Download Lecture 8 Final (with examples)

Today’s Lecture:
• Kinematics in Two Dimensions (continued)
• Relative Velocity
- 2 Dimensions
• A little bit of chapter 4: Forces and Newton’s
Laws of Motion (next time)
29 September 2009
1
Question – the moving walkway
(problem 3.50): A moving walkway
(speed ramp) at an airport is a moving conveyor belt on which you
can either stand or walk. It is intended to get you from place to
place more quickly. Suppose a moving walkway is 120 m long.
When you walk at a comfortable speed on the ground, you cover
this distance in 86 s. When you walk on the moving walkway at
this same comfortable speed, you cover this distance in 35 s. The
speed of the moving walkway relative to the ground is:
(a) 1.4 m/s
(b) 2.0 m/s
(c) 2.4 m/s
(d) 3.4 m/s
(e) 4.8 m/s
Relative Velocity (2 Dimensions)
Velocity of car A relative to car B is:





vAB  vAG  vGB  vAG  vBG
Magnitude:
2
2
v AB  v AG
 vGB
Direction:
 15.8 
 32.3

 25.0 
  tan1 
29 September 2009

 25 
2
 15.8 
2
 29.6 m s
3
Crossing a river (example 3.11):
The engine of a boat drives it across a
river that is 1800m wide. The velocity of
the boat relative to the water is 4.0 m/s
directed perpendicular to the current. The
velocity of the water relative to the shore
is 2.0 m/s.
(a) What is the velocity of the boat
relative to the shore?
(b) How long does it take for the
boat to cross the river?
Crossing a river
(a) What is the velocity of the boat
relative to the shore?
vBS  vBW  v WS
2
2
v BS  v BW
 vWS

 4.0m s    2.0m s 
2
2
 4.5m s
1 
4.0 
  tan 
 63

 2.0 
(b) How long does it take for the
boat to cross the river?
t
1800 m
 450 s
4.0m s
Problem 3.53:
A hot air balloon is moving relative to the ground at
6.0 m/s due east. A hawk flies at 2.0 m/s due north
relative to the balloon.
What is the velocity of the hawk relative to the ground?
29 September 2009
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Example – falling rain (problem 3.70): A person looking out the
window of a stationary train notices that raindrops are falling
vertically down at a speed of 5.0 m/s relative to the ground.
When the train moves at constant velocity, the raindrops make an
angle of 25 as they move past the window. How fast is the train
moving?
Problem 3.56:
Relative to the ground, a car has a velocity of 18.0 m/s,
directed due north. Relative to this car, a truck has a
velocity of 22.8 m/s, directed 52.1 degrees south of east.
Find the magnitude and direction of the truck’s velocity
relative to the ground .
29 September 2009
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Problem 3.57:
A hockey player is skating due south at a speed of 7.0
m/s relative to the ground. A teammate passes the puck to
him.The puck has a speed of 11 m/s relative to the ground
and is moving in a direction 22 degrees west of south.
Find the magnitude (relative to the ground) and direction
(relative to due south) of the puck’s velocity as observed
by the hockey player.
SUBTRACTION RULE:
The resultant vector head

v HG
Always points toward the

head
v PG
of the vector that is being
subtracted from.





vPH  vPG  vGH  vPG  vHG
29 September 2009
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29 September 2009
10
Chapter 4
Forces and Newton’s
Laws of Motion
Chapter 4: Forces and Newton’s Laws
•Force, mass and Newton’s three laws of motion
•Newton’s law of gravity
•Normal, friction and tension forces
•Apparent weight, free fall
•Equilibrium
Force and Mass
Forces have a magnitude and direction – forces are vectors
Types of forces :
• Contact – example, a bat hitting a ball
• Non-contact or “action at a distance” – e.g. gravitational force
Mass (two types):
• Inertial mass – what is the acceleration when a force is applied?
• Gravitational mass – what gravitational force acts on the mass?
Inertial and gravitational masses are equal.
Arrows are used to represent forces. The length of the arrow
is proportional to the magnitude of the force.
15 N
5N
Inertia is the natural tendency of an object to remain at rest or
in motion at a constant speed along a straight line.
The mass of an object is a quantitative measure of inertia.
SI Unit of Mass: kilogram (kg)
SI unit of force:
m
1N  kg   2
s
Newton (N)
 kg  m

2
s

Newton’s Laws of Motion
1. Velocity is constant if a zero net force acts


a  0 if F  0
2. Acceleration is proportional to the net force and inversely
proportional to mass:

a

F
m


so F  ma
Force and acceleration are in the same direction
3. Action and reaction forces are equal in magnitude and
opposite in direction
Newton’s First Law (law of inertia)


Accelerati on a  0 if F  0
Object of mass m

Velocity v  constant
The velocity is constant if a zero net force acts on the mass.
That is, if a number of forces act on the mass and their vector sum is
zero:

 
Fnet  F1  F2  ....  0
So the acceleration is zero and the mass remains at rest or has
constant velocity.