Answer:
The speed of the block when it separates from the spring will be
Explanation:
Using the Principle of Conservation of Energy, and taking into account that we have a <u>system of a spring and a block</u> that we can analyze, we can say that in two different instants, the energy must be constant.
Now, we can think in the <u>initial moment</u>, when the spring is compressed and the block is against it, and write its energy as potential energy because the kinetic energy is zero as they are not moving:
<em>where k is the spring constant, and x is the length of compression of the spring </em>(this length will be expressed in m instead of cm to be consistent with the units).
Then we can go to the <u>final moment when the block is "separating" from the spring</u>, and in that moment the potential energy will be zero, and all energy will be kinetic, wich we can write as
<em>where m is the mass of the block, and v is its speed</em> (this is what we want to calculate). Therefore, we can equalize both expressions, and clear v
Finally, we have that
wich is the speed of the block when it separates from the spring.