previous 2 Learning Goal: To practice Problem-Solving Strategy 10.1 for energy c

Question

previous 2 Learning Goal: To practice Problem-Solving Strategy 10.1 for energy conservation problems A sled is being held at rest on a slope that makes an angle with the horizontal. After the sled is released, it slides a distance di down the slope and then covers the distance d2 along the horizontal terrain before stopping. Find the coefficient of kinetic friction jy between the sled and the ground, assuming that it is constant throughout the trip. Solve Part B Find the colficent of kinatio riction p Express your answer in terms of some or all of the variables di, da, and e Hints . Submit My Answers Give Up Assess Part C

Explanation / Answer

There are three forces acting on the sled:

1. Weight (gravity)
Wgrav = (mg)(d1)cos(90°–)
Now, cos(90°–) = sin, so:
Wgrav = (mg)(d1)sin()

2. Normal force,
Fn=(mg)cos

3. Friction,
Ff = (Fn)k = (mg)(cos)k
Wfric = –(Fn)(d1) = –(mg)(cos)(k)(d1)

Total work done on the sled during the downhill phase is:

Wdownhill = (mg)(d1)sin() – (mg)(cos)(k)(d1)

Total work done during the horizontal phase is:
Whoriz = –(mg)(k)(d2)

So that means the total work done on the sled overall is:

W = Wdownhill + Whoriz
= (mg)(d1)sin() – (mg)(cos)(k)(d1) – (mg)(k)(d2)

Total work is zero (because KE is zero), so:

(mg)(d1)sin() – (mg)(cos)(k)(d1) – (mg)(k)(d2) = 0

(d1)sin() = (cos)(k)(d1) + (k)(d2)

=> (d1)sin() = [(cos)(d1) + (d2)](k)

=> k = (d1)sin() / [(cos)(d1) + (d2)]

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