Free fall is the motion of an object where gravity is the only force acting upon it. In free fall, objects accelerate downwards due to the gravitational force with an acceleration g, which is approximately 9.8 m/s2 near the surface of the Earth.
Key Concepts:
Time (t): The duration for which the object has been falling.
Gravity: The force that pulls objects towards the center of the Earth, causing free fall.
Acceleration due to Gravity (g): The constant acceleration experienced by an object in free fall, approximately 9.8 m/s2near the surface of the Earth.
Initial Velocity (u): The velocity at which an object starts its free fall. For an object dropped from rest, this is zero.
Final Velocity (vvv): The velocity of the object just before it stops accelerating, which can be calculated using kinematic equations.
Displacement (s): The distance the object has fallen, which can be calculated using kinematic equations.
Kinematic Equations for Free Fall:
Where:
v is the final velocity.
u is the initial velocity.
g is the acceleration due to gravity (9.8 m/s2)
s is the displacement
t is the time
Historical Context: Galileo vs. Aristotle
In ancient Greece, Aristotle believed that heavier objects fall faster than lighter ones. He theorized that the speed of fall was proportional to the weight of the object. This view dominated for nearly two thousand years.
However, in the late 16th and early 17th centuries, Galileo Galilei challenged Aristotle’s view through experimentation and observation. Galileo proposed that all objects, regardless of their mass, fall at the same rate in the absence of air resistance. According to Galileo, the only force acting on a falling object is gravity, and thus, they experience the same acceleration.
Galileo’s Experiment:
To demonstrate this, Galileo have dropped two spheres of different masses from the Leaning Tower of Pisa. He observed that they hit the ground at the same time, contradicting Aristotle’s theory.
Galileo’s findings laid the groundwork for the concept of free fall as we understand it today and paved the way for Newton’s laws of motion.
Examples:
- Dropping an Object from Rest:
- If you drop a stone from a height of 20 meters, how long will it take to hit the ground?
- Solution: Since u=0 (initially it was at rest) use the second equation: s=1/2 g t 2,
where s= 20 m
20=1/2×9.8×t2
20=4.9 t 2
t2=20/4.9
t ≈ 2.02 seconds.
- Solution: Since u=0 (initially it was at rest) use the second equation: s=1/2 g t 2,
- If you drop a stone from a height of 20 meters, how long will it take to hit the ground?
- Throwing an Objec1t Upward:
- If you throw a ball upwards with an initial velocity of 15 m/s, how high will it go before it starts to fall back down?
- Solution: Use v=u−g t where u= 15 m/s and v=0 at the highest point. we use negative sign (-) because the movement of the object is opposite to the force of gravity.
0=15−9.8 t
t=15/9.8
t≈1.53 seconds to reach the highest point.
Now we need to calculate the height.
Use s=u t−1/2 g t2 , we use negative sign (-) because the movement of the object is opposite to the force of gravity.
s=15×1.53−1/2×9.8×(1.53)2
s≈11.48 meters.
- Solution: Use v=u−g t where u= 15 m/s and v=0 at the highest point. we use negative sign (-) because the movement of the object is opposite to the force of gravity.
- If you throw a ball upwards with an initial velocity of 15 m/s, how high will it go before it starts to fall back down?
- Object Thrown Downwards:
- If you throw a rock downwards with an initial velocity of 5 m/s from a height of 30 meters, how long will it take to hit the ground?
- Solution: Use s=u t+1/2 g t2 , s=30 m, u=5m/s
30= 5 t+1/2×9.8×t2
30=5 t+4.9 t2
Solve the quadratic equation
4.9 t2+5 t−30=0
4.9 t2 + 5t – 30 = 0
Using the quadratic formula find t
t≈2.09 seconds.
- Solution: Use s=u t+1/2 g t2 , s=30 m, u=5m/s
- If you throw a rock downwards with an initial velocity of 5 m/s from a height of 30 meters, how long will it take to hit the ground?
- Free Fall from a Moving Vehicle
- A helicopter is ascending at 12 m/s and releases a package from a height of 100 meters. How long will it take for the package to reach the ground.
- Solution: The initial velocity u=−12 m/s (since it’s upwards, opposite ti force of gravity), and s=100 m
Use s=u t+1/2 g t2
100=−12 t+1/2×9.8×t2
Solve the quadratic equation
4.9 t2−12 t−100=0
t≈5.43 seconds.
- Solution: The initial velocity u=−12 m/s (since it’s upwards, opposite ti force of gravity), and s=100 m
- A helicopter is ascending at 12 m/s and releases a package from a height of 100 meters. How long will it take for the package to reach the ground.
Handouts
Coloured version
Printing friendly version
Model answers