Download Momentum - barransclass

Group Work
1. A 10-kg box slides on a level floor.
a. Make a force diagram for it.
b. What is its weight?
c. Its coefficient of kinetic (sliding) friction
against the floor is mk = 0.5. What is the
force of friction between box and floor?
d. What is the acceleration of the box?
2. What would the answer to d be if the
box’s mass were 20 kg?
Announcements
• Exam 1 on Moodle today
– Opened 6 AM
– Closes midnight
• 1.5-hour time limit
• Open-note, open-book, etc.
• No consultation or collaboration permitted
Momentum
the quantity of motion
Objectives
• Define momentum.
• Define impulse and describe its
relationship to momentum.
What’s the point?
• Nature keeps careful account of
momentum.
Think Question
Which process requires more time?
A. Pulling as hard as you can to accelerate a little
red wagon from rest to a speed of 1 m/s.
B. Pulling as hard as you can to accelerate a
horse trailer from rest to a speed of 1 m/s.
C. The two take the same amount of time.
Think Question
Which process requires more force?
A. Accelerating a little red wagon from rest to a
speed of 1 m/s in ten seconds.
B. Accelerating a horse trailer from rest to a speed
of 1 m/s in ten seconds.
C. The two take the same force.
Example Problem
Show that when a constant net force F is
applied to an object of mass m for a time Dt,
its change in velocity is
FDt
Dv = m
Strategy: We can find acceleration using Newton’s
second law a = F/m. Then we can find Dv using
the definition of acceleration a = Dv/Dt.
Group Work
3. From mass m, net force F, and duration Dt,
find acceleration a and velocity change Dv.
Dt
m
F
1 kg
10 N
1s
1 kg
10 N
10 s
1 kg
1N
10 s
10 kg
10 N
10 s
a
Dv
J Dp
Impulse
Impulse = FDt
where
F Is net force
Dt is duration
Impulse is a vector.
Think Question
Two objects of different masses move at the
same speed. Which one is harder to stop?
A. The lighter object.
B. The more massive object.
Think Question
Two objects with the same mass move at
different speeds. Which one is harder to
stop?
A. The faster object.
B. The slower object.
Momentum
Formula
p = mv
momentum is a vector.
Think Question
Two spaceships have the same velocity, with
one’s mass twice the other’s. The heavy one’s
momentum is:
A.
B.
C.
D.
E.
more than twice the light one’s momentum.
twice the light one’s momentum.
the same as the light one’s momentum.
half the light one’s momentum.
less than half the light one’s momentum.
Think Question
Two spaceships have the same mass, but one’s
speed is twice the other’s. The faster one’s
momentum is:
A.
B.
C.
D.
E.
more than twice the slower one’s momentum.
twice the slower one’s momentum.
the same as the slower one’s momentum.
half the slower one’s momentum.
less than half the slower one’s momentum.
Group Work
4. From m, F, Dt, Dv, find impulse J and
momentum change Dp.
m
F
Dt
1 kg
10 N
1s
1 kg
10 N
10 s
1 kg
1N
10 s
10 kg
10 N
10 s
J
Dp
Group Work
5. Show that when a net force F is applied
to an object of mass m for a time Dt, its
change in momentum is
Dp = FDt
Hint: You can find its momentum change
from its mass and its velocity change.
Impulse-Momentum Theorem
• Impulse = FDt.
• FDt = maDt = mDv = D(mv) = Dp
• So impulse = change in momentum
Poll Question
Which changes its momentum the most?
A. A moving object that stops when it hits a
barrier.
B. A moving object that bounces back from
a barrier.
Hints: How is Dp defined?
Momentum is a vector.
Which receives the greater impulse?
Rebound and Momentum
final p – initial p
initial p
final p
Dp
final p – initial p
initial p
final p = 0
Dp
Reading for Next Time
• Newton’s third law
• Conservation of momentum
• Big ideas:
– Forces are always between objects
– Objects trade momentum when they interact