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Pressure vs Velocity

a block of ma...

Question

a block of mass M moving on frictionless horizontal surface collides with spring of spring constant K and compresses it by length L. Maximum momentum of block after collision is ?
A. Ml /k
B. ?MkL
C. zero
D. kL/2M

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Solution

$M a x i m u m k i n e t i c e n e r g y o f t h e s p r i n g i s g i v e n b y : K E = \frac{1}{2} k x^{2} w h e r e k i s t h e s p r i n g c o n s \tan t x i s t h e c o m p r e s s i o n i n t h e s t r i n g x = L K E = \frac{1}{2} k L^{2} K E a l s o g i v e n a s \frac{P^{2}}{2 m} \frac{1}{2} k L^{2} = \frac{P^{2}}{2 m} P = L \sqrt{K M}$

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