A deli owner creates a lunch special display board by taking a uniform board whi

Question

A deli owner creates a lunch special display board by taking a uniform board which has a weight of 112 N, cutting it in half, hinging the halves together with a frictionless hinge, and setting it up as an inverted "V". Determine the minimum coefficient of static friction needed between the board and the ground in order for her to set the display board up with an angle of 30° between the two sides.

A deli owner creates a lunch special display board by taking a uniform board which has a weight of 112 N, cutting it in half, hinging the halves together with a frictionless hinge, and setting it up as an inverted "V". Determine the minimum coefficient of static friction needed between the board and the ground in order for her to set the display board up with an angle of 30° between the two sides.

Explanation / Answer

The normal force N1 is,

         N1 = W/2
The frictional force is,
             f = uN1

The normal force N2 is,
           N2 = uN1
If the system is in static equailibrium, the net force on

the system is zero.
(N2)(L sin75o) = (W/2)(L/2)cos75o

u(W/2)L sin75o = (W/2) (L/2)cos75o

Therefore, the minimum coefficient of static friction is,
                    u = 0.5tan75

                       = 0.134

Note: angle is 90 - 30/2 = 75o

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