2. Do Now
If a piece of paper and a textbook were dropped from the same height at the same time, which would hit the ground first?
Explain why you think this happens?

3. Free Falling Objects: Aristotle to Galileo
Obj: use kinematics to describe the motion of falling objects on Earth.

4. Uniform Exam
Awesome!
Mean score of 87%
The score on skedula (and on your paper) is not yet curved.
Yes, they will be.

5. Aristotle (384 – 322 BCE) Do Not Copy
Greek philosopher and “scientist”
Developed early theories of motion that withstood over a millennia of questioning
One of the earliest recorded proponents of empiricism
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6. Aristotle’s theories of motion
Objects have a natural place in the universe
Heavy objects belong on the ground
Light objects belong in the air
If you release an object in the air, it will return to its natural place
The heavier an object, the faster it falls towards the ground
A 4lb brick will fall 4 times as fast as a 1lb brick
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7. Take 3
Discuss Aristotle’s ideas about free falling objects with a neighbor and answer these questions
What parts of Aristotle’s theories seem incorrect to you? Why?
Which parts of his theories do you think are probably correct? Why?
Can you think of an experiment Aristotle could have done to test some of his ideas?

8. Galileo
Aristotle’s theories were widely accepted in the European science community until the late 1500s.
As scientists embraced experimentation over theorizing and observation, some cracks started appearing in Aristotle’s theories.
Many scientists and engineers questioned Aristotle’s conclusions
Galileo was one of the first to speak up
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9. Experimentation Does anyone know what this famous building is called?
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10. Galileo figured out
Set up experiment using ramp and brass spheres
He tested his theory using brass spheres rolling down inclined planes and found that the distance traveled was proportional to the square of elapsed time
d = ½ a t2
He reasoned that falling objects must be accelerating

11. No timers, no calculators
Without a vacuum tube, a calculator or a stopwatch, Galileo managed to get very close to the actual value for the acceleration of a falling object.
a = 9.8 m/s2

12. What would you think?
Imagine you’re a scientist living in the 16th century. You’ve been taught Aristotle’s theories and they seem to match your observations.
What would your reaction be to Galileo’s assertion that all falling objects have the same acceleration?

13. Was he right?
At the time of his writing, the vacuum tube had not been created
Eventually Galileo’s theory of falling objects was proven correct and would go on to inspire much of Newton’s work on motion
Droppin stuff on the moon!

14. Kinematics of falling objects
Free fall: The only force on the object is gravity.
We can use our normal kinematics equations to analyze the motion of falling objects so long as they are falling in one dimension only.
Straight up and down only
For intro physics, we will ignore air resistance (vacuum)
Pay careful attention to direction
The acceleration due to the force of gravity always points towards the Earth
The velocity of an object in free fall can be up or down

15. Finding time
How much time would it take an object released from rest to fall 10 meters (ignoring air resistance)?
Why do we have to ignore air?
Why do we automatically know this object’s acceleration?

16. You try (left)
How long would it take a 40lb sphere released from rest to fall 6m? (Ignore air resistance)
An object dropped from the top of a 30m building would take how long to hit the ground.

17. Finding final velocity
An object is released and falls for 5 seconds. What is the magnitude of its velocity at the end of the 5 second interval? (Ignore air resistance)
What formula do we use to solve this problem?
How do we rearrange it?

18. Direction
How do we know acceleration is a vector ?(look in your notes!) What is the direction for the acceleration of free falling objects? What is happening to the velocity of an object in free fall?

19. Let’s draw this.
An object is released and allowed to fall for 4s. What is the object’s final velocity?

20. Applying kinematics to free fall
What piece of information do we automatically know for free fall problems?
Does vi always have to be zero?
Do you agree? How do we know this?

21. Vi doesn’t always have to be zero

22. Do Now
A 10kg object and a 50kg object are released from rest at the same height.
Describe what you will see if we are not ignoring air resistance
Describe what you will see in a vacuum
If both objects fall for 3 seconds, what will the final speed of each object be? (Ignore friction)
Ratio: ask different students for givens, find and equations. How to rearrange equation etc…

23. Trajectory = flight path
Top of flight path

24. Direction: Rising
If an object is thrown upwards into the air, what effect does the acceleration of gravity have on the velocity?
Does acceleration ever become zero while the object is in the air?
Does velocity ever become zero while the object is in the air?

25. Top of the trajectory
Shay throws a ball into the air with a speed of 16 m/s.
From this information, can we figure out how much time it takes the ball to get to the top of its path? How?

26. Summary Rising objects still have an acceleration of 9.8m/s2
We have to remember that acceleration is going the opposite direction of velocity here
At the top of an object’s trajectory, the final velocity is 0m/s.
Even when vf = 0m/s, acceleration is still 9.8 m/s2

27. Practice (left)
For each problem, you must treat it like any kinematics equation. List the givens and match them to an equation
Carly jumps into the air with an initial speed of 0.8m/s. How high does she manage to jump?
Jeff throws a baton into the air. If it reaches a maximum height of 6m, what was the initial speed with which it was thrown?

28. Rising and Falling
Stephen jumps into the air with an initial speed of 0.7 m/s. How much time passes before he lands back on the ground?
How do we know this is a rising and falling problem?
We need to divide the problem into two problems: rising and falling
Separate givens for each problem
Be extra careful to pay attention to direction and the sign for acceleration

29. Symmetry of time
The time it takes for an object to reach its max height is the same time it takes to fall from its max height
Eg: If it takes 4.1s for an object to reach a height of 40m, it will take 4.1s for it to fall the same distance back down.
So the rising time is exactly one-half of the total time.

30. Visualizing free fall
What observations can you make about how the velocity and distance changes as the ball falls?

31. Graphing free fall
On a distance vs time graph, what shape would you expect free fall to create?
Think about what is happening to both the distance and the velocity?

32. Distance vs time

33. Velocity vs Time
What happens to the velocity of the object as it falls?
What does this look like on a v vs t graph?

34. V vs T: Down = negative

35. Calculate
A ball is thrown upwards with an initial velocity of 29.4 m/s. Calculate the distance it travels in 3 second.
Calculate its final velocity after 3 seconds.