The coefficient of static friction between a sled and the snow is 0.31, while th

Question

The coefficient of static friction between a sled and the snow is 0.31, while the coefficient of dynamic friction is 0.23. A 25 kg girl sits on her sled facing down a hill with a 15 degree slope. What is the magnitude of FSLIDE? Also, what is the minimum pushing force (FPUSH) that her friend needs to exert to start her moving down the hill? (Hint: FPUSH + FSLIDE will need to be greater than FLIM, therefore FPUSH will need to be greater than FLIM – FSLIDE) After getting a push and starting to move down the hill, will she continue to slide down the hill or come to a stop? (In other words, is FSLIDE in the dynamic case less than or greater than FFRICTION?)

Magnitude of FSLIDE ____________

Magnitude of FPUSH ____________

Magnitude of FFRICTION under dynamic conditions ____________

Will the girl continue to slide down the hill ____________

Explanation / Answer

here,

us = 0.31

uk = 0.23

mass of girl , m = 25 kg

the magnitude of Fslide , Fslide = m * g * sin(theta)

Fslide = 25 * 9.8 * sin(15)

Fslide = 63.4 N

let the magnitude of Fpush be Fpush

for the sled to move

us * m * g * cos(theta) = Fpush + Fslide

0.31 * 25 *9.8 * cos(15) = Fpush + 63.4

Fpush = 9.96 N

magnitude of friction under the dynamic condition , Ffriction = uk * m * g * cos(theta)

Ffrcition = 0.23 * 25 * 9.8 * cos(15)

Ffriction = 54.4 N

yes , as the dynamic friction force is less than the static frictional force

so, the girl will continue to slide

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