Free Fall - PowerPoint Presentation

Slide1

Free Fall or Gravity is making me do it!!Slide2

What is free fall?

Free Fall is the motion of the body when

air resistance is negligible

and the action can be considered

due to gravity alone

.

Free fall VideoSlide3

Acceleration Due to Gravity

Galileo concluded:

neglecting the effect of the air, all objects in

free fall

have the same acceleration.

It didn’t matter what they were made of, how much they weighed, what height they were dropped from, or whether they were dropped or thrown.The acceleration of falling objects, given a special symbol, g

, is equal to

9.80 m/s

2

. We can use 10 m/s

2

in our calculations.

The acceleration due to gravity is the acceleration of an object in

free fall

.Slide4

Acceleration Due to GravitySo……………………………………..

Object is in Free Fall when:

The only force acting on it is the force of gravity

Its not touching other objectsThere is no air resistance (The vacuum that you can breath)When on earth an object is in Free Fall

ay= -g =-9.81m/s2 (or 10 m/s

2 for calculations)Not on earth “little g” is different!!!!!gmercury= 3.61m/s2 gmoon = 1.62 m/s2 (approx 1/6 of earth)

g

venus

= 8.83 m/s

2

g

mars

= 3.75m/s

2Slide5

Acceleration Due to Gravity

-g because acceleration is down….its in the negative y direction

However…acceleration due to gravity (g) is positive!!!! Its only when we talk about it in an

xy system we say negativeg varies from place to place on earth…However, for our problems we are going to assume a constant g so we can use our Uniform Accelerated Motion equations (kinematic equation). Pick a g (most cases 9.81/10.0 m/s

2) and stick with it (Global vs local...specific location)

Little g is actually not called “gravity.” g is the free-fall acceleration.Slide6

If everything accelerates at the same rate, does that mean everything falls at the same rate?

Even they have a different weight?

Yes

Even if they are different sizes and shapes?

Yes

However, remember its

YES

as long as we do not include air resistance ( for example a feather falls at the same rate but is very affected by air resistance where the lacrosse ball is affected very little.Slide7

Free FallThe figure shows the motion diagram for an object that was released from rest and falls freely. The diagram and the graph would be the same for all falling objects.Slide8

Question 1A ball is tossed straight up in the air. At its very highest point, the ball’s instantaneous acceleration

a

y

isPositive.Negative.

Zero.© 2015 Pearson Education, Inc.Slide9

Question 2

An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. At which point of the trajectory is the arrow’s acceleration the greatest? The least? Ignore air resistance; the only force acting is gravity.

© 2015 Pearson Education, Inc.Slide10

Question 3

An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity.Slide11

Question 1A ball is tossed straight up in the air. At its very highest point, the ball’s instantaneous acceleration

a

y

isPositive.Negative.

Zero.

© 2015 Pearson Education, Inc.Slide12

Question 2

An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. At which point of the trajectory is the arrow’s acceleration the greatest? The least? Ignore air resistance; the only force acting is gravity.

© 2015 Pearson Education, Inc.

Same at all points.Slide13

Question 3

An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity.

DSlide14

Question 4: Analyzing a rock’s fallA heavy rock is dropped from rest at the top of a cliff and falls 100 m before hitting the ground. How long does the rock take to fall to the ground, and what is its velocity when it hits?

Draw it……..

y

i

= 100 m.Slide15

Question 4: Analyzing a rock’s fall (cont.)

Free fall is motion with constant acceleration:

a

y = 

g.. Using (vy)

i = 0 m/s and ti = 0 s, we findWe can now solve for tf:

Now that we know the fall time, we can use the first kinematic equation to find (

v

y

)

f

:Slide16

Question 5: Free Fall

A ball is dropped from rest from the top of a building. Find:

The instantaneous velocity of the ball after 6 sec.

How far did the ball fall.

The average velocity up to that point.

Answers: -60m/s, 180m, -30m/sSlide17

Question 6 Free Fall

A hammer is dropped on the moon. It reaches the ground 1s later. If the distance it fell was 0.83m:

Calculate the acceleration due to gravity on the surface of the moon.

Calculate the velocity with which the hammer reached the ground and compare to the velocity it would have, if it was dropped on the earth’s surface.

Answer:-1.66m/s

2

, -1.66m/s, -9.8m/s Slide18

Question 7Luke

Autbeloe

drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

Kinematic Equations

y

t

t

 Slide19

Question 7

An inspection of the

four equations above

reveals that the equation on the top left contains all four variables.d = vi

t + ½ a t2Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below.

-8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2-8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2-8.52 m = (-4.9 m/s2

) • (t)

2

(-8.52 m)/(-4.9 m/s

2

) = t

2

1.739 s

2

= t

2

t = 1.32 s

The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.)Slide20

Question 8Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.

Diagram:

Given:

Find:

v

i

= 26.2 m/s

v

f

= 0 m/s

a = -9.8 m/s

2

d = ??

v

f

2

= v

i

2

+ 2adSlide21

Question 8(0 m/s)

2

= (26.2 m/s)

2 + 2 •(-9.8m/s2) •d0 m2/s

2 = 686.44 m2/s2 + (-19.6 m/s

2) •d(-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2(-19.6 m/s2) • d = -686.44 m

2

/s

2

d = (-686.44 m

2

/s

2

)/ (-19.6 m/s

2

)

d = 35.0 m

The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.)