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A block is placed on a ramp of parabolic...

A block is placed on a ramp of parabolic shape given by the equation `y=x^(2)//20`. If `mu_(s) = 0.5`, then the maximum height above the ground at which the block can be placed without slipping is

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Let the block can be placed on the ramp at a height h above the ground and `theta` is inclination of the ramp at the position. In the position the component of weight along the slope of ramp is mg `sin theta` downwards.

The limiting friction force is `mu_(s)N = mu_(s)mg cos theta`
In equilibrium, `mg sin theta = mu_(s) mg cos theta`
`tan theta = mu_(s) = 0.5` but, `y=x^(2)//20`
Slope `tan theta =(dy)/(dx) = (2x)/20 = x/10 = 0.5 rArr x= 5`
From the figure maximum height,
`h=y_("max") =x^(2)/20 = 25/20 = 1.25 m`
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