Transcript Slide 1

1. Define momentum
An object’s tendency to resist
changes in motion.
Variable
p
Formula
p  mv
Vector or Scalar
SI Unit
vector
m
kg
s
2. What is the main cause of grief and loss
of points in this chapter ?
• Momentum is a Vector
• Make sure you show velocity as negative
and positive
3. How was Newton’s 2nd law of
motion originally expressed ?
F = ∆p
∆t
Or
or F = m(vf -v0)
∆t
F = mvf –mv0
∆t
or F = ma
4. How does this differ from what you learned for
Newton’s second law ? Explain the difference.
Expressed in terms of p where the second
law is in terms of a
5. What happens to momentum if
there is no ∑F ?
• No change in momentum
• Object stays at rest or constant motion
6. State the law of conservation of
momentum
• In an isolated system, the momentum before a
collision equals the momentum after the
collision.
p  p
7. Define a “system” then define
“isolated system” in terms of momentum
• System – set of objects
• Isolated system – only significant forces
are between those in the system
no external forces change the system
8. Explain the following situations using the
conservation of momentum
9. Define Impulse
• Force acting through a time interval
9.
Variable
J
Formula
J  F t
Vector or Scalar
vector
SI Unit
N s
10. How does Impulse relate to momentum ?
Give several examples
J  p
J  mv f  mv0
11. Give the impulse-momentum theorem
If,
J  F t
and
J  p
Then, F t  mv  mv
f
0
12. So a change in momentum requires
what ?
• A change is velocity
• You must have a Net Force
• No Net Force
– 1st law (no acceleration)
– No change in momentum
• Net Force
– 2nd law (acceleration)
– change in momentum
13. How is the force required effected by a change
in momentum over a long period of time ?
• If the stopping time is increased then,
the F that is decreased.
F t  p
p
F
t
Inversely Proportional
14.Use the graph to answer the following questions.
Describe a scenario for the graph
Pushing the wagon
Force (N)
8
6
What impulse is given to the wagon
from t = 0 s to t= 7 s ?
4
2
0
0
2
4
Time (s)
6
8
What is the change in the wagon’s
momentum from t = 0 s to t = 7 s ?
How fast was the wagon going after 7 seconds if its mass = 5000 kg and it
started from rest ?
15. Do the units for impulse then equal the
units for momentum ?
m
N s  kg
s
m
m
kg 2 s  kg
s
s
16. What is an elastic collision ?
• When two objects collide and continue to
move separately after the collision
Elastic collision
• What kinds of object undergo elastic collisions ?
– Rigid objects, don’t deform a lot
• What happens to momentum in an elastic collisions ?
– Momentum is conserved
• What happens to energy in an elastic collision
– Kinetic Energy is conserved
17. What is an inelastic collision ?
• Objects collide and stick together
Inelastic collision
• What kinds of object undergo inelastic collisions ?
- Objects that deform
• What happens to momentum in an inelastic collisions ?
– Momentum is conserved
• What happens to energy in an inelastic collision
– Kinetic Energy is NOT conserved
18. Elastic collision examples:
m1v1  m2 v2  m1v1  m2 v2
M 1v1  m2 v2  M 1v1  m2 v2
19. Examples of inelastic collisions
m1v1  m2v2  (m1  m2 )v
m1v1  m2 (v2 )  (m1  m2 )v
m1v1  (m1  m2 )v2
1 2
mv  mgh
2
20. Show collisions in two dimensions and
write equations for them
• Break vectors into components and write
conservation of momentum equations in
the “x” and “y”
2
1
• “x”
m1v1  (m1  m 2 )vx
• “y”
m2v2  (m1  m 2 )vy
v  vx  v y
θ
mb= 800g
vb = 30 cm/s
300
mo= 500g
vo = 50 cm/s
• A) The two balls shown in the figure collide and bounce
off each other as shown. What is the final velocity of the
500g ball if the 800g ball has a speed of 15cm/s after the
collision. B) Is the collision perfectly elastic ?
• A) .26m/s @ 280
• B) It is not perfectly elastic
Billiard ball A moving with speed va = 3.0 m/sin the +x
direction strikes an equal-mass ball B initially at rest. The
two balls are observed to move off at 450 to the x axis, ball
A above the x axis and ball B below. What are the speeds
of the two balls after colliding ?
• 2.1 m/s
A 90 kg fullback moving east with a speed of 5.0 m/s is tackled
by a 95 kg opponent running north at 3.0 m/s. If the collision is
perfectly inelastic, calculate a) the velocity of the players just
after the tackle b) the kinetic energy lost
• A) 2.9 m/s
• B) 780 J
21. To this point how have we viewed mass and
its distribution in an object?
• The mass of the object has been uniform
in all directions. So, we put a dot in the
center and assumed all mass was located
at this place.
22. What is the center of mass ?
• One particle that would move if subjected
to a net force.
23. Find the center of mass for several
situations given
24.What is the center of gravity of an object ?
• Point at which gravity acts. For our
purposes center of mass and center of
gravity are the same.
25. How can the center of gravity be found for an
irregularly shaped object ?
• Hang the object from at least two points
and find where their plumb lines cross.
26. Explain how a trapeze walker uses center of
mass/gravity to his/her advantage.
Center of mass does not have to be on the
Object !