A box of uniform density with a square base of side length b and height 2b sits
ID: 1434148 • Letter: A
Question
A box of uniform density with a square base of side length b and height 2b sits on an incline. The coefficient of static friction between the box and the incline is mu_s. The angle of the incline theta is increased from theta until the box either tips over onto its side, or slides down the incline. For what relation between fi8 and 0 does the box slide? For what relation between mu_s and theta does the box tip? If mu_s = 0.55 does the box slide down the slope or tip? At what angle of the incline does it do this?Explanation / Answer
a) For, box to slide
sN < mgsin
Also, N = mgcos
=> smgcos < mgsin
=> s < tan
For, box to tip
sN > mgsin
Also, N = mgcos
=> smgcos > mgsin
=> s > tan
where, = tan-1(b/2b)
b) If s = 0.55
The box will tip
Because, s = 0.55 and tan = b/2b = 0.5
=> s > tan
=> angle of inclination it occurs = tan-1( b/2b )
= tan-1(0.5)
= 26.56 degrees
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