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to sharpen a knife, you push with a force of 5n so that the edge of the knife is against a stone. the stone will sharpen the knife if it is spinning. the 30cm diameter stone is spinning at 200rpm and has a mass of 30kg. the coefficient of kinetic friction between the knife and the stone is 0.30. after 10 seconds of grinding what is the angular speed of the stone?



Answer :

The final angular speed will be 194 rpm.

From the statement:

force = 5 N

mass of the stone = 30 kg

diameter of the stone = 30 cm = 0.30 m

the radius of the stone will be = 0.15 m

initial angular velocity = 200rpm

coefficient of kinetic friction = 0.3

time for which knife kept on stone = 10 s

moment of inertia (I) = 0.5mr² (considering the stone as a solid ring )

                                  = 0.5 (30 × (0.15)²)

                                   = 15 × 0.0225

                                    = 0.3375 kgm²

Now ,we know that

torque = I α

Also torque = F x r       (r = perpendicular distance )

here force will be μF = 0.3F

therefore ,

Iα = μF × r

0.5 (30 × (0.15)²) × α = 0.3 × 5 × 0.15

∴ α = 0.6

the value of acceleration will be negative as the wheel is slowing down

∴ α =  - 0.6

       Now , using the 1st equation of motion

ω' = ω +αt

ω' = 200 -0.6 (10)

ω' = 194 rpm.

Hence the angular speed of the stone will be 194 rpm.

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