ImpulseContents:• Impulse/WB• Area Under Force Graph• Ft = mv• Rocket Science• Rocket Demos

Change in momentum = ImpulseImpulse = F t where

F = Forcet = 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?

1. Impulse = F t = (12 N)(4.0 s) 2. Impulse = 48 Ns

WhiteboardsImpulse

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What is the impulse of a 6.12 N force acting for 2.3 seconds?

14 Ns

Impulse = F tImpulse = (6.12 N )(2.3 s)=14 Ns

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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 t14 Ns = F(1.7 s)F = (14 Ns)/ (1.7 s) = 8.24 = 8.2 N

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Impulse is area under = (40 N)(6.0s) = 240 Ns

t

F100 N

5.0 s

Example - Impulse is area under F vs t graph

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Average F = 70 N, t = 8.0 s, Impulse = (70 N)(8.0 s) = 560 Ns

What is the impulse?

W560 Ns

t

F100 N

5.0 s

Impulse = (40 N)(3.0 s) + (70 N)(5.0 s)= 470 Ns

What is the impulse?

W470 Ns

t

F100 N

5.0 s

Impulse = (10. N)(1.73 s-0.11 s) + (28 N-10 N)(0.42 - 0.21) = 19.98 Ns (about 20 Ns)

What is the impulse of the D12 engine?

W20 Ns

Impulse = F t = mvF = Force (N)t = Elapsed time (s)m = Mass (kg)v = Change in velocity (m/s)

Force, time, mass, and velocity

Example: A pitcher pitches a 0.145 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?

1. F t = mv2. (F )(.013 s) = (0.145 kg)(-90 m/s)3. F = (0.145 kg)(-90 m/s)/(.013 s)4. F = -1003.8 N ≈ -1.0x103 N (units/sign)

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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

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

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

One last thing:Deriving Newton’s second law: m v = F t

Finally:F = m v = ma = p t t

Rocket Propulsion

Ft

=

mv

So:• F = engine thrust• t = time to burn fuel• m = mass of fuel burned• v = exhaust gas velocity

Rocket PropulsionExample 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?

Ft = mvv = 1250 m/sm = 1.2 kgt = 1 s(F)(1 s) = (1.2 kg)(1250 m/s), F = 1500 N

Rocket PropulsionExample 2: A model rocket engine develops 12 N of thrust with an exhaust velocity of 718 m/s. What is its fuel burn rate?

Ft = mvF = 12 Nv = 718 m/sm = ? kgt = 1 s(12 N)(1 s) = m(718 m/s), m = .0167 kgBurn rate = .0167 kg/s

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A certain rocket engine burns .0352 kg of fuel per second with an exhaust velocity of 725 m/s. What thrust does it generate?

25.5 N

Ft = mvF(1 s) = (.0352 kg)(725 m/s), F = 25.5 N

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The Saturn V’s first stage engines generated 33.82 MN of thrust (33.82 x 106 N) with an exhaust velocity of 2254.7 m/s. What was its fuel burn rate?

15,000 kg/s

Ft = mv(33.82 x 106 N)(1 s) = m(2254.7 m/s), m = 15,000 kgBurn Rate = 15,000 kg/s

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A D12 engine generates 11.80 N of thrust burning fuel at a rate of .0143 kg/s. What is the exhaust velocity?

825.2 m/s

Ft = mv(11.80 N)(1 s) = (.0143 kg)v, v = = 825.2 m/s

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Which Rocket Accelerates faster?

A B

Demo – F14

Rocket Propulsion

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Solid Fuel Engine:

Rocket Propulsion

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Solid Fuel Engine: Thrust of the Engine:F = mv t

•Big v means big F •Big v also means lots of pressure

•Danger Will Robinson!

© Estes

Lookout!

m = .5 kg, Ft = 20 NsFt = m v20 Ns = .5kg vv = ? (x 2.237 for mph)

© Estes

Rocket Propulsion

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Liquid Fuel Engine:

• How do you keep it from tipping?• Why the “steam” coming off?

Saturn V Animation (Flash in IE)

Saturn V Rocket - Apollo missions

First stage

Second stage

Third stage

L.E.MCommand Module

Escape Tower

http://xkcd.com/1133/ - Up goer 5 – explanation using most common 1000 words

Also many good YouTube videos of launch

Ion Propulsion systemsLow thrust/high Δv20-50 km/s exhaust velocityDawn

Gridded Xenon ion drive (Like Dawn has)

where’s the power come from?

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 = 2.62857E-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