Thomson%20Template

1
Physics 1710Chapter 9 Momentum Impulse
0

• Solution

P Conserved m1 v1i - m1 v1f m2 v2f

E Conserved ½ m1 v1i2 ½ m1 v1f2 ½ m2 v2f2
Solve for ½ m1 v1f2 Ef ½ m1 v1i2 ½ m1 v1f2
½ m2 (m1/m2)2(v1i v1f ) 2Ef Ei (m2 -
m1)/(m2m1)2
2
Physics 1710Chapter 9 Momentum Impulse
0

• Rutherford Backscattering Spectrometry

Ef Ei (m2 - m1)/(m2m1)2 k Ei
Silicon mSi 28 u
kSi 0.56
Helium mHe 4 u
Uranium mU 238 u
kU 0.93
3
Physics 1710Chapter 9 Momentum Impulse
0

• Rutherford Backscattering Spectrometry

Pulse Height Analysis
4
Physics 1710Chapter 9 Momentum Impulse
0

• Rutherford Backscattering Spectrometry

5
Physics 1710Chapter 9 Momentum Impulse
0

• 1 Lecture
• Impulse is the time integrated force.
• The motion of a system of point particles is a
  combination of motion of the center of mass (CM)
  and the motion about the CM.
• Force equals the time rate of change in momentum.

6
Physics 1710Chapter 9 Momentum Impulse
0

• Impulse and Momentum
• d p F dt
• ?p ?d p ?F dt Impulse
• The impulse on a body equals the change in
  momentum.

7
Physics 1710Chapter 9 Momentum Impulse
0

• Impulse and Momentum
• Consider the following scenarios

A
B
Which will have the greater initial velocity?
Scenario A or B?
8
Physics 1710Chapter 9 Momentum Impulse
0

• Impulse and Follow Through
• Demonstration

9
Physics 1710Chapter 9 Momentum Impulse
0

• ?p ?F dt
• ?p Fave ?t
• For a given force, the greater the time that the
  force is applied, the greater will be the impulse
  and, thus, the change in momentum.

10
Physics 1710Chapter 9 Momentum Impulse
0

• ?p ?F dt
• ?p Fave ?t
• For a impulse, the greater the time that the
  force is applied, the less will be the force.
• F d p/dt

11
Physics 1710Chapter 9 Momentum
0

• Impulse and Seat Belts
• Seat Belts ( and air bags
• and crumple zones) increase the stopping time ?t.
• If ?p is the same in two instants the impulse
  will be the same. The case with the longer ?t
  will exhibit the smaller average force.

12
Physics 1710Chapter 9 Momentum Impulse
0

• Newtons Second Law of Motion
• (What Newton actually said)
• ?F d p/dtThe net external force is equal to
  the time rate of change in the linear momentum.

13
Physics 1710Chapter 9 Momentum
0

• Stopping Force
• ?p mv
• ?t s/vave s/(v/2)
• Fave ?p/ ?t mv 2/(2s)
• Speed kills? v 2
• What about the sudden stop? 1/s

14
Physics 1710Chapter 9 Momentum Impulse
0

• The Consider Two Bodies
• ?? ??
• F12 - F21
• d p1 /dt - d p2 /dt
• then
• ?p1 - ?p2
• Thus, the momentum given to an ejected mass is
  equal and opposite to the momentum given to the
  ejecting mass.

15
Physics 1710Chapter 9 Momentum Impulse
0

• Impulse Engine
• Fthrust dp/dt - d(m v exhaust)/dt
• Fthrust dp/dt - v exhaust dm/dt

16
Physics 1710Chapter 9 Momentum Impulse
0

• Center of Mass (CM)
• RCM ?mi r/ M
• Or
• RCM ? rdm / M

17
Physics 1710Chapter 9 Momentum Impulse
0

• The center of mass (CM) of a system of particles
  of combined mass M moves like an equivalent
  particle of mass M would move under the
  influence of the resultant external force on the
  system.

18
Physics 1710Chapter 9 Momentum Impulse
0

• Total Linear Momentum
• vCM (1/M) ?i mi vi
• Thus
• PCM ?i pi total p
• aCM d vCM /dt (1/M) ?i mi d vi /dt
• aCM (1/M) ?i mi d vi /dt
• Thus
• FCM M aCM ?i mi ai