Byoi(Unparallel to vo) Using Newton third law, we can have the magnitude of the force acted on the wall by the water b)The momentum of the water in length As is P=Ap, the momentum of the water in unit P Bi (c) Regard the water and the car as a whole system, and choose it as the study object dPi=(mdv +v dm ) dP=0 mdv=(vo-v)dm 1. Using conservation of momentum, at any time t m=(m-m)→v=(1-) Use the result in(c), we can have V →ln="=ln (1 3. A rocket at rest in space, where there is virtually no gravity, has a mass of 2.55 x10 kg, of which 1.81x10kg is fuel. The engine consumes fuel at the rate of 480 kg/s, and the exhaust speed is 3.27 km/s. The engine is fired for 250 s (a)Find the thrust of the rocket engine. (b)What is the mass of the rocket after the engine burn?(c) What is the final speed attained? Solution (a) the thrust of the rocket engine is dm 327×103×480=1.57×10°(N) (b)The mass of the rocket after the engine burnv i t mv i P f t mv i f ˆ ˆ 0 ˆ 0 0 0 = −β ∆ − ∆ ∆ = ∆ = − ∆ ⇒ = r r r (Unparallel to 0 v r ) Using Newton’ third law, we can have the magnitude of the force acted on the wall by the water is 0 βv ( b) The momentum of the water in length ∆s is p p r r = ∆ , the momentum of the water in unit length is i v v i t s v i t m s mv i s P ˆ ˆ ˆ ˆ 0 0 0 0 β β= = ∆ ∆ ∆ ∆ = ∆ ∆ = ∆ r (c) Regard the water and the car as a whole system, and choose it as the study object. m v v v m v v v P P i m v v i wc x x wc d ( - )d - d 0 ˆ ( d dm) d ˆ 0 0 ⇒ = ⎪ ⎩ ⎪ ⎨ ⎧ = = = + i. Using conservation of momentum, at any time t 0 0 0 0 ( ) (1 )v m m mv = m − m v ⇒ v = − ii. Use the result in (c), we can have v m m v m m v v v m m v v v m m v v v m m v ln ln (1 ) d d d d 0 0 0 0 0 0 0 = ⇒ = − − ⇒ = − = ⇒ − ∫ ∫ 3. A rocket at rest in space, where there is virtually no gravity, has a mass of 2.55 10 kg 5 × , of which 1.81 10 kg 5 × is fuel. The engine consumes fuel at the rate of 480 kg/s, and the exhaust speed is 3.27 km/s. The engine is fired for 250 s. (a) Find the thrust of the rocket engine. (b) What is the mass of the rocket after the engine burn? (c) What is the final speed attained? Solution (a) the thrust of the rocket engine is 3.27 10 480 1.57 10 (N) d d 3 6 = = × × = × t m F ve (b) The mass of the rocket after the engine burn is