As winter is upon us, there is a possibility for ice and snow. This could be dan

Question

As winter is upon us, there is a possibility for ice and snow. This could be dangerous or lead to fun sledding down hills. For the following situations, determine if the individual would slide down the hill without any help (no one pushing them). If they would not slide on their own, determine how they could get going.
For each person, evaluate on a hill with an angle of 30, 45, and 55.
1) 100 lb person
a. Walking with rubber boots
b. On a plastic sled
c. On a metal sled
2) 150 lb person
a. Walking with rubber boots
b. On a plastic sled
c. On a metal sled
3) 200 lb person
a. Walking with rubber boots
b. On a plastic sled
c. On a metal sled
4) 250 lb person
a. Walking with rubber boots
b. On a plastic sled
c. On a metal sled
µs Surface 1 Surface 2
0.40 Rubber Snow
0.25 Plastic Snow
0.15 Metal Snow

Explanation / Answer

so on a slope the normal force N=mg cos and the maximum of the friction Ff=N=mg cos

we want to compare this to the force of gravity pulling you down the slope mg sin

the mass and g cancels so we are comparing

cos to sin or similarly

to tan .

If >=tan we don't slip, otherwise we do

so for the 30 degree hill, tan 30=.577 so all three will slip.

we will get the same for the other angles since the angle is increaseing leading to bigger tan (45 degrees has a tan of 1 and 55 a tan of 1.42)

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