free fall

Free Fall

To a physicist, the term "free fall" has a different meaning than it does to a skydiver. In physics, free fall is the (one-dimensional) motion of any object under the influence of gravity only - no air resistance or friction effects of any kind, whereas it is air resistance that makes skydiving a hobby rather than a suicide attempt!
You might think that since just about everything we observe falling is falling through the air, that "physics free fall" must be a pretty useless idea in practice. Not so! Any falling object's motion is at least approximately free fall as long as:

it is relatively heavy compared to its size. (Dropping a ball, as in the picture at right, or jumping off a chair, is a free-fall motion, but dropping an unfolded piece of paper, or the motion of a dust particle floating in the air, is not. If you crumble the paper into a "paper wad", however, its motion is approximately free fall.
it falls for a relatively short time. (If you jump off a chair, you are in free fall. After you have jumped out of an airplane and fallen for several seconds, you are not in free fall, since air resistance is now a factor in your motion.)
it is moving relatively slowly. (If you drop a ball or throw it down its motion will be free fall. If you shoot it out of a cannon, its motion won't be free fall.)

You should also note that an object doesn't have to be falling to be in free fall - if you throw a ball upward its motion is still considered to be free fall, since it is moving under the influence of gravity

http://www.batesville.k12.in.us/physics/phynet/mechanics/kinematics/FreeFallIntro.html

Free fall acceleration:
If you throw something vertically upward and could somehow eliminate or ignore the effect of drag and air on the object , Then the object accelerates constantly when it goes up and falls down , This is called free fall.
If something falls freely under the effect of earth’s gravity without any effect of air then the phenomenon is called free fall.
While the free fall , no matter how big , small or weighty the object is , every object feel the same constant acceleration , the constant acceleration during free fall is called free fall acceleration.
The free fall acceleration of earth is denoted by “g” and it’s value at the surface of earth is approximately 9.8m/s , But you should also note that the value of “g” varies slightly with change in latitude and elevation from surface of earth

Suppose the motion in vertically upward direction as positive motion and the motion in downward direction as negative motion.

we can replace the “acceleration = a” in constant acceleration equations by “free fall acceleration = -g” and as the direction of the motion of object in free fall is vertically downward or upward so we can replace the “x 0″ with “y 0″ and “x” with “y” and get our final free fall acceleration equations as:

Equation 1: $v = v_0 - gt$
Equation 2: $y - y_0 = v_0.t - \frac{1}{2} g t^2$
Equation 3: $v^2 = v_0 ^2 - 2 g(y - y_0)$
Equation 4: $y - y_0 = \frac{1}{2} (v_0 + v) t$
Equation 5: $y - y_0 = vt + \frac{1}{2} gt^2$

http://oscience.info/physics/free-fall-acceleration/

Free-fall under gravity

Galileo Galilei was the first scientist to appreciate that, neglecting the effect of air resistance, all bodies in free-fall close to the Earth's surface accelerate vertically downwards with the same acceleration: namely, $g=9.81 {\rm m s^{-2}}$ .¹The neglect of air resistance is a fairly good approximation for large objects which travel relatively slowly (e.g., a shot-putt, or a basketball), but becomes a poor approximation for small objects which travel relatively rapidly (e.g., a golf-ball, or a bullet fired from a pistol). Equations can easily be modified to deal with the special case of an object free-falling under gravity:

$\displaystyle s$	$\textstyle =$	$\displaystyle v_0 t -\frac{1}{2} g t^2,$
$\displaystyle v$	$\textstyle =$	$\displaystyle v_0 - g t,$
$\displaystyle v^2$	$\textstyle =$	$\displaystyle v_0^{ 2} - 2 g s.$

Here, $g=9.81 {\rm m s^{-2}}$ is the downward acceleration due to gravity,

is the distance the object has moved vertically between times

and

(if

then the object has risen

meters, else if

then the object has fallen $\vert s\vert$ meters), and

is the object's instantaneous velocity at

. Finally,

is the object's instantaneous velocity at time

. Suppose that a ball is released from rest and allowed to fall under the influence of gravity. How long does it take the ball to fall

meters? According to the equation, [with

(since the ball is released from rest), and

(since we wish the ball to fall

meters)],

, so the time of fall is

$\begin{displaymath} t = \sqrt{\frac{2 h}{g}}. \end{displaymath}$

Suppose that a ball is thrown vertically upwards from ground level with velocity

. To what height does the ball rise, how long does it remain in the air, and with what velocity does it strike the ground? The ball attains its maximum height when it is momentarily at rest (i.e., when

). According to the equation (with

), this occurs at time

. It follows from equation (with

, and

) that the maximum height of the ball is given by

$\begin{displaymath} h = \frac{u^2}{2 g}. \end{displaymath}$

When the ball strikes the ground it has traveled zero net meters vertically, so

. It follows from equations (with

and

) that

. In other words, the ball hits the ground with an equal and opposite velocity to that with which it was thrown into the air. Since the ascent and decent phases of the ball's trajectory are clearly symmetric, the ball's time of flight is simply twice the time required for the ball to attain its maximum height:

$\begin{displaymath} t = \frac{2 u}{g}. \end{displaymath}$

http://farside.ph.utexas.edu/teaching/301/lectures/node19.html

Examples of Free Fall (problems):

1.

John throws the ball straight upward and after 1 second it reaches its maximum height then it does free fall motion which takes 2 seconds. Calculate the maximum height and velocity of the ball before it crashes the ground. (g=10m/s²)

2.

Calculate the velocity of the car which has initial velocity 24m/s and acceleration 3m/s² after 15 second.

We use the first equation to solve this question.

3.
The boy drops the ball from a roof of the house which takes 3 seconds to hit the ground. Calculate the velocity before the ball crashes to the ground. (g=10m/s²)

Velocity is;

V=g.t

V=10m/ s².3s=30m/s

We have learned how to find the velocity of the object at a given time. Now we will learn how to find the distance taken during the motion. I give some equations to calculate distance and other quantities. Galileo found an equation for distance from his experiments.

This equation is;

Using this equation we can find the height of the house in given example above. Let’s found how height the ball has been dropped? We use 10 m/s² for g.

I think the formula now a little bit clearer in your mind. We will solve more problems related to this topic. Now, think that if I throw the ball straight upward with an initial velocity. When it stops and falls back to the ground? We answer these questions now.

Picture shows the magnitudes of velocity at the bottom and at the top. As you can see the ball is thrown upward with an initial v velocity, at the top it’s velocity becomes zero and it changes it’s direction and starts to fall down which is free fall. Finally at the bottom before the crash it reaches its maximum speed which shown as V’. We have talked about the amount of increase in the velocity in free fall. It increases 9,8m/s in each second due to the gravitational acceleration. In this case, there is also g but the ball’s direction is upward; so the sign of g is negative. Thus, our velocity decreases in 9,8m/s in each second until the velocity becomes zero. At the top, because of the zero velocity, the ball changes its direction and starts to free fall. Before solving problems I want to give the graphs of free fall motion.

As you see in the graphs our velocity is linearly increases with an acceleration “g”, second graphs tells us that acceleration is constant at 9,8m/s², and finally third graphic is the representation of change in our position. At the beginning we have a positive displacement and as the time passes it decreases and finally becomes zero. Now we can solve problems using these graphs and explanations.

http://www.physicstutorials.org/home/mechanics/1d-kinematics/free-fall

Thank you for visiting!:)

Huwebes, Setyembre 6, 2012

Free-fall under gravity