Momentum 2009.pdf
Momentum 2009.pdf
Momentum 2009.pdf
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Linear <strong>Momentum</strong><br />
Sunday, November 21, 2010<br />
1
Homework Problems<br />
Nolan - Honors Physics<br />
4,5,7,10,16,19<br />
22,25,28,30,<br />
33,37,40,42,<br />
51,62,63,64<br />
Sunday, November 21, 2010<br />
2
<strong>Momentum</strong><br />
P=mv<br />
m = mass (kg)<br />
v = velocity (m/s)<br />
p = <strong>Momentum</strong><br />
“the quantity of motion”<br />
kg m/s<br />
Sunday, November 21, 2010<br />
3
Vector Quantity<br />
As with velocity before, the<br />
direction can be expressed by<br />
angle, map directions, or only<br />
a positive or negative<br />
Sunday, November 21, 2010<br />
4
Conservation of<br />
<strong>Momentum</strong><br />
In a closed system, the total<br />
momentum will remain a<br />
constant<br />
Sunday, November 21, 2010<br />
5
Linear Collisions<br />
Sunday, November 21, 2010<br />
6
Perfectly Inelastic<br />
In the inelastic collision the two<br />
objects have the same final velocity<br />
Sunday, November 21, 2010<br />
7
Example<br />
Mass A : Vi = 25 m/s<br />
m = 4 kg<br />
Mass B : Vi = -30 m/s<br />
m = 6 kg<br />
Find the Final Velocity After<br />
an Inelastic Collision<br />
Sunday, November 21, 2010<br />
8
Example<br />
Mass A : Vi = 25 m/s<br />
m = 4 kg<br />
Mass B : Vi = -30 m/s<br />
m = 6 kg<br />
From Conservation of <strong>Momentum</strong><br />
4(25) + 6(-30) = 4(Vaf) + 6(Vbf)<br />
100 + -180 = 10 (Vf)<br />
-80 = 10 Vf<br />
Vf = -8 m/s<br />
Sunday, November 21, 2010<br />
9
Mass A : Vi = 10 m/s<br />
m = 5 kg<br />
Mass B : Vi = -15 m/s<br />
m = 7 kg<br />
V f = 4 m/s<br />
(5)(10) + (7)(-15) = 5(Va) + 7(4)<br />
(50) + (-105) = 5(Va) + (28)<br />
Example<br />
Sunday, November 21, 2010<br />
10
Inelastic<br />
Coefficient of<br />
Restitution<br />
Values from 0-1<br />
A ratio of:<br />
Separation Velocity<br />
divided by the<br />
Approach Velocity<br />
Sunday, November 21, 2010<br />
11
Find the Coefficient<br />
V = 5 m/s<br />
V = - 3 m/s<br />
V = -1 m/s<br />
V = 3 m/s<br />
Sunday, November 21, 2010<br />
12
Find the Coefficient<br />
V a = 5 - (-3) = 8<br />
V = 5 m/s<br />
V = - 3 m/s<br />
V = -1 m/s<br />
V = 3 m/s<br />
V s = 3 - (-1) = 4<br />
Sunday, November 21, 2010<br />
13
Coefficient of Restitution<br />
e = Vs / Va<br />
e = (V aF - V bF ) / (V bI -V 1aI )<br />
For the example: e = 0.5<br />
Sunday, November 21, 2010<br />
14
Inelastic Example<br />
An object hits a wall with<br />
a velocity of 5 m/s.<br />
e = 0.4<br />
Find the return velocity.<br />
Sunday, November 21, 2010<br />
15
Inelastic Example<br />
An object hits a wall with a<br />
velocity of 5 m/s. e = 0.4<br />
Va = 5 - 0 = 5 (as expected)<br />
Vs = .4 (5)<br />
2 m/s = 0 - Vf<br />
Vf= -2 m/s<br />
Sunday, November 21, 2010<br />
16
Perfectly Elastic<br />
In the elastic collision Kinetic<br />
Energy is conserved<br />
The coefficient of restitution<br />
is 1.0<br />
Sunday, November 21, 2010<br />
17
Example<br />
Mass A : Vi = 10 m/s<br />
m = 5 kg<br />
Mass B : Vi = -15 m/s<br />
m = 7 kg<br />
(5)(10) + (7)(-15) = 5(V a ) + 7(V b )<br />
10 - (-15) = V b - V a<br />
25+V a =V b<br />
50-105 = 5V a +7(V a )+7(25)<br />
Sunday, November 21, 2010<br />
18
Collisions in 2 Dimensions<br />
Sunday, November 21, 2010<br />
19
Car :<br />
Vi = 10 m/s, E<br />
m = 500 kg<br />
Truck :<br />
Vi = 15 m/s, N<br />
m = 900 kg<br />
Sunday, November 21, 2010<br />
20
Car :<br />
Vi = 10 m/s, E<br />
m = 500 kg<br />
Truck :<br />
Vi = 15 m/s, N<br />
m = 900 kg<br />
In the X<br />
(500)(10) = (1400)(V x )<br />
In the Y<br />
(900)(-15) = (1400)(V y )<br />
Sunday, November 21, 2010<br />
21
(V x )=3.571 m/s<br />
(V y )=9.643 m/s<br />
find the resultant velocity<br />
V= 10.28 m/s<br />
at 69.7 o 22<br />
Sunday, November 21, 2010
2 Dimension<br />
9 Ball :<br />
V i = 10 m/s<br />
m = 350 g<br />
2 Ball :<br />
V i = 0 m/s<br />
m = 300 kg<br />
Sunday, November 21, 2010<br />
23
9 Ball :<br />
V i = 8 m/s<br />
θ = 34 o<br />
9 Ball :<br />
V i = 10 m/s<br />
m = 350 g<br />
2 Ball :<br />
V i = 0 m/s<br />
m = 300 kg<br />
In the X<br />
(0.35)(10) + 0 = (0.35)(8cos34) + (0.3)(V x )<br />
In the Y<br />
0 + 0 = (0.35)(8sin34) + (0.3)(V y )<br />
Sunday, November 21, 2010<br />
24
Ballistic<br />
Pendulum<br />
Bullet :<br />
Vi = 250 m/s<br />
m = 50 g<br />
Log :<br />
Vi = 0 m/s<br />
m = 1.0 kg<br />
FIND THE<br />
FINAL HEIGHT<br />
Sunday, November 21, 2010<br />
25
Bullet :<br />
Vi = 250 m/s<br />
m = 50 g<br />
V i » V f » KE» PE<br />
Log :<br />
Vi = 0 m/s<br />
m = 1.0 kg<br />
0.05(250) = 1.05(V f )<br />
V f = 11.9 m/s<br />
KE = .5(1.05)(11.9 2 ) = 74.4 J<br />
PE=74.4J=(1.05)(9.8)(H)<br />
H=7.23m<br />
Sunday, November 21, 2010<br />
26
Impulse<br />
J= F t<br />
J (Impulse Ns)<br />
F (Force N)<br />
t (time s)<br />
Sunday, November 21, 2010<br />
27
Change language