Answer
given,
mass of block = 2.7 kg
speed of block = 1.1 m/s
a) spring compressed to distance of 6 cm or 0.06 m
using conservation of energy
kinetic energy is converted into spring energy
[tex]\dfrac{1}{2}mv^2= \dfrac{1}{2}kx^2[/tex]
[tex]k =\dfrac{ mv^2}{x^2}[/tex]
[tex]k =\dfrac{2.7\times 1.1^2}{0.06^2}[/tex]
k= 907.5 N/m
b) again using conservation of energy
kinetic energy is converted into spring energy
[tex]\dfrac{1}{2}mv^2= \dfrac{1}{2}kx^2[/tex]
[tex]v =\sqrt{\dfrac{kx^2}{m}}[/tex]
[tex]v=\sqrt{\dfrac{907.5\times 0.015^2}{2.7}}[/tex]
[tex]v=\sqrt{0.075625}[/tex]
v= 0.275 m/s
