Question

A small rock with mass 0.50 kg is tied to the free end of a light string that is 8.0 m
long. The rock is moving in a horizontal circle and the string makes an angle of 37° with respect
to the vertical.
a. What is the radius r of the circular path of the rock?
b. What is the tension in the string?
c. What is the period of the rock’s motion, the time it takes to complete one revolution?

Answer 1

a)

Radius of path

r = L sin x = 8 sin 37 = 4.81 m

b)

Forces along vertical

T cos 37 = mg

T cos 37 = 0.5* 9.8

T = 6.135 N

c)

Considering foces along horizontal

T sin x 37 = M v^2 / r

6.135* sin 37 = 0.5 v^2 / 4.81

V = 5.96 m/s

Time period of revolution

t = 2 pi r / v = 2*3.14* 4.81 / 5.96

t = 5.07 s

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