Answer:
11.72 mm
Explanation:
The gravitational potential energy equals the potential energy of the spring hence
[tex]PE_{gravitational}=PE_{spring}[/tex]
[tex]mgh=0.5kx^{2}[/tex] where m is the mass of object, g is the acceleration due to gravity, h is the height, k is the spring constant and x is the extension of the spring
[tex]mgdsin\theta=0.5kx^{2}[/tex] where \theta is the angle of inclination and d is the sliding distance
Making x the subject then
[tex]x=\sqrt {\frac {2mgdsin\theta}{k}}[/tex]
Substituting the given values then
[tex]x=\sqrt{\frac {2\times 11\times 9.81\times 3\times sin 38}{2.9\times 10^{4}}}= 0.117240716\approx 11.72 mm[/tex]
