phy 2 問~thx~

A bullet is fired at a speed of 350m/s vartically upwards into a wooden block.How high will the block rise when the bullet becomes embedded in it?

Along vertical direction :

Initial K.E. = (1/2)mv2 = (1/2) (10/1000) (350)2 = 612.5 J
Initial P.E. = 0
Final K.E. = 0
Final P.E. = mgh = (1.2+(10/1000)) (10) h = 12.1h J

According to conservation of mechanical energy,
612.5 + 0 = 0 + 12.1h
h = 50.6 m
The block will rise 50.6 m

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A bullet is fired at a speed of 350m/s horizontally into a wooden block.How far will the block moves when the bullet becomes embedded in it??

Initial K.E. = (1/2)mv2 = (1/2) (10/1000) (350)2 = 612.5 J
Final K.E. = 0
Work done by friction = f•s

According to conservation of energy,
f•s = 612.5
s = 612.5/f (m)
The block moves 612.6/f m, where f is the frictional force in N.

Let me show the general case for you.

Let m1 and m2 be the mass of the bullet and wooden block respectively,
u be the initial velocities of masses m1,
v be the final velocity of masses m1 and m2.


By conservation of energy, we have

(1/2)(m1)(u^2) = (1/2)(m1+m2)(v^2)

(m1)(u^2) = (m1+m2)(v^2) ..... (1)


By conservation of momentum, we have

(m1)u = (m1+m2)v ..... (2)


The momentum conserves in all cases of Mechanics while the energy conserves if and only if there is no energy loss. In this question, from (1) and (2), you can see that energy conserve when u = v. Therefore, after finding the solution out, you can check if energy converses or not.

For most of the questions, if it does not mention that the energy is conserved, you'd better use the conservation of momentum to do.

2007-02-20 11:40:11 補充：
因此, 在不知道有沒有energy loss的情況下, 應該用conservation of momentum而不是conservation of energy.公式已經寫了給你, 而我相信你也有答案, 希望你再試試, 學習是不能不勞而獲的, 歡迎你把你的做法放上來討論.

2007-02-20 11:44:20 補充：
有沒有external force, 你是知道的, 不然你可以考慮free body diagram.