Answer: [tex]2.06\ m[/tex]
Explanation:
Given
Spring is compressed by 0.1 m from its rest length
Mass of block is 0.53 kg
The coefficient of kinetic friction is [tex]\mu_k=0.24[/tex]
Spring constant [tex]k=515\ N/m[/tex]
Here, the spring energy is consumed against work done by friction force
Friction force acting on the mass is [tex]F=\mu_kmg[/tex]
Writing Elastic potential energy equals work done by friction force
[tex]\Rightarrow \dfrac{1}{2}kx^2=\mu_kmg\cdot s\\\\\Rightarrow 0.5\times 515\times 0.1^2=0.24\times 0.53\times 9.8\cdot s\\\Rightarrow s=2.06\ m[/tex]
So, the block will slide up to a distance of [tex]2.06\ m[/tex]
