Impulse Contents ImpulseWB Area Under Force Graph Ft

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

Change in momentum = 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? 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? Impulse = F t 14 Ns = F(1. 7 s) F = (14 Ns)/ (1. 7 s) = 8. 24 = 8. 2 N W

Example - Impulse is area under F vs t graph F 100 N t 5. 0 s Impulse is area under = (40 N)(6. 0 s) = 240 Ns

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What is the impulse? F 100 N t 5. 0 s Average F = 70 N, t = 8. 0 s, Impulse = (70 N)(8. 0 s) = 560 Ns W

What is the impulse? F 100 N t 5. 0 s Impulse = (40 N)(3. 0 s) + (70 N)(5. 0 s)= 470 Ns W

What is the impulse of the D 12 engine? Impulse = (10. N)(1. 73 s-0. 11 s) + (28 N-10 N)(0. 42 - 0. 21) = 19. 98 Ns (about 20 Ns) 20 Ns W

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 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. 2. 3. 4. F t = m v (F )(. 013 s) = (0. 145 kg)(-90 m/s) F = (0. 145 kg)(-90 m/s)/(. 013 s) F = -1003. 8 N ≈ -1. 0 x 103 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? (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? (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? (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 So: • F = engine thrust • t = time to burn fuel • m = mass of fuel burned • v = exhaust gas velocity F t = m v

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? 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 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? F t = m v (33. 82 x 106 N)(1 s) = m(2254. 7 m/s), m = 15, 000 kg Burn Rate = 15, 000 kg/s W

A D 12 engine generates 11. 80 N of thrust burning fuel at a rate of. 0143 kg/s. What is the exhaust velocity? F t = m v (11. 80 N)(1 s) = (. 0143 kg) v, v = = 825. 2 m/s W

Which Rocket Accelerates faster? A Demo – F 14 B

Rocket Propulsion Solid Fuel Engine: © Microsoft Encarta

Rocket Propulsion 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! © Microsoft Encarta

Rocket Propulsion Liquid Fuel Engine: • How do you keep it from tipping? • Why the “steam” coming off? © Microsoft Encarta

Saturn V Rocket - Apollo missions Escape Tower Command Module L. E. M Third stage Second stage First stage Saturn V Animation (Flash in IE)

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

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

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. 62857 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