# Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a...

## Question:

Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring, with spring constant k = 95.0 N/m, is compressed 5.00 m from its equilibrium position, and a glass sits 19.8 m from her outstretched foot. Assuming that Albertine's mass is 60.0 kg, for what value of {eq}\mu_k {/eq}, the coefficient of kinetic friction between the chair and the waxed floor, does she just reach the glass without knocking it over? Use g = 9.80 m/s{eq}^2 {/eq} for the magnitude of the acceleration due to gravity.

## Friction force and Spring potential energy:

The spring potential energy is directly proportional to the spring constant and the square fo the spring compression. And the work done by the friction is equal to the product of the friction force and displacement.

Given Data:

• Spring constant {eq}\rm (k) = 95 \ N/m {/eq}
• Compression of the spring {eq}\rm (x) = 5 \ m {/eq}
• Displacement of the glass {eq}\rm (S) = 19.8 \ m {/eq}
• Mass of the albertine {eq}\rm (m) = 60 \ kg {/eq}

Now, applying the energy conservation

{eq}\rm \dfrac{1}{2} kx^2 = \mu_{k}mg \delta S \\ 0.5 \times (95)(5)^{2} = \mu_{k} \times (60 \times 9.8) \times 19.8 \\ \mu_{k} = 0.102 {/eq}