Newtonian Mechanics MC

Atheist

2010-12-17 11:49 am

圖片參考：http://imgcld.yimg.com/8/n/HA00414085/o/701012170011413873428440.jpg

The higher the height the ball is, the larger the force the spring must applied in order to decelerate the ball. And Hooke's Law states that F=ke:
=> mg+ma=ke
Since k is constant, the compression e should be larger.
So why the statement (2) is correct?
Or the statement is talking about the result in which the ball is finally at rest?
Given that the answer of this MC question is C.
You may answer in chinese or english.

回答 (1)

天同

2010-12-17 5:07 pm

✔ 最佳答案

The "compression" in the question refers to the final compression of the spring when the ball comes to rest. Under such situation, the weight of the ball is balanced by the spring force, i.e.

mg = kx
where m is the mass of the ball, g is the acceleration due to gravity, k is th espring constant, and x is the final compression.

Clearly, x = mg/k which is independent of the height h.

Your equation: mg + ma = ke doesn't make any sense at all. It is because a and e are both time dependent.

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