A 2.85 kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 895 N/m. The spring initially is neither stretched nor compressed. The fish is released from rest.(a) What is its speed after it has descended 0.0500 m from its initial position? (b) What is the maximum speed of the fish as it descends?

a.

b. 0.5530m/s

Explanation:

a. Mass of the fish is given as and the spring's force constant as . We take as our initial position hence:

Applying the work-energy theorem:

#Take point 2, below initial position.

Since the fish starts at rest with zero gravitational potential energy, we obtain: , and for initially either stretched/compressed spring.

Therefore:

And plug values for x2 and k into equation:

Substituting energy quantities into to get:

#Substitute in :

b.To find the maximum speed of the fish as it descends:

#Maximum speeds occurs when  kinetic energy is maximum (at what point the slope is zero)

#Substitute values for m and K

Hence:

#Plug our value in to obtain

Hence the maximum speed of the fish during descent is 0.5530m/s

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