phy-motion(3)

2011-07-25 3:42 am

Aparticle is attached to one end of a light inextensible string of length 3metres. The other end of the string is attached to a fixed point O. Theparticle is set into motion horizontally at point P with speed v, so that itdescribes part of a vertical circle is O. The point P is vertically below O.
圖片參考：http://img23.imageshack.us/img23/784/76454493.jpg

Theparticle first comes momentarily to rest at the point Q, where OQ makes anangle of 15° to the vertical.a) Find the value ofvb) When the particleis at rest at the point Q, the tension in the string is 22N. Find the mass ofthe particle.

回答 (1)

天同

2011-07-25 5:25 am

✔ 最佳答案

(a) Kinetic energy of particle at P = (1/2)mv^2
where m is the mass of the particle
Vertical height reached by the particle at Q
= [3 - 3cos(15)] m = 0.1022 m
Potential enegy of particle at Q = mg(0.1022)
where gis the acceleration due to gravity, taken to be 10 m/s2

By conservation of energy,
(1/2)mv^2 = mg(0.1022)
solve for v gives v = 1.43 m/s

(b) 22 = mgcos(15)
hence, m = 22/[gcos(15)] kg = 2.28 kg

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