dm △t=255×103-480×250=1.35×10k (c)The final speed is -"="-0=hn=-327×10lh255×105-181×10 =405×103m/s 4. A barge with mass 1.50x10 kg is proceeding downriver at 6.20 m/s in heavy fog when it collides broadside with a barge heading directly across the river; see Fig. 7. The second barge has mass 2.78 kg and was moving at 4.30 m/s Immediate after impact, the second barge finds its course deflected by 18.0 in the downriver direction and its speed increased to 5.10 m/s. The river current was practically zero at the time of the accident. What is the speed and direction of motion of the first barge immediately after the collision? The coordinate system is shown in figure. Apply conservation of momentum m,I+m2V2i=m,1 +m2v2j mI 2.78×10 15×10543j-(5 Isin 18i+51eos18 =33i-1.01j =B312-1017=331+10 Suppose the angle between the first barge and x direction is 6. Then tan 6= 0.31→6= arctan(-0.31)=-17 3.31 5. A system of two spheres of identical mass m collide obliquely as shown in Figure 8. The Before collision After collision collision is inelastic. Initially one of the masse is at rest. The momenta of the particles immediately after the collision are pi and P2.O The angle between the paths of the masses after the collision is B. What is the kinetic energy of 19 the system?2.55 10 480 250 1.35 10 (k ) d d 5 4 0 t g t m m = m − × ∆ = × − × = × (c) The final speed is 4.05 10 m/s 2.55 10 2.55 10 1.81 10 0 ln 3.27 10 ln 3 5 5 5 3 = × × × − × − = − = = − × i f f i f e m m v v v v 4. A barge with mass 1.50 10 kg 5 × is proceeding downriver at 6.20 m/s in heavy fog when it collides broadside with a barge heading directly across the river; see Fig. 7. The second barge has mass 2.78 10 kg 5 × and was moving at 4.30 m/s. Immediate after impact, the second barge finds its course deflected by o 18.0 in the downriver direction and its speed increased to 5.10 m/s. The river current was practically zero at the time of the accident. What is the speed and direction of motion of the first barge immediately after the collision? Solution: The coordinate system is shown in figure. Apply conservation of momentum. i i f f m v m v m v m v 1 1 2 2 1 1 2 2 v v v v + = + So i j i j i j v v m m v v f i i f 01ˆ 1. 31ˆ 3. )] 1cos18 ˆ 5. 18 ˆ [4.3 ˆ (5.1sin 1.5 10 2.78 10 2ˆ 6. ( ) 5 5 2 2 1 2 1 1 = − − + × × = + = + − o o v v v v 3.31 1.01 3.46(m/s) 01ˆ 1. 31ˆ 3. 2 2 v1 f = i − j = + = Suppose the angle between the first barge and x direction is θ . Then o 0.31 arctan( 0.31) 17.22 3.31 1.01 tan = − ⇒ = − = − − θ = θ 5. A system of two spheres of identical mass m collide obliquely as shown in Figure 8. The collision is inelastic. Initially one of the masses is at rest. The momenta of the particles immediately after the collision are 1 p′ r and 2 p′ r . The angle between the paths of the masses after the collision is β. What is the kinetic energy of the system ? β P1 ′ r P2 ′ r Before collision After collision Fig.8 18° 1 2 Fig. 7 x y θ