F.4 physics

xtina

2010-04-19 6:02 am

a marble of mass 20G moves in a circular path of radius 10cm on a frictionless track which is banked at 20^o to the horizontal.

a)find the centripetal force needed by the marble.
b)find the normal reaction acting on it
c)find its speed and period

回答 (1)

天同

2010-04-19 5:09 pm

✔ 最佳答案

Let v be the speed of the marble and R be the normal reaction, we then have the following equations:

R.sin(20) = (20/1000).v^2/(10/100)
i.e. R.sin(20) = 0.2v^2

R.cos(20) = (20/1000)g
where g is the acceleration due to gravity, taken as 10 m/s2 for simplicity
i.e. R.cos(20) = 0.02 x10 = 0.2

Combining the two equations
tan(20) = 0.2v^2/0.2
hence, v = 0.603 m/s

(a) Centripetal force = 0.02 x 0.603^2/0.1 N = 0.073 N

(b) R = 0.2/cos(20) N = 0.21 N

(c) speed = 0.603 m/s
period = 2 x pi x 0.1/0.603 s = 1 s

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