Physic 110 Lecture 04 from Chapter 2'''Sections 3 to 5

1
Physic 110 Lecture 04 from Chapter
2...Sections 3 to 5

• Free Fall
• and the
• Acceleration Of Gravity

2
Free Fall

• All objects moving under the influence of gravity
  only are said to be in free fall
• Free fall does not depend on the objects
  original motion
• All objects falling near the earths surface fall
  with a constant acceleration
• The acceleration is called the acceleration due
  to gravity, and indicated by g

3
Galileo Galilei

• 1564 - 1642
• Galileo formulated the laws that govern the
  motion of objects in free fall
• Also looked at
• Inclined planes
• Relative motion
• Thermometers
• Pendulum

4
Quick Quiz

• A tennis player on serve tosses a ball straight
  up. While the ball is in free fall, does its
  acceleration
• a) increase
• b) decrease
• c) increase an then decrease
• d) decrease and then increase
• e) remain constant?

5
Quick Quiz

• A tennis player on serve tosses a ball straight
  up. While the ball is in free fall, does its
  acceleration
• a) increase
• b) decrease
• c) increase an then decrease
• d) decrease and then increase
• e) remain constant

6
Quick Quiz

• For the same tennis ball tossed up for a serve,
  does its speed
• a) increase
• b) decrease
• c) increase an then decrease
• d) decrease and then increase
• e) remain constant?

7
Quick Quiz

• For the same tennis ball tossed up for a serve,
  does its speed
• a) increase
• b) decrease
• c) increase an then decrease
• d) decrease and then increase
• e) remain constant

8
Acceleration due to Gravity

• Symbolized by g
• g 9.80 m/s² (or 32.2 ft/s2 )
• When estimating, use g 10 m/s2
• g is always directed downward
• toward the center of the earth
• Ignoring air resistance and assuming g doesnt
  vary with altitude over short vertical distances
• free fall is Uniformly Accelerated Motion

9
Free Fall an object dropped

• Initial velocity is zero
• Let up be positive
• Use the kinematic equations
• Generally use y instead of x since vertical
• Acceleration is g -9.80 m/s2

vo 0 a g
10
Free Fall -- object thrown upward
vtop 0

• Initial velocity is upward, so positive
• The instantaneous velocity at the maximum height
  is zero
• a g -9.80 m/s2 everywhere in the motion

a
vf
vo
11
Thrown upward, cont.

• The motion may be symmetrical
• Then tup tdown
• Then vf -vo
• The motion may not be symmetrical
• Break the motion into various parts
• Generally up and down

12
Example Problem 1

• You are curious how high you are able to throw a
  baseball. To find out, you throw a baseball
  straight and up measure the length of time it
  is in the air.
• Question 1 If the ball took 6 seconds from time
  of toss to time of ground strike, how high did
  you throw it?
• Question 2 With your arm, should you consider
  trying to pitch for the DuHawks fast pitch
  softball team?

13
Free Fall -- object thrown upward
a 9.81 m/s2

• Uniformly Accelerated Motion
• Accel. a g -9.80 m/s2
• Time of flight 6 s
• Initial velocity ?
• Final velocity ?
• Max height ?
• Velocity at max height 0 m/s

vo
vf
14
Free Fall -- object thrown upward
a 9.81 m/s2

• Uniformly Accelerated Motion
• Accel. a g -9.80 m/s2
• Time of flight 6 s
• Initial velocity ?
• Final velocity ?
• Max height ?
• Velocity at max height 0 m/s

vo
vf
15
Free Fall -- object thrown upward
vtop
a 9.81 m/s2

• Time to get to top of motion. 3 s
• Time to drop back to start level 3 s
• Accel. a g -9.80 m/s2
• max velocity 0 m/s
• vf -vo

vo
vf
Use
16
Max height ? Ground Level
vtop
Use
Where t 3.0 s a -9.81 m/s2
vtop 0.0 m/s xf 0.0 m
vf
17
Ground Level ? Ground Level
What can be found from ground level to ground
level? Since
Then using
vo
xo
Find vo -vf
vf
Answer vf-29.4m/s
18
Ground Level ? Max height
xtop
Then once vf is known, use any of the other
uniformly accelerated motion equations over the
first half of the flight.
vo
xo
vf
19
solution
For example May be used to find xtop.
20
Summary
vtop
xtop
t total 6.0 s tup 3.0 s tdown
3.0 s a -9.81 m/s2 vo
29.4 m/s vtop 0.0 m/s vf
-29.4 m/s xo 0.0 m xtop
44.1 m xf 0.0 m
vo
vf
xo
vf
Ball speed
21
Non-symmetrical Free Fall

• Need to divide the motion into segments
• Possibilities include
• Upward and downward portions
• The symmetrical portion back to the release point
  and then the non-symmetrical portion

22
Workout Problem 2

• A ball is thrown upward from the ground with an
  initial speed of 25 m/s.
• At the same time, another ball is dropped from a
  building 15 m high.
• After how long will the balls be at the same
  height?
• What height will this be?

23
Solution
Ball 1
Ball 2
Equations
24
Solution
Let and
so
or
?
Then x is found as
With values this gives t as
25
Combination Motions
26
Homework Assignment 04

• Conceptual questions
• Chapter 2 8 on page 46

• Problems
• Chapter 2, Problem 43 on page 50
• Chapter 2, Problem 64 on page 51
• Chapter 2, Problem 67 on page 51