a massless spring is compressed between two blocks,one of mass M and the other of mass 5M,on a frict

题目

a massless spring is compressed between two blocks,one of mass M and the other of mass 5M,on a frictionless horizontal table.If this system is released from rest the potential energy in the spring is converted into kinetic energy of the blocks such that the block of mass M gets ( )of the total energy?
A.5/6 B.4/5 C.1/2 D.1/5 E.1/6

答案

D
first,the forces and time exerted on both blocks are the same,thus both blocks got the same impluse(Ft) at the moment the potential energy of the spring becomes 0.According to the Impluse-momentum theorem,the change in momentum equals to the impluse(p=Ft).the momentum p=mv and the kinetic energy KE=0.5mv^2,so KE=0.5pv.
because both blocks got the same force,according to Neton's second law,a=F/m,the ratio of the accelaration of the tow blocks would be 5M:M=1:5
because the time is the same,the ratio of the final velocity of the two blocks is 1:5
and the ratio of the Kinetic energy is equal to te ratio of the final velocity is also 1:5
so the answer is D