Abox rests on a rough board 10 meters long. when one end of the board is slowly raised to aheight of 6 meters above the other end, the box begins to slide. the coefficient of static frictionis

0.75

Explanation:

Maximum height the board was raised = 6m,

Length of the rough board = 10m

Angle at which the board was inclined when raised to 6m = sin(angle) = opposite/ hypothenus =

6/ 10 = 0.6

The angle = sin inverse of 0.6 = 36.9o

Coefficient of static friction = Frictional force (max)/ force of normal (the weight of the body will be broken along x-y plane with the y plane tend to want to sink the box which will be opposite in direction to the force of normal while the x plane parallel to the surface of the board tend to push it downwards.

Frictional force = horizontal component of the weight of the body along the plane other board = mgsin(the angle)

Force of normal = vertical component of the weight acting downward = mgcos(the angle)

Coefficient of static friction ( when frictional force is max and the body is about move but stationary) = mgsin(the angle)/ mgcos(the angle) = sin36.9/cos36.9 = 0.75

a straight line sloped