Download Lecture 15 - USU Department of Physics

Physics of Technology
PHYS 1800
Lecture 15
Introduction
Section 0
Momentum
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 1
PHYSICS OF TECHNOLOGY
Spring 2009 Assignment Sheet
Date
Day
Lecture
Chapter
Jan 5
M
Class Admin: Intro.Physics Phenomena
1
6
T
Problem solving and math
App. B, C
7
W
Units, Scalars, Vectors,
1
9
F*
Speed and Velocity
2
Jan 12
M
Acceleration
2
14
W
Free Falling Objects
3
16
F*
Projectile Motion
3
Jan 19
M
Martin Luther King
No Class
21
W
Newton’s Laws
4
23
F*
Mass and Weight
4
Jan 26
M
Motion with Friction
4
28
W
Review
1-4
1-4
29
Th
Test 1
30
F
Circular Motion
5
Feb 2
M
Planetary Motion and Gravity
5
4
W
Energy
6
6
F*
Harmonic Motion
6
Feb 9
M
Momentum
7
11
W
Impulse and Collisions
7
13Introduction
F*
Rotational
8
Section
0 Motion
Lecture 1 Slide 2
Feb 16
M
Presidents Day
No Class
17
Tu
Angular Momentum (Virtual Monday)
8
18
W
Review
5-8
19
5-8
H
Test 2
INTRODUCTION TO Modern Physics PHYX 2710
20
F*
Static Fluids, Pressure
9
Fall 2004
Feb 23
M
Flotation
9
*Homework
25
WHandout
Fluids in Motion
9
27
F*
Temperature and Heat
10
Mar 2
M
First Law of Thermodynamics
10
Physics of Technology—PHYS 1800
4
W Spring 2009Heat flow and Greenhouse Effect Momentum
10
6
F*
Climate Change
-
Homework Due
-
1
2
3
4
5
-
6
Lecture 15 Slide 2
7
Physics of Technology
PHYS 1800
Lecture 15
Momentum
Introduction
Section 0
Lecture 1
Slide 3
Introduction
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 3
Describing Motion and Interactions
Position—where you are in space (L or meter)
Velocity—how fast position is changing with time (LT-1 or m/s)
Acceleration—how fast velocity is changing with time (LT-2 or m/s2)
Force— what is required to change to motion of a body (MLT-2 or kg-m/s2 or N)
Energy—the potential for an object to do work. (ML2T-2 or kg m2/s2 or N-m or J)
Work is equal to the force applied times the distance moved. W = F d
Kinetic Energy is the energy associated with an object’s motion. KE=½ mv2
Potenital Energy is the energy associated with an objects position.
Gravitational potential energy PEgravity=mgh
Spring potential energy PEapring= -kx
Introduction
Section 0
Lecture 1
Slide 4
In this chapter we will develop the concept of…MOMENTUM…and and its associated law of
Conservation of Momentum and apply this to collisions.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 4
Defining Work
• Work is equal to the force applied times the
distance moved.
– Work = Force x Distance:
– Work output = Work input
W=Fd
• units: 1 joule (J) = 1 Nm = 1 kg m2 / s2 [ML2T-2]
Introduction
Section 0
Lecture 1
Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 5
Momentum and Collisions
• How can we describe the change in velocities of
colliding football players, or balls colliding with bats?
• How does a strong force applied for a very short time
affect the motion?
• Can we apply Newton’s Laws to collisions?
• What exactly is momentum? How is it different from
force or energy?
• What does “Conservation of Momentum” mean?
Initial time
Δt=tfinal – tinitial
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
ΔW=F Δd
Slide 6
with Δd=dfinal – dinitial
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Final time
Δp=F Δt
Momentum
with Δt=tfinal – tinitial
Lecture 15 Slide 6
What happens when a ball bounces?
• When it reaches the floor, its
velocity quickly changes
direction.
• There must be a strong force
exerted on the ball by the floor
during the short time they are
in contact.
• This force provides the
upward acceleration necessary
to change
the direction
of the1 Slide
Introduction
Section 0 Lecture
ball’s velocity.
7
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 7
What happens when a ball bounces?
• Forces like this are difficult
to analyze:
• Strong forces that act for
a very short time.
• Forces that may change
rapidly during the collision.
• It will help to write Newton’s
second law in terms of the
total change in velocity over
time, instead of acceleration:
Introduction
Section 0
Lecture 1
v 
Fnet  ma  m 
t 
Slide 8
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 8
Momentum and Impulse
• Multiply both sides of Newton’s second law
by the time interval over which the force acts:
• The left side of the equation is impulse, the
(average) force acting on an object multiplied
by the time interval over which the force acts.
 v 
Fnet  ma  m

 t 
Fnet t  mv
• How a force changes the motion of an object
depends on both the size of the force and how
long the force acts.
• The right side of the equation is the change
in the momentum of the object.
Introduction
Section 0
Lecture 1
Slide 9
• The momentum of the object is the mass of
the object times its velocity.
p  mv
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009

