Newtons Laws EX 6

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The girl accelerates down the hill, so we choose the x-direction along the slope of the hill where her initial velocity down the hill is vx0=0 m/s, her velocity at the bottom is vx=1 m/s, the distance she slides is Δx=3 m. We calculate the acceleration of the girl down the hill from the equation:

vx2vxo2=2aΔx
120=2a3
a=0.17m/s2

We can use Newton's Second Law to find the force of friction Ff. There are three forces acting on the girl: FN, Ff and FG. We can draw a free body diagram.

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Now, we compute the components of these three forces:

Forces x-component y-component
FG 200 cos(-55°) = 115 N 200 sin(-55°) = -163 N
FN 0 FN
Ff Ff 0
ΣF 20×0.17=3.4 N 0

Since we are only interested in finding the force of friction, we do not need to consider the y-direction.

115Ff=3.4

Ff=1153.4=111.6 N