Motion in one Dimension 4 - motion of free fall
Motion in one Dimension 4 - motion of free fall
There is another theme for one Dimensional motion.
Figure4-1
A man is holding a ball on the top of the building. The height of building is 100 m.
Now he set it free from his hand softly. He did not throw it to downward. Just set it free by spreading fingers.
Then the ball falls freely.
Of course, there is no resistance. No air resistance, No wind.
We know this phenomena in our life.
The ball will get speed gradually as time goes.
Why is it faster continuously?
Maybe most of you know the reason.
The reason is that because of gravity the ball is faster more and more.
We will discuss about the gravity issue later.
Why does it become faster gradually?
The speed, the magnitude of velocity is changing with respect to the rate of time.
What is the root for the change?
Anyway there is acceleration. For making acceleration, we need physical force. What forces are there on the ball. It's gravitational force. Because of gravity there is acceleration, and through the acceleration the velocity is being changed.
Most of motion on the surface of the Earth is approximately constant acceleration motion. We call it gravitational acceleration. We mark it by "g"
The magnitude of g is about 9.8 m/s2, and the direction is vertically down direction to the surface of the earth.
Actually the direction is toward center of the Earth.
It's constant acceleration motion.
So we can apply the 3 formulas to this motion of the ball.
1) V = V0 + at
(2) S = V0 t + 1/2 * at2
(3) 2aS = V2 - V02
( t: time to be taken for S distance moving of the car ,
a: constant acceleration ,
S: distance moved after time t ,
V0: initial velocity ,
V: velocity after time t, or velocity when the car moves S distance )
I will set the surface of the earth by 0 position. And the top of the building is (+) 100 (m) position. And I will mark (-) for down direction. In the same way upward direction by (+) direction.
The ball on the top has displacement. It's physical vector quantity for ball's position.
The magnitude of displacement is (+) 100 (m). And the direction is (+) direction from the origin( the surface of the Earth).
Let's check the initial velocity. It's 0 m/s and (-) direction.
The acceleration becomes g(gravitational acceleration), and the direction is (-).
Then what will be the velocity when the ball reaches the surface?
By using 3rd formula, we can find it.
2 x 9.8 x 100 = V2 - 02 ( All units are MKS )
HW4.1) Find out the Velocity when the ball reaches the surface to two decimal places.
Keep in mind that velocity is vector. We should find out the magnitude and the direction.
You can use alculator.
Then how long will it take from top to surface?
We can also find it using 1st formula.
HW4.2) Calculate the time to reach to the surface from the top.
It moves straight line vertically. Therefore we can call it one dimensional motion.
Especially we define it free fall motion on the surface of the Earth.
There is another theme for one Dimensional motion.
Figure4-1
A man is holding a ball on the top of the building. The height of building is 100 m.
Now he set it free from his hand softly. He did not throw it to downward. Just set it free by spreading fingers.
Then the ball falls freely.
Of course, there is no resistance. No air resistance, No wind.
We know this phenomena in our life.
The ball will get speed gradually as time goes.
Why is it faster continuously?
Maybe most of you know the reason.
The reason is that because of gravity the ball is faster more and more.
We will discuss about the gravity issue later.
Why does it become faster gradually?
The speed, the magnitude of velocity is changing with respect to the rate of time.
What is the root for the change?
Anyway there is acceleration. For making acceleration, we need physical force. What forces are there on the ball. It's gravitational force. Because of gravity there is acceleration, and through the acceleration the velocity is being changed.
Most of motion on the surface of the Earth is approximately constant acceleration motion. We call it gravitational acceleration. We mark it by "g"
The magnitude of g is about 9.8 m/s2, and the direction is vertically down direction to the surface of the earth.
Actually the direction is toward center of the Earth.
It's constant acceleration motion.
So we can apply the 3 formulas to this motion of the ball.
1) V = V0 + at
(2) S = V0 t + 1/2 * at2
(3) 2aS = V2 - V02
( t: time to be taken for S distance moving of the car ,
a: constant acceleration ,
S: distance moved after time t ,
V0: initial velocity ,
V: velocity after time t, or velocity when the car moves S distance )
I will set the surface of the earth by 0 position. And the top of the building is (+) 100 (m) position. And I will mark (-) for down direction. In the same way upward direction by (+) direction.
The ball on the top has displacement. It's physical vector quantity for ball's position.
The magnitude of displacement is (+) 100 (m). And the direction is (+) direction from the origin( the surface of the Earth).
Let's check the initial velocity. It's 0 m/s and (-) direction.
The acceleration becomes g(gravitational acceleration), and the direction is (-).
Then what will be the velocity when the ball reaches the surface?
By using 3rd formula, we can find it.
2 x 9.8 x 100 = V2 - 02 ( All units are MKS )
HW4.1) Find out the Velocity when the ball reaches the surface to two decimal places.
Keep in mind that velocity is vector. We should find out the magnitude and the direction.
You can use alculator.
Then how long will it take from top to surface?
We can also find it using 1st formula.
HW4.2) Calculate the time to reach to the surface from the top.
It moves straight line vertically. Therefore we can call it one dimensional motion.
Especially we define it free fall motion on the surface of the Earth.
