Question

Assuming that Albertine's mass is 60.0 kg , for what value of μk, 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/s2 for the magnitude of the acceleration due to gravity. g

Answer 1

Answer:

$\mu_k=0.101$

Explanation:

It is given that,

Mass of Albertine, m = 60 kg

It can be assumed, the spring constant of the spring, k = 95 N/m

Compression in the spring, x = 5 m

A glass sits 19.8 m from her outstretched foot, h = 19.8 m

When she just reach the glass without knocking it over, a force of friction will also act on it. Using the conservation of energy for the spring mass system such that,

$\dfrac{1}{2}kx^2=\mu_k mgh$

$\mu_k=\dfrac{kx^2}{2mgh}$

$\mu_k=\dfrac{95\times (5)^2}{2\times 60\times 9.8\times 19.8}$

$\mu_k=0.101$

So, the coefficient of kinetic friction between the chair and the waxed floor is 0.101. Hence, this is the required solution.