(a)Use conservation of momentum mv=(m+ Mv'-r'=m m+ (b)Assume the position which the pendulum is at rest is zero potential energy position, use CWE M+m M+m (M+m)y2=(M+m)gh→v=√2sh→v M+m、2gh 10×10-+25×√2×981×10=352ms 5. Two objects, A and B, collide. a has mass 2.0 kg, and b has mass 3.0 kg. The velocities before the collision are vi =(15m/s)i+(30m/s)j and viB =(10m/)i+(.0m/s).After the collision,vA=(60m/s)i+(30m/s)j. The final velocity of B is 4i+5j(m/s) Solution Applying the conservation of the momentum, we have mAVAi+mBB=mAAf+mBBS So the final velocity of B is m1B-m,4)=二(下a-下4)+ →fs2(15i+30+6-30)-10+5j=4+5(m/) I. Give the solutions of the following problems 1. A massive anchor chain of length /is held vertical from its top link so that its lowest link is barely in contact with the horizontal ground The chain is dropped. When the top link has fallen a distance y(see Figure 5), show that the ude of the normal fo the chain is 3 mgy/ Solution Choose the anchor chain on the ground as the study object, which have length y and mass m=y. The chain on the ground get the gravitation m'g, the force N acted by the floor and impulse force Tacted by the falling chain. So(a) Use conservation of momentum m M mv mv m M v v + = ( + ) '⇒ '= (b) Assume the position which the pendulum is at rest is zero potential energy position, use CWE theory. gh m M m v m M m (M m)v' (M m)gh v' 2gh v ' 2 2 1 2 + = + + = + ⇒ = ⇒ = (c) 2 9.81 10 352 m/s 10 10 10 10 2.5 2 3 3 × × × = × × + = + = − − gh m M m v 5. Two objects, A and B, collide. A has mass 2.0 kg, and B has mass 3.0 kg. The velocities before the collision are v i j iA ˆ (30m/s) ˆ = (15m/s) + r and v i j iB ˆ (5.0m/s) ˆ = (−10m/s) + r . After the collision, v i j fA ˆ (30m/s) ˆ = (−6.0m/s) + r . The final velocity of B is (m/s) 4ˆ 5 ˆ i + j . Solution: Applying the conservation of the momentum, we have A Ai B Bi A Af B Bf m v m v m v m v v v v v + = + So the final velocity of B is (m/s) 10ˆ 5 ˆ 4ˆ 5 ˆ ) 15ˆ 30 ˆ 6ˆ 30 ˆ ( 3 2 ( ) ( ) 1 v i j i j i j i j v v v m m m v m v m v m v Bf Ai Af Bi B A A Ai B Bi A Af B Bf ⇒ = × + + − − + = + = + − = − + v v v v v v v v III. Give the Solutions of the Following Problems 1. A massive anchor chain of length l is held vertical from its top link so that its lowest link is barely in contact with the horizontal ground. The chain is dropped. When the top link has fallen a distance y (see Figure 5), show that the magnitude of the normal force of the ground on the chain is 3 mgy/l. Solution: Choose the anchor chain on the ground as the study object, which have length y and mass y l m m'= . The chain on the ground get the gravitation m' g ，the force N acted by the floor and impulse force T acted by the falling chain. So Origin l y i ˆ Fig.5