Free-fall

1. Free-fall An object in free-fall is only subject to the force of gravity (weight) Fnet = Fg (Neglect Air Resistance)

2. In Free-fall: Fg Fg Fg F = ma a = F/m Fg Fg so acceleration must be constant Fg Fg

3. Galileo Galileo dropped two cannon balls of different weights from the top of Leaning Tower of Piza. The two cannon balls reached the ground at the same time. He proved that when objects of different weights are dropped at the same height and time, they take the same amount of time to fall to the ground (ignoring air resistance).

4. Using Newton’s second law, we can conclude that the force of gravity on an object is proportional to the mass of the object. Yes, They Rounded!

6. Important! Since the acceleration of gravity is down, when in free-fall, ignoring air resistance: g =a = - 9.8 m/s2

7. What observations can you make about the picture?

8. ∆y = ½at2 Δv= aΔt If vi and ti are equal to Zero vf = at

9. Free-Fall Motion A 1-kg rock is thrown into the air at 10 m/s upward. Neglecting air resistance, what is the net force acting on the rock? Answer: In the absence of air resistance, the only force exerted on the 1 kg rock is simply the force due to gravity, mg, at any speed along its trajectory! Net Force = mg = (9.8m/s2)(1kg)= 9.8N

10. Remember: g = -10 m/s2 0 m/s 10 m/s - 10 m/s - 20 m/s 20 m/s 30 m/s - 30 m/s Ignoring Air Resistance

11. Sign Conventions for Free-Fall • At point A the change in y is 0, the velocity is positive. • At point B the change in y is positive, the velocity is zero. • At point C the change in y is 0, the velocity is negative. • At point D, the change in y is negative, the velocity is negative. • The acceleration for all the points is -9.8 m/s2 A B C D - + 0 0 Dy v a - - + 0 Up “+” Down “-” -9.8 -9.8 -9.8 -9.8 Zero Reference Point

12. Remember Motion Graphs? Object is slowing down - acceleration + velocity x v t Object is speeding up - acceleration - velocity t a t

13. Which object hits the ground first? (ignore air friction) • Which object hits the ground first when we include air friction?

14. With Air Resistance No Air Resistance

15. Why did air resistance slow down the feather so much and not the elephant?

16. So what is Terminal Velocity? Well, eventually, the force of air resistance becomes large enough to balance the force of gravity. At this instant in time, the net force is 0 Newtons — the object stops accelerating. The object is said to have "reached a terminal velocity." Fg = FR a = 0 m/s2

17. Skydiving Observe the motion of the skydiver below. As the skydiver falls, he encounters the force of air resistance. The amount of air resistance is dependent upon two variables: the speed of the skydiver, and the cross-sectional area of the skydiver. • Draw FBDs at the following points. Describe the direction of the net force, acceleration, and velocity. • Just released from the helicopter. • Falling for a few seconds. • Falling for a few seconds more to a point where the air resistance force equals the gravitational force. • Deployment of a parachute. • Repeat of (3) for the parachute. • Now draw velocity and acceleration motion map showing the motion.

18. Parachutes

19. Find the acceleration for A, B, C, and D. • a = (Fnet / m) = (1000 N) / (100 kg) = 10 m/s/s • a = (Fnet / m) = (600 N) / (100 kg) = 6 m/s/s • a = (Fnet / m) = (200 N) / (100 kg) = 2 m/s/s • a = (Fnet/m) = (0 N) / (100 kg) = 0 m/s/s. Which diagram represents terminal velocity?

20. Air Resistance • A sky diver in the spread-eagle position opens the parachute. (She has reached terminal velocity before she opens the parachute) • Is the diver accelerated? • Which direction? Explain your answer. • As an object falls through air, it usually encounters some degree of air resistance. • The actual amount of air resistance encountered by an object depends upon a variety of factors. • The two most common factors which have a direct effect upon the amount of air resistance present are the speed of the object and the cross-sectional area of the object. Increased speeds result in an increased amount of air resistance. Increased cross-sectional areas result in an increased amount of air resistance. Yes, she is accelerated in the upward direction. She is slowing down, yet still falling.

21. Watch This!

23. In situations in which there is air resistance, massive objects fall faster than less massive objects. Why? Massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals their gravity force. Basically the more massive object accelerates longer before reaching terminal velocity.

24. Free-Fall Practice • Draw Picture • List Givens • Write Equations • Solve For Unknowns

25. Fun Problems!!!! 1) A penny is dropped from the top of a rollercoaster. The height of the ride is 110m. (neglect air resistance) • Find the speed of the penny when it hits the ground. • Find the time it takes for the penny to fall to the ground. • Would it be different for a quarter? (how about with air resistance?)

26. 2) A stone is thrown straight upward with a speed of 20 m/s. a) How high does it go? b) How long does it take to rise to its maximum height?

27. 3) An object is thrown straight upward and falls back to the thrower after a round trip time of 0.80 s. How fast was the object thrown?

28. 4)A cell phone is thrown upward from the edge of a building with a velocity of 20 m/s. Where will the object be at 3s after it is thrown? After 5s.?

29. 5) George throws an apple vertically upward from a height of 1.3 m with an initial velocity of +24 m/s. • Will the apple reach a friend in a tree 5.3 m above the ground? • If the apple is not caught, how long will the apple be in the air before it hits the ground?