A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old)...

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a = Velocity final – Velocity initial time Solve for Velocityfinal with algebra A new (but old) formula Velocityfinal= Velocityinitial + at

Transcript of A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old)...

Page 1: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

a = Velocityfinal – Velocityinitial

time

Solve for Velocityfinal with algebra

A new (but old) formula

Velocityfinal= Velocityinitial + at

Page 2: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Velocityfinal= Velocityinitial + at

Calculate the instantaneous speed at the 10 s mark for a car that accelerates at 2 m/s² from a position at rest

Velocityfinal= Velocityinitial + at = 0 m/s +2 m/s² (10 s) = 20 m/s

Page 3: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Free Fall

Definition- when an object is moving solely (only) under the influence of gravity….

Page 4: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Example of gravity

Dropping a ball?

Throwing a ball?

Yes

Yes, once it leaves your hand

Page 5: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Experience tells you that objects speed up (or accelerate) as they fall

All objects always accelerate at the same rate

(when we ignore air resistance)

Page 6: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Ignoring air resistance

Page 7: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

On the moon

http://www.youtube.com/watch?v=U7db6ZeLR5s

Page 8: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

So what is that magical number that all objects accelerate at?

9.8 m/s²

Page 9: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Finish the definition of free fall

Definition- when an object is moving solely (only) under the influence of gravity….

(when we ignore air resistance)

Page 10: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

The History of the Law of Falling Bodies

Galileo Galilei

(1564-1642)

Page 11: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Galileo is said to have dropped two unequal weights from the top of the Leaning Tower of Pisa to prove his theory. Galileo claimed that a naturally falling object would gain equal amounts of velocity in equal amounts of time.

If correct, this means that i) the object’s speed increases as it falls and ii) the rate at which it picks up speed does not change during the fall.

Page 12: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

However, for medieval science, freely falling objects moved too quickly and the clocks could not record quickly enough .

So Galileo devised to slow down the motion by replacing thefalling object with a ball rolling down a gently inclined plane.

Page 13: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

The velocity of a free-falling object which has been dropped from a position of rest is

dependent upon the time for which it has fallen.

Time (s) Velocity (m/s) 0 0 1 9.8 2 19.6

3 29.4

4 39.2

5 49.0

Page 14: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Gravity

1) Causes free falling objects to accelerate at 9.8 m/s² toward the center of the earth.

2) The symbol is g (for acceleration due to gravity)

Page 15: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

GravityPositive or

negative?...that’s the question!

By convention….+ 9.8 when an object

is falling towards the earth

- 9.8 when an object is moving away from the earth

Page 16: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

How fast something is moving is very different from how far

How far does an object fall in 1 s?

It is 4.9 m….why?

In free fall, the object started from rest and is not at a constant speed

Velocityavg=Vfinal + Vinitial

2

Page 17: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

How far will an object drop?

d= ½ gt²

I drop a rock off of a bridge, and 4.2 s later, I hear a splash. What is the height of the bridge?

d= ½ (9.8 m/s²) (4.2 s)²

= 86 m

Page 18: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Kinematics Formula Summary

1. vf = vi + g t

2. d = vi t + ½½g t

2 if velocity is 0 then the equation

3. vf2 = vi

2 + 2 gd

Page 19: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Practice Problem

You drop a ball from rest off a 120 m high cliff. Assuming air resistance is negligible (free fall), how long is the ball in the air?

What is the ball’s speed when it strikes the ground at the base of the cliff?

Page 20: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Answer

t = 4.95s

vf =48.5m/s

Page 21: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Reviewhttp://onlinephys.com

/freefall6.gif

http://onlinephys.com/freefall5.gif

Page 22: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

What’s the story?

Page 23: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Free Fall with Upward Motion

• When something is thrown straight upward under the influence of gravity, and then returns to the thrower, this is very symmetrical = parabola

• The object spends half its time traveling up; half traveling down.

Page 24: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Free Fall with Upward Motion

• Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with.

• Acceleration is 9.8 m/s2 and directed DOWN the entire time the object is in the air!

Page 25: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Free Fall with Upward Motion

Page 26: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

Free Fall with Upward Motion

Homer Hickham used this fact to determine how high his rocket went  and that the rocket boys didn’t start the fire in Welch

Page 27: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.

October Sky

http://www.youtube.com/watch?v=udHB3tftPz4

Page 28: A = Velocity final – Velocity initial time Solve for Velocity final with algebra A new (but old) formula Velocity final = Velocity initial + at.