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MS101: Physics
Chapter 7Dr. Ahmed Amin Hussein
May 3, 2023 Prepared By: Dr. Ahmed Amin 1
Chapter 7: Linear Momentum
May 3, 2023 2Prepared By: Dr. Ahmed Amin
Definition of Momentum Impulse Conservation of Momentum Center of Mass Motion of the Center of Mass Collisions (1d, 2d; elastic,
inelastic)
Momentum
May 3, 2023 3Prepared By: Dr. Ahmed Amin
• The MOMENTUM of a body is equal to the product of its mass and its velocity.
• Is momentum a vector or a scalar?• What are the SI units of momentum?
p m
v
§7.2 Momentum
May 3, 2023 4Prepared By: Dr. Ahmed Amin
Consider two interacting bodies with m2 > m1:
If we know the net force on each body then tm
t netFav
The velocity change for each mass will be different if the masses are different.
F21 F12
m1 m2
May 3, 2023 5Prepared By: Dr. Ahmed Amin
tm 2111 Fv
Rewrite the previous result for each body as:
ttm 211222 FFv
Combine the two results: ifif mmmm
222111
2211
vvvvvv
May 3, 2023 6Prepared By: Dr. Ahmed Amin
The quantity (mv) is called momentum (p). p = mv and is a vector.
The unit of momentum is kg m/s.
From slide (3):
21
2211
ppvv
mm
The change in momentum of the two bodies is “equal and opposite”. Total momentum is conserved during the interaction; the momentum lost by one body is gained by the other.
§7.3 Impulse
May 3, 2023 7Prepared By: Dr. Ahmed Amin
Definition of impulse: t Fp
One can also define an average impulse when the force is variable.
Example
May 3, 2023 8Prepared By: Dr. Ahmed Amin
[C] A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft.
(a) remains stationary, (b) moves away from the shore, (c) moves toward the shore(d) Not enough information given
Impulse
May 3, 2023 9Prepared By: Dr. Ahmed Amin
• A force applied over a period of time is called an IMPULSE.
• What are the SI units of Impulse?
I F t
The Impulse-Momentum Theorem
May 3, 2023 10Prepared By: Dr. Ahmed Amin
• When a net force acts upon a body for a period of time, the Impulse applied by the force is equal to the body’s change in Momentum!
F t m
v m(
v f
v 0)
Example
May 3, 2023 11Prepared By: Dr. Ahmed Amin
A batter hits a 500g ball with a force of 200N. If the time of contact was 0.205 seconds, find the impulse of the ball.
I F tI 200N 0.205secI 41N sec
Example
May 3, 2023 12Prepared By: Dr. Ahmed Amin
A batter hits a 500g ball with a force of 500N. If the time of contact was 0.205 seconds, find the impulse of the ball.
I F ta) 0 N·sb) 102.5 N·s c) 51250 N·sd) 250000 N·se) I have no clue…
Example
May 3, 2023 13Prepared By: Dr. Ahmed Amin
A force of 30 N is applied for 5 sec to each of two bodies of different masses.
30 N
m1 or m2
Take m1 < m2
(a) Which mass has the greater momentum change?
t Fp Since the same force is applied to each mass for the same interval, p is the same for both masses.
May 3, 2023 14Prepared By: Dr. Ahmed Amin
(b) Which mass has the greatest velocity change?
mpv
Since both masses have the same p, the smaller mass (mass 1) will have the larger change in velocity.
(c) Which mass has the greatest acceleration?
t
va
Since av the mass with the greater velocity change will have the greatest acceleration (mass 1).
Example
May 3, 2023 15Prepared By: Dr. Ahmed Amin
An object of mass 3.0 kg is allowed to fall from rest under the force of gravity for 3.4 seconds. What is the change in momentum? Ignore air resistance.
Want p = mv.
(downward) m/s kg 100m/sec 3.33
vpvav
mtg
t
Example
May 3, 2023 16Prepared By: Dr. Ahmed Amin
What average force is necessary to bring a 50.0-kg sled from rest to 3.0 m/s in a period of 20.0 seconds? Assume frictionless ice.
N 5.7s 0.20
m/s 0.3kg 0.50av
av
av
F
tm
t
tvpF
Fp
The force will be in the direction of motion.
The Law of Conservation of Momentum
May 3, 2023 17Prepared By: Dr. Ahmed Amin
• Internal forces are forces that act within a system, external forces are forces that act on a system from outside…
• If a system is not affected by any net external force, it is said to be “ISOLATED”.
• In an isolated system, the total linear momentum is always conserved!
§7.4 Conservation of Momentum
May 3, 2023 18Prepared By: Dr. Ahmed Amin
v1i
v2i
m1 m2
m1>m2
m1 m2
A short time later the masses collide.
What happens?
May 3, 2023 19Prepared By: Dr. Ahmed Amin
During the interaction:
N1
w1
F21
x
y
1121
11 0
amFF
wNF
x
y
2212
22 0
amFF
wNF
x
y
There is no net external force on either mass.
N2
w2
F12
May 3, 2023 20Prepared By: Dr. Ahmed Amin
The forces F12 and F21 are internal forces. This means that:
ffii
ifif
2121
2211
21
pppp
pppppp
In other words, pi = pf. That is, momentum is conserved. This statement is valid during the interaction only.
Example
May 3, 2023 21Prepared By: Dr. Ahmed Amin
Example (text problem 7.18): A rifle has a mass of 4.5 kg and it fires a bullet of 10.0 grams at a muzzle speed of 820 m/s. What is the recoil speed of the rifle as the bullet leaves the barrel?
As long as the rifle is horizontal, there will be no net external force acting on the rifle-bullet system and momentum will be conserved.
m/s 1.82m/s 820kg 4.5kg 01.0
0
br
br
rrbb
fi
vmmv
vmvm
pp
Example - Recoil
May 3, 2023 22Prepared By: Dr. Ahmed Amin
A hunter shoots a 0.22 rifle and the 3.0 kg gun recoils with a speed of 0.042 m/s. If the bullet has a mass of 0.5 g, find the muzzle speed of the gun.
(P)before (P)after
Prifle Pbullet before Prifle Pbullet after
mV rifle mV bullet before
mV rifle mV bullet after
3000g0ms 0.5g0m
s 3000g 0.042ms 0.5gV m
s 0 126 gm
sec0.5V
126 gmsec
0.5V
V 252 ms
564mph
TMA Exercises
May 3, 2023 23Prepared By: Dr. Ahmed Amin
Problems :
Questions # # 5, 7, 15, 17
