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What is a vacuum?

Brain Bites - NASA

School blocks YouTube?
Download file below.

 vacuum_hi.mov

Video Instruction

showmethephysics.com

Slideshow

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' 

 V_i = 0

a = g = +9.8m/s²
(make down +)

… an object is ascending:

a = g = -9.8 m/s²
(make down -)

a. Simple Freefall Problems

"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"

 
V_i = 0   (Object is dropped)
a = +9.8 m/s²
d = ?
t = .30 seconds

"Step 3 -  Substitute and Solve"

d = V_it + 1/2at² 

d = 0m/s(.30 sec)+1/2(9.8 m/s²)(.30 s)²

d = 0 + 4.9(.09)

d = .44 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

V_i = 0 m/s

a = +9.8 m/s²

(dropped)

V_f = ?

t = .30 sec

"Search the Mechanics Section on the equation sheet to find the equation that fits"

V_f = V_i + at

OR

a = (V_f - V_i)/t

V_f = 0 + 9.8 m/s²(.3 sec)

V_f = 2.9 m/s

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

[ Flash ]

Find the rocket's maximum altitude.

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

Find the rocket's maximum altitude.

Altitude??

V_i = +29 m/s

V_f = 0 m/s
a = g = -9.8 m/s²

d = ?

 V_f² = V_i² + 2ad

0 = 841 + -19.6d

-841 = -19.6d

43 m

Uniform or Non-uniform Acceleration? 

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

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

d = V_it + 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.

a_y = -10. m/s² (g)

y_i = ?

V_i = 8 m/s

y_f = 0 (hit the ground)

t = 3.0 sec

∆d = V_it + 1/2at²

y_f - y_i = V_it + 1/2at²

y  = y_i + V_it + 1/2at²

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

0  = y_i + 24 m + -45 m

-y_i = 24 m + -45 m

-y_i = -21 m

y_i = 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

a_y = +10. m/s² (g)

∆d = +21 m

V_i = +8.0 m/s

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

V_f = ?

V_f² = V_i² + 2ad

V_f² = 64 + 2(10 m/s²)21m

V_f = 22 m/s down

OR

V_f = 8.0m/s + -10m/s²(3 sec)

V_f = -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.

a_y = 10. m/s² (g)

d = ?

V_i = 0 m/s

t = .40 sec

∆d = V_it + 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.

∆d_y = V_iyt + 1/2a_yt²

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

Objects Propelled Horizontally

 

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