P1246990955UKLCW

1
(No Transcript)
2
System and Surroundings
3
The Momentum Principle
Newtons second law A
fundamental principle

• cause-effect relationship
• change in momentum is in same direction as net
  force
• applies to each component of momentum
• net force is due to interaction of the system
  with the surroundings
• time interval is the duration of the interaction
• if no interaction, momentum of the system is
  constant

4
Conservation of momentum
If net force is zero (no net interaction), then
the systems momentum is constant. (Its an
isolated system.) Otherwise momentum is added to
(or subtracted from) the system. (Its an open
system.) The amount of momentum added to or
subtracted from the system is called impulse.
5
Superposition
If forces of N and N act
on a system, what is the net force on the system?
6
Momentum Update
If you know the initial momentum and the momentum
added to or subtracted from the system (impulse),
then you can calculate the final momentum.
7
Approximations
Exactly correct for constant net force! only
approximately correct for a small time interval.
As the time interval gets smaller, the
approximation becomes increasingly accurate.
8
Applying Newtons second law(the momentum
principle)

• Define your system.
• Make a list of objects in the surroundings that
  interact (via touching or action at a distance)
  with the system. Write the net force on the
  system.
• Choose the initial and final clock readings (or
  time interval).
• Write the initial and final momentum of the
  system.
• Apply the momentum principle and solve for
  unknowns. It may help to apply it in component
  form.
• Check whether your answer makes sense.

9
Example
A tennis ball (m0.057 kg) tossed upward by
Serena Williams is moving upward with a speed of
5 m/s at the instant it leaves her hand. 0.02 s
later, it is moving upward with a speed of 4.8
m/s. Sketch the change in momentum of the tennis
ball. Sketch the impulse on the tennis ball. What
is the net force on the ball during this time
interval?
10
Example
The tennis ball tossed by Serena is moving upward
at a speed of 0.1 m/s at some instant before it
reaches its peak, and 0.02 s later, after it has
reached its peak, it is moving downward at 0.1
m/s. Sketch the change in momentum of the tennis
ball during this interval. What is the direction
of the net force on the ball during this time
interval?
11
Example
Suppose you have a fan cart whose mass is 0.4 kg.
With the fan turned on, the force acting on the
cart due to the air and friction with the track
is N and constant. You give the cart
a push and release the cart at position 0 m with initial velocity m/s.
What is the momentum of the cart 3 seconds later?
12
(No Transcript)
13
Example
A 1000 kg car speeds up from 20 m/s to 22 m/s in
0.5 s while moving in the x direction. 1. What
is the net force on the car? 2. What objects are
interacting with the car during this time
interval? 3. If during this time interval, the
force of Earth on the car is N
and the force of the air on the car is 0 N, what is the force of the road on the car?
14
(No Transcript)
15
Poll
When a ball is tossed upward, what is the
direction of the net force on the ball when it is
at its peak?

• Upward
• Downward
• Neither because it is zero since the momentum of
  the ball is zero at its peak.

16
Poll
When a ball is tossed upward, what is the
direction of the balls change in momentum when
it is at its peak?

• Upward
• Downward
• Neither because it is zero since the momentum of
  the ball is zero at its peak.

17
Poll
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. The net
force is in the x direction B. The net force is
in the x direction C. The net force is zero 1)
A only 2) B only 3) C only 4) A and B 5) B and
C 6) A and C 7) A, B, and C
18
Poll
Cart A moves to the left at nearly constant
speed. Cart B moves to the left, gradually
speeding up. Cart C moves to the left, gradually
slowing down.
Which cart(s) experience(s) a net force to the
left? 1) A only 2) B only 3) C only 4) A and
B 5) B and C 6) A and C 7) A, B, and C
19
Poll
The x-component of momentum of an object is found
to increase with time t 0 s px 30 kg m/s t
1 s px 40 kg m/s t 2 s px 50 kg m/s t
3 s px 60 kg m/s What can you conclude
about the x-component of the net force acting on
the object? 1) Fnet,x 0 2) Fnet,x is
constant 3) Fnet,x is increasing with time 4) Not
enough information is given to determine which is
true.
20
Poll
A hockey puck is sliding along the ice with
nearly constant momentum kg m/s when
it is suddenly struck by a hockey stick with a
force N that lasts for only 3
milliseconds (3 x 10-3 s). What is the new
(vector) momentum of the puck? 1)
kgm/s 2) kgm/s 3) 14.86 kgm/s 4) 16, 0, 11 kgm/s 5) kgm/s
21
Poll
You push a book across a table. In order to keep
the book moving with constant momentum, you have
to keep pushing with a constant force. Which
statement explains this? 1) A net force is
necessary to keep an object moving. 2) To make
the net force on the book zero, you must push
with a force equal and opposite to the friction
force on the book. 3) The force you exert must be
slightly larger than the friction force.