Question 192: Work, Energy and Power & Circular Motion

Question

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 given by

Accepted Answer

Let the length of the inclined plane is = $$l$$. So only $${l \over 2}$$ part will have friction.
According to work-energy  theorem, $$W = \Delta k = 0$$ 
(Since initial and final speeds are zero)
$$	herefore$$  Work done by friction + Work done by gravity $$=0$$
i.e., $$ - \left( {\mu \,mg\,\cos \,\phi } ight){\ell  \over 2} + mg\ell \,\sin \,\phi  = 0$$
or $${\mu  \over 2}\cos \,\phi  = \sin \phi $$
or $$\mu  = 2\,	an \,\phi $$

Answer

$$2\,\cos \,\,\phi $$

Answer

$$2\,sin\,\,\phi $$

Answer

$$\,	an \,\,\phi $$

Answer

$$2\,	an \,\,\phi $$

Work, Energy and Power & Circular Motion

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 given by

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