Question

Biologists have studied the running ability of the northern quoll, a marsupial indigenous to Australia In one set of experiments, they studied the maximum speed that quolls could run around a curved path without slipping. One quoll was running at 2.4 m/s around a curve with a radius of 1.6 m when it started to slip. What was the coefficient of static friction between the quoll's feet and the ground in this trial?

Answer 1

To solve this problem and find the coefficient of static friction, we will start by considering the balance between the frictional force in the animal and its centripetal force, therefore,

$F_f = F_c$

The friction force is defined as

$F_f = \mu_s N$

Here,

$\mu_s =$ Coefficient of static friction

N = Normal Force

And Centripetal Force is defined as,

$F_c = \frac{mv^2}{r}$

Here,

m = Mass

v = Velocity

r = Radius

Equating,

$\mu_s N = \frac{mv^2}{r}$

Rearraning to find the coefficient of static friction,

$\mu_s = \frac{mv^2}{rN}$

$\mu_s = \frac{mv^2}{r(mg)}$

$\mu_s = \frac{v^2}{rg}$

Replacing,

$\mu_s = \frac{(2.4)^2}{(1.6)(9.8)}$

$\mu_s = 0.3673$

$\mu_s = 0.37$

Therefore the coefficient of static friction between the quoll's feet and the ground in this trial is 0.37