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Ph sics 131:
Physics
131 Re
Review
ie
Agenda for Today

Review Ch 99-12 and 14
Physics 201: Lecture 1, Pg 1
Impulse-Momentum Theorem

An impulse on an object leads to a change in the objects
momentum. (This is a vector)
J x  p x
J x  pfx  pix
pfx  pix  J x

The momentum ‘after’ an interaction, like a collision or explosion,
equals the momentum before the interaction plus the impulse that
arises from the interaction.
Physics 201: Lecture 1, Pg 2
Clicker Question 1:
You drop an egg onto A) the floor B) a thick piece of
foam rubber
rubber. In both cases
cases, the egg does not bounce
(Assume the egg hits each surface with the same
speed).
I which
In
hi h case iis th
the magnitude
it d off the
th average force
f
greater?
t ?
A) Floor
B) Foam
C) It’s the same
Pre-class Quiz: This is why cars
have crumple zones, to increase
t and decrease the force.
J y  mv
Favg y t  mv
mv
Favg y 
t
Physics 201: Lecture 1, Pg 3
Conservation of Momentum

Newton’s
Newton
s second law for a system
 ext
Fnet


dp

dt
The total momentum of an isolated system remains constant

Isolated system
y
= no external forces
Physics 201: Lecture 1, Pg 4
Clicker Question 2:
A mosquito and a truck have a head-on collision. Which
h a llarger change
has
h
off momentum?
t ?
A. The mosquito.
B. The truck.
C. They have the same change of momentum.
D. Can
Can’tt say without knowing their initial velocities.
Physics 201: Lecture 1, Pg 5
Clicker Question 2.5:
Two blocks of masses m and 2m are placed in
contact on a horizontal, frictionless surface, with the
more massive block on the left. A force of
magnitude F = 10.0 N, pointing to the right, is
applied to the more massive block for a time of 5.00
s. What is the net impulse imparted to the more
massive block?
(A)
(B)
(C)
(D)
(E)
11.2 N-s
16.7 N-s
33
33.3
3N
N-ss
50.0 N-s
25.0
25 0 N-s
Ns
Physics 201: Lecture 1, Pg 6
Clicker Question 2.5:
Two blocks of masses m and 2m are placed in contact on a
horizontal, frictionless surface, with the more massive block on
the left. A force of magnitude F = 10.0 N, pointing to the right,
is applied to the more massive block for a time of 5
5.00
00 ss. What
is the net impulse imparted to the more massive block?
Physics 201: Lecture 1, Pg 7
Energy is Conserved

Energy is “Conserved”
Conserved meaning it can not
be created nor destroyed
g form
 Can change
 Can be transferred

Total Energy does not change with time.
This is a BIG deal!
Physics 201: Lecture 1, Pg 8
Collisions


Momentum is almost always conserved during as
collision (external forces are generally small
compared to collision forces)
T
Two
kinds
ki d off collisions
lli i
 Elastic-KE is conserved
 Very special case
 Inelastic-KE is not conserved
 Can be assumed if


Objects stick together
Damage is done during collision
Physics 201: Lecture 1, Pg 9
Elastic Collision
During
D
i an elastic
l ti collision
lli i b
both
th momentum
t
and
d
mechanical energy are conserved:

m1v1f  m2 v2 f  m1 v1i  m2 v2 i
1
2

(1)
m1v1f  m2 v 2 f  m1 v1i  m2 v 2 i
2
1
2
2
1
2
2
1
2
2
(2)
Combining equation (1) and (2) we get that
“speed of approach equals speed of recession”:
v2 f  v1f  v2 i  v1i 

Together with equation (1) you can solve for just about any
1 d elastic collision
1-d
Physics 201: Lecture 1, Pg 10
Clicker Question 3:
There are two identical carts (with the same mass) on
a frictionless straight horizontal track. Cart B is
initially stationary
stationary, and cart A collides into cart B.
B
Can A reverse its direction of motion after the
collision?
(A) No, never.
(B) Yes
Yes.
(C) It depends on the details of the collision.
Physics 201: Lecture 1, Pg 11
Problem
A ball of clay of mass m = 0.2
0 2 kg strikes a block of mass M =
8.0 kg which slides on a frictionless table as it compresses
a spring with spring constant k = 60 N/m. The initial speed
of the ball of clay is v = 12 m/s
m/s. The spring is initially at its
relaxed length. What is the maximum compression of the
spring, d, after the collision (the clay sticks to the block)?
Vafter collision = 0.29 m/s
x = 0.108 m
Physics 201: Lecture 1, Pg 12
Problem
A ball of clay of mass m = 0.2
0 2 kg strikes a block of mass M =
8.0 kg which slides on a frictionless table as it compresses
a spring with spring constant k = 60 N/m. The initial speed
of the ball of clay is v = 12 m/s
m/s. The spring is initially at its
relaxed length. What is the maximum compression of the
spring, d, after the collision (the clay sticks to the block)?
Vafter collision = 0.29 m/s
x = 0.108 m
Physics 201: Lecture 1, Pg 13
Clicker Question 4:
A pendulum consists of a mass m = 0.2 kg on the end
of a string of length L = 0
0.3
3m
m. At the moment the
mass at its lowest point, it is observed that the
speed of the mass is v = 2.2 m/s.
What can we say about the work Ws done by the
string?
A. Ws > 0
B. Ws < 0
C. Ws = 0
Physics 201: Lecture 1, Pg 14
The Work-Energy Theorem

Wtot = ½mvf2 - ½mvi2

Put positive work into an object, its speed
increases!

