- #1
rudransh verma
Gold Member
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- Homework Statement
- The upper half of an inclined plane with inclination ##\phi## is perfectly smooth,while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is
- Relevant Equations
- ##Fnet=ma##
##v^2=u^2+2as##
For lower half ,$$Fnet=-\mu F_N+mg\sin \phi$$
For upper half,
$$v^2=u^2+2as$$ (s is half of the total slant distance)
$$v^2=0+2\frac{mg\sin \phi}ms$$
$$v=\sqrt{2g\sin \phi s}$$
again for lower half,
$$v^2=u^2+2as$$
$$0=2g\sin \phi s+2\frac{-\mu F_N+mg\sin \phi}ms$$
$$\mu=\frac{2gm\sin \phi}{F_N}$$
$$\mu=2\sin \phi$$
For upper half,
$$v^2=u^2+2as$$ (s is half of the total slant distance)
$$v^2=0+2\frac{mg\sin \phi}ms$$
$$v=\sqrt{2g\sin \phi s}$$
again for lower half,
$$v^2=u^2+2as$$
$$0=2g\sin \phi s+2\frac{-\mu F_N+mg\sin \phi}ms$$
$$\mu=\frac{2gm\sin \phi}{F_N}$$
$$\mu=2\sin \phi$$