What is a vacuum?

Brain Bites - NASA

School blocks YouTube? Download file below.

 vacuum_hi.mov

 

 

B. Free fall - falling where the only force is gravity (no friction)

 

1. Free fall Word Problems

"Use same method and equations as before,

except always remember when you read... "

'…an object is dropped' 

 Vi = 0

 

a = g = +9.8m/s2
(make down +)

… an object is ascending:

a = g = -9.8 m/s2
(make down -)

 

 

V vs t plot, Object Ascending?

 

Ex) Object thrown up Vi = 110 m/s,
sketch a V vs t plot of the object
 from the throw to the peak (use a = -10 m/s2)

 

 

 

 

 

 

a. Simple Freefall Problems

Leaning Tower of Pisa, in Pisa, Italy.

 (Wednesday 19 May 2004, 17:37)
The lean of this tower has been tried to fix several times.
The most recent time I believe was in 2001 when they tried to drill into the
 ground and pour cement underneath the sandy surface.

 

 

 

Ex) A coin is dropped in a vacuum tube, find its displacement after .30  seconds.

 

 

"Step 1 - Read and

underline all the

important information"

 

Ex) A coin is dropped in a vacuum tube, find its displacement after .30 seconds.

 

 

"Step 2 - Turn all your

 information into letters"


 
Vi = 0   (Object is dropped)
a = +10. m/s2
d = ?
t = .30 seconds


"Step 3 -  Substitute

and Solve"

 

 

 

d = Vit + 1/2at2 

 

 

d = 0m/s(.30 sec)+1/2(10. m/s2)(.30 s)2

 

 

 

 

d = 0 + 5(.09)

 

 

 

d = .45 m

 

 

 

Ex) A coin is dropped in a vacuum tube, find the coin's velocity after .30 seconds

 

 

 

Ex) A coin is dropped in a vacuum tube, find the coin's velocity after .30 seconds

 

 

Vi = 0 m/s

a = +10. m/s2

(dropped)

Vf = ?

t = .30 sec

 

 

"Search the Mechanics

Section on the equation

sheet to find the

equation that fits"

 

Vf = Vi + at

OR

a = (Vf - Vi)/t

 

 

Vf = 0 + 10. m/s2(.3 sec)

 

 

 

 

Vf = 3.0 m/s

 

 

 

Ex) A rocket is fired vertically upward with an initial velocity of 29 m/s.

Find the rocket's maximum altitude.

 

 

 

 

At Maximum Altitude,

Vf = 0 m/s

 

 

 

 

 

 

 

Ex) A rocket is fired vertically upward with an initial velocity of 29 m/s .  

Find the rocket's maximum altitude.

 

Altitude??

Vi = +29 m/s

Vf = 0 m/s
a = g = -9.8 m/s2

d = ?

 


 Vf2 = Vi2 + 2ad

(0 m/s)2=(+29 m/s)2+2(-9.8m/s2)d


 

0 = 841 + -19.6d

 

 

-841 = -19.6d

 

 

43 m

 

 

 

Ex) An object dropped on planet X falls 64 m in 4 seconds. 
Find the acceleration due to gravity on planet X.

 

Ex) An object dropped on planet X falls 64 m in 4 seconds.  Find the acceleration due to gravity on planet X.

 

 

Vi= 0 m/s
d = 64 m
t = 4 sec
a = ?

 

 

d = Vit + 1/2 at2

 

 

64 m = 0 m/s(4 sec) + 1/2a(4 sec)2

 

 

64 m = 0 + 8a

 

 

a = 8 m/s2

AP Question

A ball is thrown upward from a position (y0)above the ground  with a velocity of 16 m/s.

 

Find y0 if it took 3.0 seconds for the ball to hit the ground.

 

A ball is thrown upward from a position  (y0) above the ground with a velocity of 8 m/s.

 

Find y0 if it took 3.0 seconds for the ball to hit the ground.

ay = -10. m/s2 (g)

yi = ?

Vi = 8 m/s

yf = 0 (hit the ground)

t = 3.0 sec

 

d = Vit + 1/2at2

yf - yi = Vit + 1/2at2

y  = yi + Vit + 1/2at2

0  = yi + 8 m/s(3.0 sec) + 1/2(-10.m/s2)(3.0 sec)2

0  = yi + 24 m + -45 m

 

-yi = 24 m + -45 m

 

-yi =  -21 m

 

yi = 21 m

 

 

 

 

 

 

 

What velocity does the ball to hit the ground?

Make down positive

Make this a problem of a ball falling from a height of 21 m and a velocity of 8 m/s down

ay = +10. m/s2 (g)

∆d = +21 m

Vi = +8.0 m/s

(vel. become +8 m/s when ball returns to original position)

Vf = ?

 

Vf2 = Vi2 + 2ad

Vf2 = 64 + 2(10 m/s2)21m

 

Vf = 22 m/s down

 

OR

 

Vf = 8.0m/s + -10m/s2(3 sec)

 

Vf = -22 m/s

 

 

 

Paul Hewitt Question

When you drop a ball it accelerates downward at 9.8 m/s2. If you instead throw it downward, then its acceleration immediately after leaving your hand, assuming no air resistance, is

A.  9.8 m/s2

B.  more than 9.8 m/s2

C.  less than 9.8 m/s2.

D.  Cannot say, unless the speed of throw is given.

 

 

Ex) A basketball player jumped straight up to grab a rebound. If she was in the air for 0.80 second, how high did she jump?

Treat this as a problem where the player comes down from the peak of her rebound.

 

ay = 10. m/s2 (g)

d = ?

Vi = 0 m/s

t = .40 sec

 

d = Vit + 1/2at2

 

 

d = 1/2(10 m/s2)(.4 sec)2

 

d = .80 m

 

Ex) A stone is thrown vertically upward with a speed of 12.0 m/s from the edge of a cliff 70.0 m high.

a) how long does it take to reach the bottom of the cliff?

 

t = ? (how long)

ay = 9.80 m/s2 (down positive)

Viy = -12.0 m/s2 

∆dy = +70.0 m  (down positive)

 

∆dy = Viyt + 1/2ayt2

 

70.0 m = -12.0 m/s2t + 4.9 m/s2t2

 

0 = -12.0 m/s2t + 4.9 m/s2t2 - 70 m

 

Quadratic, positive root = 5.20 sec

 

 

 

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