Kgg
Name: _____________________
Period: _____________________
Momentum and Impulse
Momentum
Momentum is how hard it is to stop something
and is a product of an object’s mass and its
velocity. Momentum is increased if either
the mass or velocity is increased.
Increasing mass
increases momentum.
Momentum is a vector
p = mv
m = 30 kg
v = 4 m/s
Velocity (in m/sec)
v = 5 m/s
p = 40 kgm/s
2 kg
v = 3 m/s
p = 0 kgm/s
v = -3 m/s
p = -6 kgm/s
If a vector is at an angle, you can
find its components.
If in one dimension,
just add or subtract.
Net momentum can be negative.
Sum of all
Momentum
2 kg
pnet = Σp
Σp = p1 + p2 + …
8 kg
v = 3 m/s
p = 6 kgm/s
p=
py =
12(sin30º)
= 6 kgm/s
12
kgm
/s
Net momentum can be zero.
6 kg
v = -3 m/s
p = -24 kgm/s
pnet = Σp = 6 – 24 = –18 kgm/s
Add up all of the momentums
v = 3 m/s
p = 18 kgm/
9 kg
v = -2 m/s
p = -18 kgm/s
Net momentum
can be also
be zero if all
of the objects
are at rest.
pnet = Σp = 18 – 18 = 0 kgm/s
An impulse is a force acting over time. Impulse is like work: an impulse causes a change
of momentum, just like work causes a change of energy.
Impulse
Force
(in N)
I = Ft
I
I = ∆p
Time
(in sec)
An impulse changes momentum.
+I
3 sec
8N
= pafter
v = 8 m/s
m=
3 kg
pbefore + Impulse = pafter
0 kgm/s + 24 kgm/s = 24 kgm/s
JI = ∆p = 8(3) = 24 kgm/s
cstephenmurray.com
30º
Together multiple objects have a net momentum. Net momentum is easy to calculate.
Calculate each individual momentum and add them together.
Net Momentum
m=
3 kg
px = 12(cos30º) = 10.4 kgm/s
You add momentum vectors like
all other vectors: find components;
find total x and y; etc.
(See “Adding Vectors”)
ptotal = +8 kgm/s
pbefore
v = 0 m/s
direction
Being a vector, momentum must have magnitude and direction and must be treated
like all vectors. It can have components and can be added or subtracted.
p2 = -4 kgm/s
Impulse
(in kgm/sec)
Momentum can
be negative.
2 kg
p1 = +12 kgm/s
sit
p = mv = (30kg)(4m/s)
= 120 kgm/s
Something must be moving
to have momentum.
8 kg
v = 3 m/s
p = 24 kgm/s
v = 3 m/s
p = 6 kgm/s
Momentum
(in kgm/sec)
Increasing velocity
increases momentum.
8 kg
2 kg
Net
Momentum
Ex. Calculate the momentum of
a 30 kg object going 4 m/s?
Mass (in kg)
Ex. Calculate the impulse of a
4 N force acting for 6 seconds.
F=4N
t = 6 sec
I = _____
I = Ft = (4)(6)
= 24 kgm/s = ∆p
A positive impulse causes a
positive change of momentum.
before
2 kg
vB = 3 m/s
pB = 6 kgm/s
after
+6N
2 sec
2 kg
vA = 9 m/s
pA = 18 kgm/s
∆p = pf – pi = 18 – 6
= 12kgm/s = 6(2) = Impulse
It sets
Force ≠ impulse. A small force
can cause the same impulse as a
big force if it acts for enough time.
100 N (1 sec) = 100 kgm/s
1 N (100 sec) = 100 kgm/s
A negative impulse causes a
negative change of momentum.
before
2 kg
vB = -1 m/s
pB = -2 kgm/s
after
-4N
1 sec
2 kg
vA = -3 m/s
pA = -6 kgm/s
∆p = pf – pi = -6 – (-2) = -6+2
= -4kgm/s = -4(1) = Impulse
Copyright © 2009, C. Stephen Murray
Name: _____________________
Period: _____________________
10. Can an object have momentum in space?
1. Momentum
A. pf – pi.
2. Impulse
B. Equal to Σp.
3. ∆p
C. It is important to know how big and in
what direction.
11. If you increase a moving object’s mass, how does its
momentum change?
4. Vector
D. How an object changes momentum.
5. Magnitude
E. The “25” in 25 kgm/s.
12. If an object changes momentum there must be a change of
___________ or __________.
6. pnet
velocity
mass
F. The product of mass and velocity.
Which has more momentum?
velocity is negative
14. How can an object have the same speed and mass, but
change its momentum?
0
7. A bowling ball at rest or a bowling ball going 1 m/s?
8. A fast baseball or a slow bowling ball?
13. How can momentum be negative?
Direction changes
15. How can multiple objects have a net momentum of zero?
O
9. A 1000 kg object at rest or a 1 kg object moving 0.2 m/s?
Ifall
objects are at rest
A.
B.
C.
D.
3 kg
3 kg
3 kg
3 kg
Mass A
Mass B
Mass C
Mass D
v = 0 m/s
v = -4 m/s
6 kg
4 kg
1 kg
6 kg
v = 0 m/s
v = -2 m/s
v = 5 m/s
v = 2 m/s
Above shows an object at different positions.
v = 5 m/s
v = 3 m/s
16. Calculate the object’s momentum at position A.
ISkgints
19. Calculate pnet of A and B above.
42kgm s
17. Calculate ∆v between positions A and B.
20. Calculate pnet of B and D .
m s
Okays
18. Calculate ∆p between positions B and D.
6 125 6kgm
21. Calculate pnet for all four objects.
s
22. 6 N pushes to the right on a 3 kg mass for 8 seconds.
A. Calculate the impulse.
30kgm s
24. Draw the net momentum for the following:
p2
848
B. How much momentum was gained by the object?
23. A 15 N force pushes on an object for 10 seconds. How
much momentum did it gain?
is
p3
p1
25. Find the px and py of the following object.
26. A 4 kg object is moving 2 m/s to the right. A 6 N force
pushes to the left for 3 seconds.
A. Calculate pbefore.
8kg s
/s
m
N
kg θ = 42º
6
Peel 8kg.ms
Py 16.1kgms
27. A 20 kg object is at rest. A 6 N force pulls to the right on
the object for 10 seconds.
A) Find the impulse on the object.
18
C. What is ∆p for this object?
Go
What is it’s 60
final velocity?
B) Find the final momentum of the object.
10h8m1s
D. What is its final momentum (pf )?
cstephenmurray.com
=
i
B. Calculate the impulse.
10kg
v
4
s
C)
Girls
Copyright © 2009, C. Stephen Murray