PH101 Serway Chapter 1

1
PH 105-003/4 ---- Friday, Aug. 22, 2007
Problem on uniform acceleration (from Ch. 2)A
bike moving at constant velocity 5 m/s passes a
car stopped at a light, as the light turns green
and the car begins to accelerate at 2 m/s2.(a)
When does the car pass the bike (in sec.)?

• 5
• 0.1

Equations vf vi a Dt xf xi vi t ½ a t2
2
A bike moving at constant velocity 5 m/s passes a
car stopped at a light, as the light turns green
and the car begins to accelerate at 2 m/s2.(a)
When does the car pass the bike?
(b) Where does this happen?

1. 10 m from light
2. 15 m
3. 20 m
4. 25 m
5. 40 m
6. 50 m

Equations vf vi a Dt xf xi vi t ½ a t2
3
Problem on uniform accelerationA bike moving at
constant velocity 5 m/s passes a car stopped at a
light, as the light turns green and the car
begins to accelerate at 2 m/s2.(a) When does
the car pass the bike?(b) Where does this
happen?
(c) How fast is the car moving then (in m/s)?

• 10
• 0.1

• Equations
• vf vi a Dt
• xf xi vi t ½ a t2

4
Components of a Vector
PH 105-003/4Friday, Aug. 29, 2007

• A component is a projection of a vector along an
  axis
• Any vector can be completely described by its
  components
• It is useful to use rectangular components
• These are the projections of the vector along the
  x- and y-axes

5
Math Review
Trigonometry
c
a
sinQ a/c, cosQ b/c tanQ a/b
Q
b
c2 a2 b2
(Pythagorean Theorem)
V
vy
Example
Q
V 785 km/h, find Vx and Vy
Vx
Vx VsinQ 489 km/h Vy VcosQ 614
km/h CHECK 7852 4892 6142
6
Position and Displacement
PH 105-003/4Wednesday, September 5, 2007

• The position of an object is described by its
  position vector,
• The displacement of the object is defined as the
  change in its position

7
Instantaneous Velocity

• The instantaneous velocity is the limit of the
  average velocity as ?t approaches zero
• As the time interval becomes smaller, the
  direction of the displacement approaches that of
  the line tangent to the curve

8
Average Acceleration
9
Motion with Uniform Acceleration in 3D

• The velocity vector can be obtained from the
  definition of acceleration
• The position vector can be expressed as a
  function of time

10
Simplest case of uniformly-accelerated 2D
motionProjectile motion (free fall)
PH 105-003/4Friday, September 7, 2007

• a constant (0, -g, 0) -g j
• ax 0, ay -g, az 0

vx vix ax t x xi vix t ½ ax t2 vy
viy ay t y yi viy t ½ ay t2
vx vix (constant) x xi vix t vy viy gt
(NOT const.) y yi viy t ½ g t2
active figure 4.07
11
Clicker Question The dome light breaks off in a
car moving at a constant velocity 30 m/s. It
will hit the floor of the car
v 30 m/s
A
B
C

1. Directly under its starting point
2. Behind its starting point
3. Ahead of its starting point

12
Assumptions of Projectile Motion

• The free-fall acceleration is constant over the
  range of the motion
• It is directed downward
• This is the same as assuming a flat Earth over
  the range of the motion
• It is reasonable as long as the range is small
  compared to the radius of the Earth
• The effect of air friction is negligible
• With these assumptions, an object in projectile
  motion will follow a parabolic path (y x2)

13
Sample clicker question (test-taking skills)A
man walks 40 meters in 20 seconds. What is his
average velocity, in m/s?
PH 105-003/4 -- Monday, September 10, 2007

1. 0
2. 1
3. 2
4. 3
5. 4
6. 5
7. 6
8. 7

14
Sample clicker question (test-taking skills) A
man walks 40 meters in 20 seconds. What is his
average velocity, in m/s?

1. 0
2. 1
3. 2
4. 3
5. 4
6. 5
7. 6
8. 7

15
Range of a Projectile
vx vix (constant) x xi vix t vy viy gt
(NOT const.) y yi viy t ½ g t2
means where does it return to y0?
0 0 viy t ½ g t2
viy ½ g t
t 2viy/g
is when, not where!
x 0 vix t 2 vix viy /g 2 vicosq vi sinq
/g
16
Range of a Projectile
17
Uniform Circular Motion

• Trajectory is a circle, so
• ri ri r
• Use definitions of a, v
• Dv a Dt, Dr v Dt
• If Dq small,
• Dv v Dq, Dr r Dq, so
• aDt vDq, Dr, vDtr Dq
• Divide a/v v/r, or
• a v2 / r

18
Clicker question (vectors)A man walks 30 m
north, then 40 m east. The magnitude of his
total displacement is (in m)

1. 10
2. 30
3. 40
4. 50
5. 70

19
Clicker Question relative motionA UA student is
driving (horizontally) 40 m/s in a convertible
when 1 cm diameter hail starts to fall,
vertically at 30 m/s.The speed with which the
hail strikes her is

1. 30 m/s
2. 40 m/s
3. 50 m/s
4. 60 m/s
5. 70 m/s