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? 發問於 科學及數學其他 - 科學 · 1 十年前

A sphere X of mass m, travelling with speed u ,makes a collision with a sphere Y of mass 2m which is at rest. After the collision ,the velocities of X and Y are V1 and V2 respectively .Which of the followings is a possible pair of values V1 and V2 ?

_____V1____________V2 _________

A.___0.5u__________0.5u_________

B.___1.5u_________ - 0.25u_______

C.____0____________0.5u_________

D.___-0.5u__________0.75u________

2 個解答

• 1 十年前
最愛解答

conservation of momentum

initial momentum = mu

final momentum = mv1+2mv2

u = v1 +2v2

using above forumla, eliminating ans A

conservation of kinetic energy: final energy must be less than initial energy

initial energy = 1/2 m u^2

final energy = 1/2 m v1^2 + m v2^2

u^2 = v1^2 + 2v2^2

ans B & D, final energy &gt; initial energy --&gt; rejected

• 1 十年前

According Conservation of momentum, the total momentum of a closed system of objects (which has no interactions with external agents) is constant.

So, before collision

total momentum = mu+2m*0=mu

After collision, the total momentum should also be mu too

A 0.5u*m+0.5u*2m=1.5mu

B 1.5u*m-0.25u*2m=mu

C 0+2m*0.5*u=mu

D -0.5u*m+0.75u*2m=mu

However, B is impossible since the direction is wrong.

D is also impossible, consider the kinetic energy

Before collision

kinetic energy=(1/2)mu^2

After collision

kinetic energy=(1/2)m(-0.5u)^2+1/2(2m)(0.75u)^2=0.6875mu^2>0.5mu^2

The kinetic energy has increased and this should be ipossible