A 250 g block is dropped onto a relaxed veritcal spring that has a spring constant of k=2.5 N/cm. The block becomes attached to the spring and compresses the spring 12 cm befor momentarily stopping. While the spring is being compressed, what work is done on the block by a) the gravitational force on it and b) the spring force? c) what is the speed of the block before it hits the spring? (Assume that fricion is negligible) d) If the speed at impact is doubled, what is the maximum compression of the spring?
First I would convert k=2.5N/cm into N/m. Then I would also convert 12 cm into m. For a) I think I would uses f=mg d cos theda and then I would use W=1/2kx_1^2 -1/2 kx_f^2 . But I don't think that would be a valid way to solve the problem.
b)I would solve for the normal force but What is the equation?
c)Would I use k=1/2mv^2 and solve for v?
d)I would use the same equation from c) and just double v. And I would solve for d?
a) you are dead wrong. Where is Theta in the problem? work by gravity= mg(h+x) where h is the height above the original spring position from which the block is dropped, and x is the amount of string compression.
b) work by spring = 1/2 k x^2
Speed of block:
1/2 mv^2= mgh
Now, double v. 1/2 mv^2 + mgx= 1/2 kx^2
what happens to x? If mgx is small as to compared to the other terms, x^2= m/k v^2
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