Put negative work into an object, its speed
decreases!

Be careful, we are interested in total work done!!!
 We
W mustt look
l k att all
ll forces
f
acting,
ti
nott just
j t one!!
Physics 201: Lecture 1, Pg 15
Clicker Question 5:
Suppose a cable pulls an elevator of mass M up a
height h at constant speed v.
v What is the net work
done (sum of the work done by all external forces)
on the elevator as it moves up this height h?
(A)
(B)
(C)
(D)
(E)
Mgh
0
(1/2) M v2
-Mgh
- (1/2) M v2
Physics 201: Lecture 1, Pg 16
The Work-Energy Theorem
Wtot = K
WC + WNC = K
WNC = K – WC
WNC = K + U
Physics 201: Lecture 1, Pg 17
Conservation of Mechanical Energy
G d when
Good
h only
l gravity
it or a spring-like
i
lik force
f
are doing
d i
work on an object
Emech f = Emech i
Kf + Uf = Ki + Ui
½ksf2 + ½mv
½k
½ f2 + mgh
hf = ½ks
½k i2 + ½mv
½ i2 + mgh
hi
Physics 201: Lecture 1, Pg 18
Clicker Question 6:
Ball A is dropped from rest from a window. At the same
instant, ball B is thrown downward; and ball C is thrown
upward from the same window. Which statement
concerning the balls is necessarily true if air resistance is
neglected?
A. At some instant after it is thrown, the acceleration of
ball C is zero
B. All three balls reach the ground with the same velocity
C. All three balls strike the ground at the same time
D All three balls have the same acceleration at any
D.
instant
E. All three balls have the same velocityy at anyy instant
Physics 201: Lecture 1, Pg 19
Two cases

First case: Point mass objects
 An object that is so small compared with its
distance from the axis we can forget about its
size
i and
d consider
id allll off iits mass acting
i at one
point
  = mr2

Second case: common objects around common
rotation axes
 Textbook pg 318
Physics 201: Lecture 1, Pg 20
Clicker Question 7:
Which dumbbell has the larger moment of inertia about the midpoint of the
rod? The connecting rod is massless.
A. Dumbbell A.
B Dumbbell
B.
D bb ll B
B.
C. Their moments of inertia are the same.
Physics 201: Lecture 1, Pg 21
Newton’s second law in rotation land



Sum of the torques will equal the moment of
inertia times the angular acceleration
 = 
An unbalanced net torque will result in an angular
acceleration
Physics 201: Lecture 1, Pg 22
Clicker Question 8:
Which third force on the wheel, applied at point P, will make the net
torque zero?
Physics 201: Lecture 1, Pg 23
Positive vs. Negative torque


Torque can be positive or negative
Call counterclockwise positive rotation
Positive rotation
F1
F2

F1 wants to rotate negative; F2 positive
Physics 201: Lecture 1, Pg 24
Static Equilibrium

An object is in static equilibrium if all the forces and
torques acting on it sum to zero

FX = 0 and
d FY = 0

As well

We will learn to apply these laws to problems and solve
for various unknowns
 = 0
Physics 201: Lecture 1, Pg 25
Clicker Question 9:
Which object is in static equilibrium?
Physics 201: Lecture 1, Pg 26
Clicker Question 10:
A 1-kg ball is hung at the end of a rod
1-m long.
g If the system
y
balances at a p
point on the rod 0.25 m from the
end holding the mass, what is the mass of the rod?
a) ¼ kg
b) ½ kg
1m
c) 1 kg
d) 2 kg
1kg
e) 4 kg
Physics 201: Lecture 1, Pg 27
Clicker Question 10:
1m
1kg
Physics 201: Lecture 1, Pg 28
Clicker Question 11:



A uniform p
plank ball has a mass 2M and a bowling
g ball
has a mass M. The length of the plank is 5m and it rests
horizontally on two supports, as shown in the drawing,
with 2m of the p
plank hanging
g g over the right
g support.
pp
To what distance xtip (measured from the right-most
support) can the bowling ball be rolled onto the
overhanging part of the plank before the plank just begins
to tip?
(a) xtipp = 0.3 m
(b) xtip = 0.5
05m
(c) xtip = 0.7 m
(d) xtipp = 0.8 m
(e) xtip = 1.0 m
Physics 201: Lecture 1, Pg 29
Clicker Question 11:
Physics 201: Lecture 1, Pg 30
Linear and Angular
g
Linear
Displacement s
Velocity
y
v
Acceleration a
Inertia
m
K
½ m v2
N2L
F = ma
Momentum
p = mv
Angular



