A small block of mass m on a horizontal frictionless surface is attached to a horizontal spring that has force constant k. The block is pushed against the spring, compressing the spring a distance d. The block is released, and it moves back and forth on the end of the spring. During its motion, what is the maximum speed of the block?
Question
Answer:
[tex]v_{max} = |d|\cdot \sqrt{\frac{k}{m} }[/tex]
Explanation:
The maximum speed of the block occurs when spring has no deformation, that is, there is no elastic potential energy, which can be remarked from appropriate application of the Principle of Energy Conservation:
[tex]\frac{1}{2}\cdot k \cdot d^{2} = \frac{1}{2}\cdot m \cdot v^{2}[/tex]
[tex]k \cdot d^{2} = m\cdot v^{2}[/tex]
[tex]v_{max} = |d|\cdot \sqrt{\frac{k}{m} }[/tex]