Object has a high coefficient of friction on snow.?

Question

Coefficient of friction is 0.75. Object is 700 N placed on a slope of 50 degrees.
a) Does this object slide freely or does it require a push?
b) What force is trying to cause this object to slide?

Are these theory questions or questions that need to answered with mathematical proof. What is the mathethetical proof it here are any?

Answer 1

There is some math involved, and it requires an understanding of what the coefficient of friction is. First off, let's see what kindo f forces are in play, and then we'll analyze.

If an object is on an incline, there are several forces at work - a force that acts straight down due to gravity, a force normal (perpendicular) to the surface, and a force along the surface. Put together, they constitute a right triangle, with the force of gravity being the hypotenuse. We can thus calculate the normal force and the force along the surface.

The normal force is found by taking the force of gravity and multiplying it by cos 50:

Fn = Fg * cos 50
Fn = (700 N)(cos 50)
Fn = 449.95 N

Likewise, the force along the surface is found through sin 50:
Fs = Fg * sin 50
Fs = (700N)(sin 50)
Fs = 536.23 N

So, this goes to show that there is a force of 536.23 N acting to pull the object down the slope.

The force of friction acts to hold an object in place. If you've ever put something on an incline, sometimes it doesn't roll down. This is due to a force due to friction that is acting against the object and holding it in place:

Ff = mu-s * Fn

where mu-s (Greek letter mu with subscript s) is the coefficient of static friction. (There is also a force of kinetic friction, mu-k, that acts on moving objects.) In our case, we have the following:

Ff = mu-s * Fn
Ff = 0.75 * 449.95 N
Ff = 337.46 N

So, here we see that there is a force of 337.46 N acting to hold the object in place. But, since we have a larger force of 536.23 N acting to pull the object down the slope, the object moves.

If Ff and Fs turned out to be the same, then the object would need a gentle nudge to get it to move down the slope. The larger Ff is over Fs, the larger a push you'll need.

Answer 2

Ok you have set up Santa to land in 5' of snow-don't mess with Santa or the Elves will find you and deal with you!