Answer:
a) [tex]k = 2851.2\,\frac{N}{m}[/tex], b) [tex]v = 0.54\,\frac{m}{s}[/tex]
Explanation:
a) According to the Principle of Energy Conservation, the kinetic energy of the box is transformed into elastic potential energy.
[tex]\frac{1}{2}\cdot (2.2\,kg)\cdot (1.8\,\frac{m}{s} )^{2} = \frac{1}{2}\cdot k \cdot (0.05\,m)^{2}[/tex]
The spring constant is:
[tex]k = 2851.2\,\frac{N}{m}[/tex]
b) The initial speed needed to compress the spring by 1.5 centimeters is:
[tex]\frac{1}{2}\cdot (2.2\,kg)\cdot v^{2} = \frac{1}{2}\cdot (2851.2\,\frac{N}{m} )\cdot (0.015\,m)^{2}[/tex]
[tex]v = 0.54\,\frac{m}{s}[/tex]
