1. Tardigrade
  2. Question
  3. Physics
  4. A ramp is constructed in parabolic shape such that the height y of any point on its surface is given in terms of the point's horizontal distance x from the bottom of the ramp by y=x2 / 2 L. A block of granite is to be set on the ramp the coefficient of static friction is 0.80 . What is the maximum x coordinate xM at which the block can be placed on the ramp and remain at rest, if L=10 m ?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A ramp is constructed in parabolic shape such that the height $y$ of any point on its surface is given in terms of the point's horizontal distance $x$ from the bottom of the ramp by $y=x^{2} / 2 L$. A block of granite is to be set on the ramp the coefficient of static friction is $0.80 .$ What is the maximum $x$ coordinate $x_{M}$ at which the block can be placed on the ramp and remain at rest, if $L=10\, m ?$Physics Question Image

Work, Energy and Power

Solution:

image
$y=\frac{x^{2}}{2 L} \Rightarrow \frac{d y}{d x}=\left(\frac{x}{L}\right)=\tan \theta$
When the block is placed at a slope ' $\tan \theta$ ', the F.B.D. is as shown in the figure. At $x_{ M }$
$M g \sin \theta=f_{\max }=\mu N=\mu M g \cos \theta$
$\Rightarrow \tan \theta=\mu$ or $\frac{x_{M}}{L}$
$\Rightarrow x_{M}=\mu \cdot L$
$\Rightarrow x_{M}=(0.8)(10 m )=8 m$