1. Define momentum An object’s tendency to resist changes in motion.
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Transcript of 1. Define momentum An object’s tendency to resist changes in motion.
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1. Define momentum
An object’s tendency to resist changes in motion.
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Variable Formula Vector or Scalar SI Unit
p
p mv
vectorm
kgs
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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
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3. How was Newton’s 2nd law of motion originally expressed ?
F = ∆p Or F = mvf –mv0
∆t ∆t
or F = m(vf -v0) or F = ma
∆t
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4. How does this differ from what you learned for Newton’s second law ? Explain the difference.
Expressed in terms of where the second law is in terms of
p
a
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5. What happens to momentum if there is no ∑F ?
• No change in momentum
• Object stays at rest or constant motion
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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
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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
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8. Explain the following situations using the conservation of momentum
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9. Define Impulse
• Force acting through a time interval
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Variable Formula Vector or Scalar SI Unit
J
J F t vector N s
9.
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10. How does Impulse relate to momentum ? Give several examples
J p
0fJ mv mv
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11. Give the impulse-momentum theorem
and
J F t
J p
0fF t mv mv
Then,
If,
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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
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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
Ft
Inversely Proportional
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14.Use the graph to answer the following questions.
Pushing the wagon
0
2
4
6
8
0 2 4 6 8
Time (s)
Fo
rce
(N
)
Describe a scenario for the graph
What impulse is given to the wagon from t = 0 s to t= 7 s ?
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 ?
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15. Do the units for impulse then equal the units for momentum ?
mN s kg
s
2
m mkg s kgs s
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16. What is an elastic collision ?
• When two objects collide and continue to move separately after the collision
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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
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17. What is an inelastic collision ?
• Objects collide and stick together
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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
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18. Elastic collision examples:
1 1 2 2 1 1 2 2m v m v m v m v
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1 1 2 2 1 1 2 2M v m v M v m v
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19. Examples of inelastic collisions
1 1 2 2 1 2
1 1 2 2 1 2
( )
( ) ( )
m v m v m m v
m v m v m m v
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1 1 1 2 2( )m v m m v
21
2mv mgh
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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”
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2
1&2
1
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• “x”
• “y”
2 2 1 2( ) ym v m m v
1 1 1 2( ) xm v m m v
x yv v v
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• 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
300
θ
mb= 800gvb = 30 cm/s
mo= 500gvo = 50 cm/s
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Billiard ball A moving with speed vaa = 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
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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
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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.
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22. What is the center of mass ?
• One particle that would move if subjected to a net force.
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23. Find the center of mass for several
situations given
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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.
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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.
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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 !