2. KINEMATICS : 2. KINEMATICS 2.4 Acceleration of Free Fall 1 Copyright Science Department, TKGS 2009
Objectives : Objectives state that the acceleration of free fall for a body near to the Earth is constant and is approximately 10 ms-2.
describe the motion of bodies with constant weight falling with or without air resistance, including reference to terminal velocity Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Galileo’s Inclined Planes
Galileo developed his concept of acceleration by experimenting with inclined planes (slope).
For a ball rolling down an inclined slope of different angles, it picks up the same amount of speed in successive seconds.
Question
On which slope would the ball pick up speed the fastest? Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall (Conceptual Physics P. G. Hewitt) Vertical Slope
Free Fall : Free Fall Aristotle believed that there were two kinds of motion: natural motion and violent motion.
Natural motion, meant that every object has a proper place in this universe. For instance, a stone would fall because it strives to get there.
He believed that heavier objects would fall faster than lighter objects.
Do you agree with him? Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall 384 – 322 BC
Free Fall : Free Fall Galileo didn’t. To disprove Aristotle‘s views, he dropped objects of different weights from the top of the Leaning Tower of Pisa.
Except for the small effect of air resistance, he found that objects of various weights, when released at the same time, fell together and hit the ground at the same time. Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Activity
Take a coin from your wallet and hold it in one hand. Hold your rolled-up tissue paper in the other hand and stand on your chair. Drop both items from the same height at the same time. Which one touches the ground first? Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Falling without Air Resistance
All objects, regardless of shape, size, material or weight, fall with the same acceleration in the absence of air.
Acceleration due to gravity, g = 10 ms-2
(Actual value is currently 9.81 ms-2 and varies from place to place on Earth) Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall Sketch the speed-time graph for an object falling with g .
Sketch the acceleration-time graph for an object falling with g.
Free Fall : Free Fall Example 1
John released a ball 5 m above the ground. (Ignore air resistance)
What is the speed when it reaches the ground?
How long does it take to reach the ground?
u = 0 ms-1 a = 10 ms-2 s = 5 m
Using v2 = u2 + 2as
= 2(10)(5)
= 100
Final speed, v = 10 ms-1
ii) Using
Time taken Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Example 2
John throws a ball vertically upwards at a speed of 15 ms-1.
What is the velocity of the ball when it falls into his hands again?
What is the maximum height reached?
Velocity of the ball = 15 ms-1 (Downwards)
u = 15 m/s v = 0 m/s a = -10 ms-2
Using v2 = u2 + 2as
s =
=
= 11.25 m Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Falling with Air Resistance
Objects falling without (or with negligible) air
resistance fall with 10 m s-2. If air resistance is
present, objects will fall with a constant speed.
Air resistance:
1. Opposes the motion of moving objects
2. Increases with the speed of the object
3. Increases with surface area
4. Increases with density of air
Do you know which skydiver falls faster? Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall Falling with Air Resistance
Knowing that
Air resistance increases with speed of an object,
Air resistance tends to oppose the motion of objects
If allowed to fall with air resistance, what will happen
to the speed of an object.
It will reach a constant speed
Why? Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall
Free Fall : Free Fall At the start Picks up speed Fastest
(v = 0) (v > 0) (v constant) Weight Weight Weight Air Resistance Air Resistance a = g = 10 m/s2 a < g a = 0 m/s2 Air Resistance = Weight Terminal Velocity
Free Fall : Free Fall Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall Falling with Air Resistance Speed of the object increases with time at a decreasing rate until it reaches a constant speed.
Terminal velocity
What is the acceleration in area A4?
Zero
Free Fall : Free Fall Parachutist
A parachutist jumps from an aircraft. After some time, he releases his parachute. Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall Speed increases at a decreasing acceleration Parachutist reaches a terminal velocity of 50 m/s Parachutist opens parachute Terminal velocity of 5 m/s
Challenge Your Mind! : Challenge Your Mind! Who gets to fall at a higher terminal velocity?
Heavier guy Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall The heavier parachutist must fall faster than the light parachutist for air resistance to cancel his greater weight.
Free Fall : Free Fall Food for Thought
Under the influence of air resistance, if you throw a ball up and let it fall into your hands again, would the ball take less time to go up than to come down? Copyright Science Department, TKGS 2009 2.4 Acceleration of Free Fall