1. Impulse
Contents:
Impulse/WB
Area Under Force Graph
Ft = mv
Rocket Science
Rocket Demos

2. Change in momentum = Impulse
Impulse = F t where
F = Force
t = time that the force is exerted
(F or t = 0???)
Example: What impulse is imparted by exerting a 12 N force for 4.0 s?
Impulse = F t = (12 N)(4.0 s)
Impulse = 48 Ns

3. Whiteboards
Impulse
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4. What is the impulse of a 6.12 N force acting for 2.3 seconds?
14 Ns
Impulse = F t
Impulse = (6.12 N )(2.3 s)=14 Ns W

5. A rocket engine is rated at 14 Ns of impulse, and burns for 1
A rocket engine is rated at 14 Ns of impulse, and burns for 1.7 seconds. What is the thrust of the engine?
8.2 N
Impulse = F t
14 Ns = F(1.7 s)
F = (14 Ns)/ (1.7 s) = 8.24 = 8.2 N W

6. Impulse is area under = (40 N)(6.0s) = 240 Ns
Example - Impulse is area under F vs t graph t F
100 N
5.0 s
Impulse is area under = (40 N)(6.0s) = 240 Ns

7. Whiteboards
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8. What is the impulse? 100 N F t W 5.0 s
Average F = 70 N, t = 8.0 s, Impulse = (70 N)(8.0 s) = 560 Ns W
560 Ns

9. What is the impulse? 100 N F t W 5.0 s
Impulse = (40 N)(3.0 s) + (70 N)(5.0 s)= 470 Ns W
470 Ns

10. What is the impulse of the D12 engine?
Impulse = (10. N)(1.73 s-0.11 s) + (28 N-10 N)( ) = Ns (about 20 Ns) W
20 Ns

11. Force, time, mass, and velocity Impulse = F t = mv
F = Force (N)
t = Elapsed time (s)
m = Mass (kg)
v = Change in velocity (m/s)
Example: A pitcher pitches a kg baseball at 40. m/s, and the batter hits it directly back at 50. m/s to the outfield. What is the average force exerted by the bat if the collision lasted .013 s?
F t = mv
(F )(.013 s) = (0.145 kg)(-90 m/s)
F = (0.145 kg)(-90 m/s)/(.013 s)
F = N ≈ -1.0x103 N (units/sign)

12. Whiteboards
Ft = mv
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13. What force for 10. seconds makes a 2
What force for 10. seconds makes a 2.0 kg rocket speed up to 75 m/s from rest?
15 N
(m)(v) = (F )( t)
(2.0 kg)(75 m/s) = (F )(10 s)
F = (2.0 kg)(75 m/s)/(10 s) = 15 N

14. A baseball bat exerts a force of 200. N on a. 50 kg ball for
A baseball bat exerts a force of 200. N on a .50 kg ball for .10 seconds. What is the ball’s change in velocity?
40. m/s
(m)(v) = (F )( t)
(.50 kg)(v) = (200. N )(.10 s)
v = (200. N )(.10 s)/(.50 kg) =
40. m/s

15. Jolene exerts a 50. N force for 3. 0 seconds on a stage set
Jolene exerts a 50. N force for 3.0 seconds on a stage set. It speeds up from rest to .25 m/s. What is the mass of the set?
6.0 x 102 kg
(m)(v) = (F )( t)
(m)(.25 m/s) = (50. N )(3.0 s)
m = (50. N )(3.0 s)/(.25 m/s) =
600 kg = 6.0 x 102 kg

16. One last thing:
Deriving Newton’s second law:
m v = F  t
Finally:
F = m v = ma = p
t t

17. Rocket Propulsion Ft = mv So: F = engine thrust
 t = time to burn fuel
m = mass of fuel burned
v = exhaust gas velocity
Ft =
mv

18. Rocket Propulsion
Example 1: A rocket burns fuel at a rate of 1.2 kg/s, with an exhaust velocity of 1250 m/s. What thrust does it develop?
Ft = mv
v = 1250 m/s
m = 1.2 kg
t = 1 s
(F)(1 s) = (1.2 kg)(1250 m/s), F = 1500 N

19. Rocket Propulsion
Example 2: A model rocket engine develops 12 N of thrust with an exhaust velocity of 718 m/s. What is its fuel burn rate?
Ft = mv
F = 12 N
v = 718 m/s
m = ? kg
t = 1 s
(12 N)(1 s) = m(718 m/s), m = kg
Burn rate = kg/s

20. Whiteboards
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21. A certain rocket engine burns
A certain rocket engine burns kg of fuel per second with an exhaust velocity of 725 m/s. What thrust does it generate?
25.5 N
Ft = mv
F(1 s) = (.0352 kg)(725 m/s),
F = 25.5 N W

22. The Saturn V’s first stage engines generated 33. 82 MN of thrust (33
The Saturn V’s first stage engines generated MN of thrust (33.82 x 106 N) with an exhaust velocity of m/s. What was its fuel burn rate?
15,000 kg/s
Ft = mv
(33.82 x 106 N)(1 s) = m( m/s),
m = 15,000 kg
Burn Rate = 15,000 kg/s W

23. A D12 engine generates 11. 80 N of thrust burning fuel at a rate of
A D12 engine generates N of thrust burning fuel at a rate of kg/s. What is the exhaust velocity?
825.2 m/s
Ft = mv
(11.80 N)(1 s) = (.0143 kg)v,
v = = m/s W

24. Which Rocket Accelerates faster?B
Demo – F14

27. Rocket Propulsion
Solid Fuel Engine:
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28. Rocket Propulsion Thrust of the Engine: F = mv t Big v means big F
Solid Fuel Engine:
Big v means big F
Big v also means lots of pressure
Danger Will Robinson!
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29. © Estes

30. m = .5 kg, Ft = 20 Ns Ft = m v 20 Ns = .5kg v
Lookout!
m = .5 kg, Ft = 20 Ns
Ft = m v
20 Ns = .5kg v
v = ? (x for mph)
© Estes

31. Rocket Propulsion Liquid Fuel Engine: How do you keep it from tipping?
Why the “steam” coming off?
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32. Saturn V Rocket - Apollo missions
Escape Tower
Command Module
L.E.M
Third stage
Second stage
First stage
Saturn V Animation (Flash in IE)

33. Ion Propulsion systems
Low thrust/high Δv
20-50 km/s exhaust velocity
Dawn

34. Gridded Xenon ion drive (Like Dawn has)
where’s the power come from?
Gridded Xenon ion drive (Like Dawn has)

35. How what is the “burn” rate for this engine?
The Dawn spacecraft has a mass of about 770 kg, and an ion drive with an exhaust velocity of 35,000 m/s that generates about 92 millinewtons of thrust. (.092 N)
How what is the “burn” rate for this engine?
Ft = mv
(.092 N)(1.0 s) = m(35,000 m/s)
m = E-06 kg/s
How big a change in velocity can 50 kg of fuel give the spacecraft?
The final mass will be 770 – 50 = 720 kg, on the average the spacecraft will have a mass of 745 kg
So the delta v is approximately:
(745 kg)(Δv) = (50 kg)(35,000 m/s)
Δv ≈ 2350 m/s