Momentum
Lecture 15 Slide 9
Momentum and Impulse
A bowling ball and a tennis ball can have the same momentum, if
the tennis ball with its smaller mass has a much larger velocity.
Introduction
Section 0
Lecture 1
Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 10
Impulse-Momentum Principle
The impulse acting on an object produces a change
in momentum of the object that is equal in both
magnitude and direction to the impulse.
impulse = change in momentum
= p
In analogy,
Introduction
Section 0

Lecture 1
work
INTRODUCTION TO Modern Physics PHYX 2710
Slide 11
= change in energy
= ΔE
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 11
Impulse-Momentum Principle
When a ball
bounces back
with the same
speed, the
momentum
changes from
mv to -mv, so
the change in
momentum is
2mv. Introduction
Section 0
Lecture 1
Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 12
A Closer Look at Collisions
Look
here
carefully!
Introduction
Section 0
Lecture 1
Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 13
Compression on an Atomic Scale
Bonds between atoms in a compressed solid can be treated as
compressed springs.
+
+
+
+
Ultimately the forces come from electrostatic interactions
between electrons and protons (and a little quantum mechanics).
+
+
Section 0
Lecture 1
Slide 14
+
+
Introduction
Fspring=-k Δx
+
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 14
What Happens During the Collision?
• Does Newton’s third law
still hold?
– For every action, there is an
equal but opposite reaction.
– The defensive back exerts a
force on the fullback, and the
fullback exerts an equal but
opposite force on the
defensive back.
Introduction
Section 0
Lecture 1
Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 15
Conservation of Momentum
• Does Newton’s third law
still hold?
– For every action, there is an
equal but opposite reaction.
– The defensive back exerts a
force on the fullback, and the
fullback exerts an equal but
opposite force on the
defensive back.
Introduction
Section 0
Lecture 1
Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 16
Conservation of Momentum
– The impulses on both
are equal and opposite.
– The changes in
magnitude for each are
equal and opposite.
– The total change of the
momentum for the two
players is zero.
Introduction
Section 0
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 17
Conservation of Momentum
If the net external
force acting on a
system of objects
is zero, the total
momentum of the
system is
conserved.
Introduction
Section 0
Lecture 1
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 18
A 100-kg fullback moving straight downfield collides with a 75-kg
defensive back. The defensive back hangs on to the fullback, and
the two players move together after the collision. What is the
initial momentum of each player?
Introduction
Section 0
Lecture 1
Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 19
What is the initial momentum of each player?
Fullback:
p = mv
= (100 kg)(5 m/s)
= 500 kg·m/s2
Introduction
Section 0
Lecture 1
Defensive back:
p = mv
= (75 kg)(-4 m/s)
= -300 kg·m/s2
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 20
What is the total momentum of the system?
Total momentum:
ptotal = pfullback + pdefensive back
= 500 kg·m/s - 300 kg·m/s
= 200 kg·m/s
Introduction
Section 0
Lecture 1
Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 21
What is the velocity of the two players immediately after the collision?
Total mass:
m = 100 kg + 75 kg
= 175 kg
Velocity of both:
v = pIntroduction
m 0 Lecture 1 Slide 22
total / Section
= (200 kg·m/s) / 175 kg
= 1.14 m/s
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 22
Recoil
• Why does a shotgun slam against your shoulder
when fired, sometimes painfully?
• How can a rocket accelerate in empty space
when there is nothing there to push against
except itself?
Introduction
Section 0
Lecture 1
Slide 23
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 23
Physics of Technology
Next Lab/Demo:
Energy & Oscillations
Momentum and Collisions
Thursday 1:30-2:45
ESLC 53
Ch 6 and 7
Next Class:
Wednesday 10:30-11:20
BUS 318 room
Review
Ch 6
Slide 24
Read Ch 7
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Momentum
Lecture 15 Slide 24