Question #102544

A box of mass 75 kg is placed on an inclined plane. When the angle of the plane is

increased to 30º, the box begins to slide downwards. Calculate the coefficient of static

friction between the plane and the box. Draw the free body diagram. Take g=10.0 ms^-2.

increased to 30º, the box begins to slide downwards. Calculate the coefficient of static

friction between the plane and the box. Draw the free body diagram. Take g=10.0 ms^-2.

Expert's answer

As per the given question,

mass of the box=75kg

Angle of inclination"=30^\\circ"

g "=10m\/sec^2"

The block diagram of the question is given below,

"mg\\sin30=f_s"

"\\Rightarrow mg\\sin30=\\mu N--------(i)"

Now,

"N=mg\\cos 30=75\\times10\\times \\dfrac{\\sqrt{3}}{2}------(ii)"

From equation (i) and (ii)

"\\Rightarrow 75\\times 10\\times \\dfrac{1}{2}=75\\times 10\\times \\dfrac{\\sqrt{3}}{2}\\mu"

"\\mu=\\dfrac{1}{\\sqrt{3}}"

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