.

B

Free Fall: air resistance is not considered (either negligable, or we pretend there is no air). Acceleration formulas hold true, an object will continue accelerating untill it hits the ground.

Real Fall: air resistance increases with velocity and will slow acceleration. A terminal velocity will be reached.

The more massive the object, the greater the gravitational force pulling it down. Therefore a massive object has to reach a higher speed compared to a lighter object, before air resistance counteracts the gravitational pull.

In total: the more massive the object, the greater the terminal velocity.

March 23, 2015

An object, initially at rest, falls from a height of 12 metres. What will its height be when it reaches half of its maximum speed?

March 23, 2015

The graph below shows the speeds of two cars.

At time 0 car B passes car A, which is starting from rest.

1.) what will the distance be between the two cars after 60 sec.?

2.) At what time will car A pass car B?