Mechanics question

2008-07-08 10:08 pm

Two objects P and Q of masses 1kg and 2kg respectively having the same
momentum and constant resisting force are gradually brought to rest. what is the ratio of the stopping distance for P and that of Q?

請列出計算過程和講解

更新1:

我也是計到2:1 但題目答案是4:1 有可能出佢出錯嗎?

回答 (1)

Uncle Michael

2008-07-09 12:44 am

✔ 最佳答案

Let the initial velocity of P be vP m s-1,
and the initial velocity of Q be vQ m s-1.

Initial momentum of P = (1) vp = vP kg m s-1
Initial momentum of Q = (2) vQ = 2vQ kg m s-1

Initial momentum of P = Initial momentum of Q
vP = 2vQ

Let the constant resisting force be F N.

Let the stopping distance of P be sP m,
and the stopping distance of Q be sQ m.

To stop the object P:
Work done by the resisting force = Initial K.E. of P
F sP = (1/2) (1) (vp)2
F sP = (1/2) (1) (2vQ)2
sP = 2(vQ)2

To stop the object Q:
Work done by the resisting force = Initial K.E. of Q
F sQ = (1/2) (2) (vQ)2
SP = (vQ)2

(Stopping distance of P) : (Stopping distance of Q)
= sP : sQ
= 2(vQ)2 : (vQ)2
= 2 : 1
=

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