Physics 100

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Physics 100

• Sections A1, A2, A3 and A4

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Physics 100

• Chapter 2 (Section 5)

Freely Falling Bodies
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Freely Falling Bodies
Free Fall Motion The idealized motion of bodies
in the gravitational attraction of the earth
ignoring

• Air resistance
• The earths roation
• The decrease in acceleration with increasing
  altitude

4
Freely Falling Bodies
Galileos experiment proved that the
gravitational acceleration is independent of
bodies wieght
t 0.0 s
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Freely Falling Bodies
Galileos experiment proved that the
gravitational acceleration is independent of
bodies wieght
t 0.0 s
t 1.0 s
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Freely Falling Bodies
Galileos experiment proved that the
gravitational acceleration is independent of
bodies wieght
t 0.0 s
t 1.0 s
t 2.0 s
t 3.0 s
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Freely Falling Bodies
The constant acceleration of a freely falling
body is called acceleration due to gravity (g).
g 9.8 m/s2, 980 cm/s2 or 32 ft/s2
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Freely Falling Bodies
y
O
t 0, v 0
-10 m
-20 m
-30 m
-40 m
-50 m
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Freely Falling Bodies
y
O
t 0, v 0
-10 m
-20 m
-30 m
-40 m
-50 m
10
Freely Falling Bodies

• At t 0, v0 0
• At t 1.0 s, what is y and v?

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Freely Falling Bodies

• At t 0, v0 0
• At t 1.0 s, what is y and v?
• y y0 v0t (1/2) at2
• 0.0 (0 m/s) (1s) (1/2) (-9.8 m/s2)(1.0
  s)2
• - 4.9 m

12
Freely Falling Bodies

• At t 0, v0 0
• At t 1.0 s, what is y and v?
• y y0 v0t (1/2) at2
• 0.0 (0 m/s) (1s) (1/2) (-9.8 m/s2)(1.0
  s)2
• - 4.9 m
• v v at
• 0 m/s (-9.8 m/s2)(1.0 s) -9.8 m/s

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Freely Falling Bodies
y
O
t 0, v 0
t 1, y -4.9 m v -9.8 m/s2
-10 m
-20 m
-30 m
-40 m
-50 m
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Freely Falling Bodies

• At t 2.0 s, what is y and v?
• y y0 v0t (1/2) at2
• 0.0 (0 m/s) (2s) (1/2) (-9.8 m/s2)(2.0
  s)2
• - 19.6 m
• v v at
• 0 m/s (-9.8 m/s2)(2.0 s) -19.6 m/s

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Freely Falling Bodies
y
O
t 0, v 0
t 1, y -4.9 m v -9.8 m/s2
-10 m
t 2, y -19.6 m v -19.6 m/s2
-20 m
-30 m
-40 m
-50 m
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Freely Falling Bodies
y
O
t 0, v 0
t 1, y -4.9 m v -9.8 m/s2
-10 m
t 2, y -19.6 m v -19.6 m/s2
-20 m
-30 m
-40 m
t 3, y -44.1 m v -29.4 m/s2
-50 m
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Freely Falling Bodies
Example 2.7

• You throw a ball vertically upward from the roof
  of a tall building. The ball leaves you hand at a
  point even with the roof railing with an upward
  speed of 15.0 m/s the ball is then in free fall.
  On its way back down, it just misses the railing.
  At the location of the building, g9.8 m/s2. Find
  a) the position and velocity of the ball 1.00 s
  and 4.00 s after leaving your hand b) the
  veolcity when the ball is 5.00 m above the
  railing c) the maximum height reached and the
  time at which it is reached d) the acceleration
  of the ball when it is at its maximum height.

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Freely Falling Bodies
Example 2.7
y(m)
15
10
5
t0, v015.0 m/s
0
-5
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7

• At t 1.00 s, what is y and v?

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Freely Falling Bodies
Example 2.7

• At t 1.00 s, what is y and v?
• y y0 v0t (1/2) at2
• (0)(15.0 m/s)(1.00s)
• (1/2)(-9.8m/s2)(1.00 s)2
• 10.1 m

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Freely Falling Bodies
Example 2.7

• At t 1.00 s, what is y and v?
• y y0 v0t (1/2) at2
• (0)(15.0 m/s)(1.00s)
• (1/2)(-9.8m/s2)(1.00 s)2
• 10.1 m
• v v0 at
• (15.0 m/s) (-9.8 m/s2)(1.00 s)
• 5.2 m/s

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Freely Falling Bodies
Example 2.7
y(m)
15
t 1, y 10.1 v 5.2 m/s
10
5
0
-5
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7

• At t 4.00 s, what is y and v?
• y y0 v0t (1/2) at2
• (0)(15.0 m/s)(4.00s)
• (1/2)(-9.8m/s2)(4.00 s)2
• -18.4 m
• v v0 at
• (15.0 m/s) (-9.8 m/s2)(4.00 s)
• -24.2 m/s

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Freely Falling Bodies
Example 2.7
y(m)
15
10
5
0
-5
t4 y-18.4 m v-24.4 m/s
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7

• At y 5.00 m, what is v?
• v2 v02 2 a (y - y0)
• (15.0 m/s)2 2 (-9.8 m/s2)(5 m - 0)
• ? v 11.3 m/s

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Freely Falling Bodies
Example 2.7
y(m)
15
10
5
0
-5
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7

• When v 0, what is the position of the particle
  (what is y)?
• v2 v02 2 a (y - y0)
• (0.00 m/s)2 (15.0 m/s)22(-9.8 m/s2)(y-0)
• ? y -(15.0 m/s)2 / (-2 9.8)
• y 11.5 m

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Freely Falling Bodies
Example 2.7

• At what time this will happen (v 0)?
• v v0 at
• 0 (15.0 m/s) (-9.8 m/s2) t
• ? t -15.0 / (-9.8)
• t 1.53 s

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Freely Falling Bodies
Example 2.7
y(m)
15
t 1.53 s y 11.5 m v 0 m/s
10
5
0
-5
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7

• At what time will the particle be back to its
  same hieght (y 0)?
• y y0 v0t (1/2) at2
• 0 0 (15.0 m/s) t (1/2) (-9.8 m/s2)t2
• 0 t ( 15.0 4.9 t)
• ? Either t 0 or t 3.06 s

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Freely Falling Bodies
Example 2.7

• Wat is the velocity of the particle when it is
  back to its same hieght (y 0)?
• v v0 at
• (15.0 m/s) (-9.8 m/s2)(3.06 s)
• - 15.0 m/s

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Freely Falling Bodies
Example 2.7
y(m)
15
10
t 3.06 s y 0 m v -15.0 m/s
5
0
-5
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7
ay-t graph
ay
t
O
-9.8 m/s2
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Freely Falling Bodies
Example 2.7
vy (m/s)
vy-t graph
15
10
5
0
1
2
3
4
t(s)
-5
-10
-15
-20
-20
-25
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Freely Falling Bodies
Example 2.7
vy (m)
15
x-t graph
10
5
0
1
2
3
4
t(s)
-5
-10
-15
-20
-20
-25
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And the lessons stop Chemistry next week