Question

2. A large pack of snow of mass m sits at the top of a trail at a ski resort. Friction keeps the snow pack in place, but when it starts to get hotter out the coefficient of friction changes and the snow will slide down the mountain in an avalanche. If the slope of the trail is at an angle θ with respect to the ground, what is the coefficient of static friction when the avalanche occurs, in terms of the given variables and any known constants?

Answer 1

Answer:

tanΘ

Explanation:

Let gravitational acceleration be g. When the avalanche starts to occur, the gravity force that is parallel to the slope is the same as friction force.

Gravity force that is parallel to the slope can be written as:

G = mgsinΘ

The friction force is the product of normal force and coefficient:

$F_f = N\mu$

where normal force N is the gravity in the direction perpendicular to the slope

$F_f = \mu mgcos\theta$

As stated before, gravity force that is parallel to the slope is the same as friction force:

$G = F_f$

$mgsin\theta = \mu mgcos\theta$

$\mu = sin\theta / cos\theta = tan\theta$