Section 2.1-2.3, 2.9
motion is neither created nor destroyed, but transferred via interactions.
Q1.9.a:
A child rides on a merry-go-round,
traveling from location A to
location C at a constant speed.
What is the direction of the
change in the child’s momentum,
between locations A and C?
A
B
C
D
E
Q1.9.c:
Suppose you are driving a 1000 kg car at 20 m/s in the +x
direction. After making a 180 degree turn, you drive the car
at 20 m/s in the –x (opposite) direction. What is the
magnitude of the change of the momentum ∆𝒑 of the car ?
a)
b)
c)
d)
e)
0 kg· m/s
2.0x104 kg· m/s
4.0x104 kg· m/s
6.0x104 kg· m/s
8.0x104 kg· m/s
2.2 Momentum Principle
Motion system 
 Interactio ns
 Impulse
all . external
Momentum system 

psystem 
all . external

I
all . external
 
I  Ft
Q 2.2 a
An object is moving in the +x direction.
Which of the following statements about the net force acting on the
object could be true?
a)
b)
c)
d)
e)
f)
g)
The net force is in the +x direction
The net force is in the –x direction
The net force is zero
A and B
B and C
A and C
A, B and C
Q 2.2 b
Three carts are moving on three tracks. Which cart(s) experience a net
force to the left?
A.
B.
C.
D.
E.
F.
Green Cart which moves to the left at constant speed.
Red Cart which moves to the left, gradually speeding up.
Blue Cart which moves to the left, gradually slowing down.
Both Green and Red carts
Both Blue and Red carts
Both Green and Blue carts
Problem-Solving Style Example
A hockey puck is sliding along the ice with nearly constant momentum
< 10, 0, 5 > kg m/s when it is suddenly struck by a hockey stick with a force < 0, 0, 2000 > N
that lasts for only 3 milliseconds (3x10-3 s). What is the new (vector) momentum of the puck?
•Draw a diagram.
•Define the “system.”
•Meaningful and distinct symbols for the given and desired quantities.
•Mathematical relations phrased in terms of these symbols before numbers are used.
•Clear & Correct algebra
•Units accompanying all numbers.
•Correct Answer submitted in WebAssign
Q 2.3 d: You practice on paper like homework
Inside a spaceship in outer space there is a small steel ball. At a
particular instant, the ball has momentum < -8, 3, 0 > kg· m/s and is
pulled by a string, which exerts a force < 20, -10, 0 > N on the ball.
What is the ball’s (vector) momentum 2 seconds later?
A.
B.
C.
D.
E.
< -28, 23, 0 > kg· m/s
< 12, -7, 0 > kg· m/s
36.2 kg· m/s
< 32, -17, 0 > kg· m/s
< 40, -20, 0 > kg· m/s
Students collide
•
•
•
•
•
•
•
•
•
•
The initial momentum of the one-student system is nonzero.
The initial momentum of the two-student system is zero.
We're interested in the force exerted on one student, so we apply the Momentum
Principle to a system consisting of one student.
We can estimate Δt from the compression distance in the collision.
The final momentum of the one-student system is nonzero.
The net force on the two-student system is zero because the interatomic force
exerted by student 1 on student 2 is equal in magnitude but opposite in direction
to the force exerted by student 2 on student 1.
A good estimate of the initial speed of one of the running students is 0.1 m/s.
The Momentum Principle can't be applied in this analysis because we have no way
of estimating Δt.
The final momentum of the two-student system is nonzero.
The Momentum Principle when applied to the two-student system is simply 0 = 0
and doesn't give us any information.
Updating Position in Computer
Simulations
Position Update (ch
 1)
robject new  robjectold  vobjectave t

vobjectave 

pobjectave
mobject
t
Update
(ch 2)

 Momentum

pobjectnew  pobjectold  Fnet object ave t
Note: If t is small enough, old speed is close enough to average, old force is
close enough to average to approximate in simulation.
A “while loop”
while t<tmax
t  t  t



pobject  pobject  Fnet object t

p


object
robject  robject 
t
mobject
1-D Motion fan cart (1-D). Suppose you have a fan cart whose mass is 400 gram
and it’s on a huge, 8m long track. Initially you set the cart moving down the track in
the x-direction at location <0.5,0,0>m with velocity <1.2,0,0>m/s. The force due to the
fan is <0.2,0,0>N; comparatively, friction is negligible. What are the momentum and
position of the cart 3 seconds later?