Gravity and Free Fall

1. Chapter 5 Section 5C Gravity and Free Fall

2. The Law of Gravitation • 1. Anything that has mass is attracted by the force of gravity. • 2. Any two masses exert an attractive force on each other. • This force increases as the mass of either object increases.

3. M = mass of each bodyG = proportionality constant = d = distance between centers

4. Another form of the same formula • Expl: • Compute the gravitational force between two 2.5 kg lead spheres if their centers are 1.5 meters apart.

5. The Range of Gravity • Do you think that a star in another galaxy is too far away to exert a gravitational force on you? • If you say no, then you’d be wrong. • Despite the distance between the two objects, the gravitational attraction between them never disappears. • These long range gravitational forces give the galaxy its shape.

6. Gravitational Acceleration • Near Earth’s surface, the gravitational attraction of Earth causes all falling objects to have an acceleration of 9.8 m/s2. • By Newton’s Second Law, the net force, mass, and acceleration are related according to the formula: F=ma • According to this law, the force on an object that has an acceleration of 9.8 m/s2 is as follows: F=m x 9.8 m/s2

7. http://abcnews.go.com/US/felix-baumgartner-supersonic-skydive-swimming-touching-water/story?id=17479415#.UI-8DobpxWEhttp://abcnews.go.com/US/felix-baumgartner-supersonic-skydive-swimming-touching-water/story?id=17479415#.UI-8DobpxWE

8. Free Fall • Objects whose only acceleration is due to gravity are in free fall. • Theoretically, objects in free fall continue to accelerate as long as they are falling. • All free falling objects accelerate at the same rate regardless of their mass.(9.8 m/s2)

9. Galileo's Famous Experiment

10. Free Fall Which of these objects would fall with a greater acceleration if they were dropped from a bridge at the same time? All objects fall with the same acceleration, no matter how large or small their mass is!

11. Gravitational Acceleration and Weight • Whether you are standing, jumping, or falling, Earth exerts a gravitational force on you. • The gravitational force exerted on an object is called the object’s weight. • W stands for weight. • Weight = mass x acceleration due to gravity (9.8 m/s2) • w = mg

12. Weight and Mass • Weight and mass are not the same, but they are connected. • Weight is a force, and mass is a measure of the amount of matter an object contains. • As mass increases, weight increases as well.

13. Expl: • What is the weight in Newtons of a 0.442 kg soccer ball? • w = mg • w = 0.442 kg x 9.81 • w = 4.34 N

14. Weightlessness and Free Fall • You’ve probably seen pictures of astronauts and equipment floating inside the space shuttle. • Any item not fastened down in the shuttle floats through the cabin because they are experiencing weightlessness.

15. Free Fall and Distance • If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. • Time (s) Velocity (m/s) • 0 0 • 1 - 9.8 • 2 - 19.6 • 3 - 29.4 • 4 - 39.2 • 5 - 49.0

16. Free Fall and Distance • v = velocity • g = acceleration due to gravity • t = time • Recall: • For an object in gravitational free fall:

17. Expl: • How far will an object free fall if it starts from rest and drops for 3.346 s? • d = 54.9 m

18. Terminal Velocity Consider a skydiver: • At the start of his jump the air resistance is _______ so he • ____ downwards. zero accelerates 2) As his speed increases his air resistance (drag) will _______ increase 3) Eventually the air resistance will be big enough to _______ the skydiver’s weight. At this point the forces are balanced so his speed becomes ________ - this is called TERMINAL VELOCITY balance constant

19. KEY Gravity (constant value & always present…weight) Air resistance (friction) Net force (acceleration OR changing velocity) How the forces change with time.

20. Terminal Velocity Consider a skydiver: • 4) When he opens his parachute the air resistance suddenly ________, causing him to start _____ ____. increases slowing down 5) Because he is slowing down his air resistance will _______ until it balances his _________. The skydiver has now reached a new, lower ________ _______. decrease weight terminal velocity

21. Momentum – Section 5D

22. Let’s start with everyday language What do you say when a sports team is on a roll? They may not have the lead but they may have ___________ MOMENTUM A team that has momentum is hard to stop.

23. What is Momentum? An object with a lot of momentum is also hard to stop Momentum = p = mv Units: kg∙m/s^2 m=mass v=velocity Momentum is also a vector (it has direction)

24. Let’s practice • A 1200 kg car drives west at 25 m/s for 3 hours. What is the car’s momentum? • Identify the variables: • 1200 kg = mass • 25m/s, west = velocity • 3 hours = time P = mv = 1200 x 25 = 30000 kg m/s^2, west

25. How hard is it to stop a moving object? To stop an object, we have to apply a force over a period of time. This is called Impulse Impulse = FΔt Units: N∙s F = force (N) Δt = time elapsed (s)

26. How hard is it to stop a moving object? • Using Newton’s 2nd Law we get FΔt= mΔv Which means Impulse = change in momentum

27. Why does an egg break or not break? • An egg dropped on a tile floor breaks, but an egg dropped on a pillow does not. Why? FΔt= mΔv In both cases, m and Δv are the same. If Δt goes up, what happens to F, the force? Right! Force goes down. When dropped on a pillow, the egg starts to slow down as soon as it touches it. A pillow increases the time the egg takes to stops.

28. Practice Problem A 57 gram tennis ball falls on a tile floor. The ball changes velocity from -1.2 m/s to +1.2 m/s in 0.02 s. What is the average force on the ball? Identify the variables: Mass = 57 g = 0.057 kg Δvelocity = +1.2 – (-1.2) = 2.4 m/s Time = 0.02 s using FΔt= mΔv F x (0.02 s) = (0.057 kg)(2.4 m/s) F= 6.8 N

29. Car Crash Would you rather be in a head on collision with an identical car, traveling at the same speed as you, or a brick wall? Assume in both situations you come to a complete stop. Take a guess http://techdigestuk.typepad.com/photos/uncategorized/car_crash.JPG

30. Car Crash (cont.) Everyone should vote now Raise one finger if you think it is better to hit another car, two if it’s better to hit a wall and three if it doesn’t matter. And the answer is…..

31. Car Crash (cont.) The answer is… It Does Not Matter! Look atFΔt= mΔv In both situations,Δt, m, andΔv are the same! The time it takes you to stop depends on your car, m is the mass of your car, and Δv depends on how fast you were initially traveling.