I
½ I 2
 = I
L = Iw
Physics 201: Lecture 1, Pg 31
Conservation of Angular Momentum
Newton’s
Newton
s second law for rotations



L
 ext 
t

The angular momentum of an isolated system is conserved
Physics 201: Lecture 1, Pg 32
Clicker Question 12:
You are holding a spinning bicycle wheel while standing on a
stationary turntable. If you suddenly flip the wheel over so that it is
spinning in the opposite direction, the turntable will:
a) remain stationary
b) start to spin in the same
direction as before flipping
c) to spin in the same direction as
after flipping
Physics 201: Lecture 1, Pg 33
Clicker Question 13:
You want to measure the moment of inertia for a rotating oval
object. Initially, this object has an angular speed of 35 rad/s.
You drop a ring of mass 30 kg and radius 0
0.2
2 m on top of the
object. The ring and object apply frictional forces on each other
and eventually come to have the same angular speed of 24
rad/s.
What is the moment of inertia of the object?
(a) 4.67 kg m2
( ) 2.62 kg m2
(b)
(c) 3.45 kg m2
((d)) 8.92 kg
g m2
i
2
(e) 1.23 kg m
initial
ring
f
final
Physics 201: Lecture 1, Pg 34
Clicker Question 14:
A 15 kg uniform disk of radius R = 0.25 m has a string
wrapped around itit, and weight is hanging on the string
with m = 4.1 kg. The system of the weight and disk is
released from rest. When the 4.1 kg weight is moving
with a speed of 1
1.5
5 m/s
m/s, what is the angular speed of the
disc?
(a)
(b)
(c)
(d)
(e)
0.375 rad/s
0.5 rad/s
1.5 rad/s
6 rad/s
8 rad/s
Physics 201: Lecture 1, Pg 35
Clicker Question 15:
A 15 kg uniform disk of radius R = 0.25 m has a string
wrapped around itit, and weight is hanging on the string
with m = 4.1 kg. The system of the weight and disk is
released from rest. When the 4.1 kg weight is moving
with a speed of 1
1.5
5 m/s
m/s, what is the kinetic energy of the
entire system?
(a)
(b)
( )
(c)
(d)
(e)
13 J
4.6 J
7.8
8J
15 J
9
9.2
2J
Physics 201: Lecture 1, Pg 36
Clicker Question 16:
A 15 kg
g uniform disk of radius R = 0.25 m has a string
g
wrapped around it, and weight is hanging on the string
with m = 4.1 kg. The system of the weight and disk is
released from rest. When the 4.1 kg
g weight
g is moving
g
with a speed of 1.5 m/s, what is the kinetic energy of the
entire system?
Physics 201: Lecture 1, Pg 37
Clicker Question 17:
A 15 kg uniform disk of radius R = 0.25 m has a string
wrapped around itit, and weight is hanging on the string
with m = 4.1 kg. The system of the weight and disk is
released from rest. When the 4.1 kg weight is moving
with a speed of 1
1.5
5 m/s
m/s. If the system started at rest
rest,
how far has the weight fallen in this time?
(a)
1.2 m
(b)
0.5 m
(c)
0.3 m
(d)
0
0.9
9m
(e)
3.17 m
Physics 201: Lecture 1, Pg 38
Clicker Question 18:

An 0.80 kg object is attached to one end of a spring, and
the system is set into simple harmonic motion
motion. The
displacement of x of the object as a function of time is
shown in the drawing. What is the angular frequency ?
(a)
(b)
(c)
(d)
(e)
4 rad/s
0
0.25
25 rad/s
1.57 rad/s
15
5 rad/s
ad/s
2.2 rad/s
What is the frequency f?
Physics 201: Lecture 1, Pg 39
Clicker Question 19:

An 0.80 kg object is attached to one end of a spring, and
the system is set into simple harmonic motion
motion. The
displacement of x of the object as a function of time is
shown in the drawing. What is the magnitude of the
speed of the object at t = 2 s?
( )
(a)
(b)
(c)
(d)
(e)
0.4 m/s
0 m/s
0.13 m/s
0.78 m/s
2.0 m/s
Physics 201: Lecture 1, Pg 40
Clicker Question 20:

An 0.80 kg object is attached to one end of a spring, and
the system is set into simple harmonic motion
motion. The
displacement of x of the object as a function of time is
shown in the drawing. What is the magnitude of the
acceleration of the object at t = 1 s?
( )
(a)
(b)
(c)
(d)
(e)
4 m/s2
0 m/s2
1.64 m/s2
0.20 m/s2
2.0 m/s2
Physics 201: Lecture 1, Pg 41
Clicker Question 21:

An 0.80 kg object is attached to one end of a spring, and
the system is set into simple harmonic motion
motion. The
displacement of x of the object as a function of time is
shown in the drawing. What is the spring constant k?
(a)
(b)
(c)
(d)
(e)
4 N/m
0.25
0 25 N/m
1.28 N/m
0
0.78
8 N/m
/
2.0 N/m
Physics 201: Lecture 1, Pg 42