You are sucker for scenic overlooks, so you want to build a house overhanging a

Question

You are sucker for scenic overlooks, so you want to build a house overhanging a hanging it is by taking a 5'000 concrete beam and 500 Cf 1 C 01,86 degree with one edge at the cliff ledge and the other tie to You plan to hold it up with a sturdy cable, which you is 40 a can hold up an unlimited weight. The tree,from the edge of the cliff. You don't want your house to go crashing down the side of the cliff like in the homework problem, so this time it is a paperweight Japanese house (literally - made of shoji paper and wood) with a mass of only 12.000 kg. The center of mass of the chalet is 300 m from the ledge of the cliff. However, you were a little bit short on nails, so nothing is holding up the concrete beam from sliding down the cliff except the frictional force between it and the cliff, and it's just barely about to give way. Find the coefficient of static friction between the concrete beam and the cliff.

Explanation / Answer

Distance between the tree and the edge of the beam   500+40 = 540 m

height of the tree = 400 m

angle between the cable and the beam

tan(p) = 400/540

p = 36.53 deg.

forces acting on the beam

1. tension of the cable T, making an angle p with the beam

2. its ownweight 5000 kg downward 250m away from the cliff edge

3. weight of the house 1200 kg, 30 m away from the edge of te cliff

4. Normal reaction of the cliff perpendicular to the cliff surface N

5. friction f upward perppendiular to the beam

equating the horizontal and verticall forces

N = TCos(p)

TSin(p) + f = 5000g+12000g

f = uN, u is the co-efficient of friction between the cliff ad the beam.

eliminating N and f

T(sin(p) +uCos(p) ) = 17000g

Now taking moments about the cliff edge

TSin(p) *500 = 5000g*250 +12000g*300

T = 159699 N

Sin(36.53) +uCos(36.53) = 17000*9.8/159699

                                         = 1.043

co-efficient of friction   u = 0.557

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