Posted by **greg** on Saturday, March 1, 2008 at 11:26pm.

Fig. 6-48 shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.038 kg, the string has length L = 1.2 m and negligible mass, and the bob follows a circular path of circumference 0.75 m. What are (a) the tension in the string and (b) the period of the motion?

- PHYSICS -
**drwls**, Sunday, March 2, 2008 at 1:00am
The angle of the pendulum from vertical is

A = arcsin r/L = arcsin [0.75/(2 pi L)]

= 5.71 degrees

You will need this angle later.

The vertical and horizontanl equations of motion are:

T sin A = m V^2/R

T cos A = m g

which tells you that

tan A = 0.100 = V^2/gR

V^2 = 0.100*9.8m/s^2*0.1194m = 0.1170 m^2/s^2

V = 0.342 m/s

(a) T = mg/cosA = 0.038kg*9.8m/s^2/.9950

= 0.3743 Newtons

(b) Period = (circumference)/V

= 2 pi R/sqrt(g R tan A)

for small angles A, tan A = R/L, so

Period = 2 pi R /sqrt (g R *R/L)

= 2 pi sqrt (L/g)

which is the same as the formula for a pendulum oscillating in a plane (one dimension)

Period = 2.2 seconds

Check my work

- PHYSICS -
**greg**, Sunday, March 2, 2008 at 1:26am
Thanks!

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