An object of mass 3kg is held at rest on a rough plane. The plane is inclined at 30º to the horizontal and has a coefficient of friction of 0.2. The object is released, what acceleration does the object move with?
We need to use Newtons law F=ma going down the slope.
We can see that the only forces acting in this direction are the component of the weight and friction, so we have that: F = Wsin30 - μR = 3a
We have that μ = 0.2, W = 3g, R = Wcos30 = 3gcos30
Hence, F = 3gsin30 - 0.2(3gcos30) = 3a
and so, (1/2)g - (√3/10)g = a
Therefore, acceleration = (1/2 - √3/10)g
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