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A block of mass m is placed on a surface with a vertical cross section given by y = x^3/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is ?

A block of mass m is placed on a surface with a vertical cross section given by y = x^3/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is ?

Grade:11

1 Answers

Vikas TU
14149 Points
3 years ago
Let m be the mass of the block and μ​ be the coefficient of friction. For the sliding plane, we have
 
mgsinθ = μmgcosθ
⇒tanθ = μ
Now, we may write⇒dydx=tanθ=μ=12
We have given, y=x^3/6
∴dy/dx=x^2/2=12⇒x2=1
∴ y=16 m

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