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

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

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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

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

Impulse is area under = (40 N)(6.0s) = 240 Ns t F 100 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? W 560 Ns t F 100 N 5.0 s

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

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

Impulse = F  t = m  v F = 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 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 = m  v 2.(F )(.013 s) = (0.145 kg)(-90 m/s) 3.F = (0.145 kg)(-90 m/s)/(.013 s) 4.F = N ≈ -1.0x10 3 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 10 2 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 10 2 kg

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

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

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

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 =.0167 kg Burn 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 F  t = m  v F(1 s) = (.0352 kg)(725 m/s), F = 25.5 N W

The Saturn V’s first stage engines generated MN of thrust ( x 10 6 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 10 6 N)(1 s) = m( m/s), m = 15,000 kg Burn Rate = 15,000 kg/s W

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

Which Rocket Accelerates faster? A B Demo – F14

Rocket Propulsion © Microsoft Encarta Solid Fuel Engine:

Rocket Propulsion © Microsoft Encarta Solid Fuel Engine: Thrust of the Engine: F = m  v  t Big  v means big F Big  v also means lots of pressure Danger Will Robinson!

© Estes

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

Rocket Propulsion © Microsoft Encarta 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 stageSecond stageThird stageL.E.MCommand Module Escape Tower

- Up goer 5 – explanation using most common 1000 words Also many good YouTube videos of launch

Ion Propulsion systems Low thrust/high Δv km/s exhaust velocity Dawn

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 = 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