f6 physics circular motion *2

2009-10-27 4:35 am

1. a coin of mass 30g is placed on a horizontal circular table. the maximum fiction between the coin and the table is 1N and the table is rotating in constant angular velocity. if the distance between the coin and the rotation axis is 8cm, find the minumun value of the rotation period for the coin to slip.

2.a spring of natural length 40cm is hung vertically with a bob attached to it , the extension is2 cm. the spring is then placed on a smooth table with its free end attached to a fixed point on the table. if the bob is made to rotate in a horizontal circular path on the table with angular velocity of 5rad s^-1, find the radius of the circular path

回答 (1)

Prof. Physics

2009-10-27 5:51 am

✔ 最佳答案

1. Centripetal force, F = mrw^2

= mr(2pi/T)^2

= 4mrpi^2 / T^2

The frictional force on the coin accounts for its centripetal force.

For the coin about to slip, f <= F

So, 1 <= 4(0.03)(0.08)pi^2 / T^2

Period, T >= 0.308 s

The minimum period time is 0.308 s.

2. Let m be the mass of the bob

Initially, by Hooke's law

mg = kx

m(10) = k(0.02)

Force constant, k = 500m

Now, the tension in the spring accounts for the centripetal force

ke = mrw^2

(500m)e = mr(5)^2

500e = 25(0.4 + e)

20e = 0.4 + e

e = 40.4/19 = 0.021 m

So, the extension is 0.021 m

And the radius of the circular path = 0.4 + 0.021 = 0.421 m

參考: Physics king

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