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 = (mv^2)/(r)`

Here,

m = Mass

v = Velocity

r = Radius

Equating,

`\mu_s N = (mv^2)/(r)`

Rearraning to find the coefficient of static friction,

`\mu_s = (mv^2)/(rN)`

`\mu_s = (mv^2)/(r(mg))`

`\mu_s = (v^2)/(rg)`

Replacing,

`\mu_s = ((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