A block is placed on a parabolic shape ramp given by equation y = x 2 20 . If the coefficient of static friction μ s is 0 . 5 , then what is the maximum height above the ground at which the block can be placed without slipping?

Question

A block is placed on a parabolic shape ramp given by equation y = x 2 20 . If the coefficient of static friction μ s is 0 . 5 , then what is the maximum height above the ground at which the block can be placed without slipping?, 2 . 5 m, 1 . 25 m, 0 . 5 m, 0 . 25 m

MARKS App · Accepted Answer

The block will start slipping when the slope of the curve will be equal to tan θ where θ is angle of repose. The slope of the curve at any x will be, m = d y d x = x 10 . Equating, μ s = x 10 ⇒ 0 . 5 = x 10 ⇒ x = 5 m Height at x = 5 will be, h = x 2 20 = 1 . 25 m

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