Question

A child ties a rock to a string and whirls it around in a horizontal circle.

Part A

Assuming a 1.46m -long string making 20.0? angle below the horizontal, find the speed of the rock.

Express your answer with the appropriate units.

Part B

Find the period of its uniform circular motion.

Express your answer with the appropriate units.

Answer 1

Here ,

let the tension in the string is T ,

radius of the path , r = L*cos(20)

r = 1.46 * cos(20)

r = 1.37 m

Now, for the balancing forces in the y - direction

T*sin(20) = mg -----(1)

balancing the force in x - forces,

T*cos(20) = mv^2/1.37 ---(2)

now, (2)/(1)

cos(20)/sin(20) = v^2/(1.37 * 9.8)

solving for v

v = 6.1 m/s

the speed of the rock is 6.1 m/s

B)

Now,

Period = 2*pi*r/v

Period = 2 * pi*1.37/6.1

Period = 1.42 s

the period of its uniform circular motion is 1.42 s